problem solving use multiplication 8 2

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Multiplication Word Problem Worksheets

This page hosts a vast collection of multiplication word problems for 3rd grade, 4th grade, and 5th grade kids, based on real-life scenarios, practical applications, interesting facts, and vibrant themes. Featured here are various word problems ranging from basic single-digit multiplication to two-digit and three-digit multiplication. Another set of printable worksheets hone children's multiplication skill by multiplying large numbers. Free worksheets are included.

Single-digit Multiplication Word Problems

The printable PDF worksheets presented here involve single-digit multiplication word problems. Each worksheet carries five word problems based on day-to-day scenarios.

Download the set

Multiplication Word Problems: Two-digit times Single-digit

The word problems featured here require a grade 3 learner to find the product by multiplying a two-digit number by a single-digit multiplier.

Multiplication Word Problems: Two-digit times Two-digit

The worksheets presented here involve multiplication of two-digit numbers. Read the word problems and find the product. Apply long multiplication (also known as column multiplication) method for easy calculation.

Theme Based Word Problems

Our engaging theme-based pdf worksheets help young minds understand the fundamentals of multiplication. Answer the word problems based on three fascinating themes - Winter Season, Ice rink and Library.

Multiplication Word Problems: Three-digit times Two-digit

Read the word problems featured in these printable worksheets for grade 4 and find the product of three-digit and two-digit numbers. Write down your answers and use the answer key below to check if they are right.

Three-digit Multiplication Word Problems

Solve these well-researched word problems that involve three-digit multiplication. Perform multiplication operation and carry over numbers carefully to find the product.

Multiplication: Three or Four-digit times Single-digit

The word problems featured here are based on practical applications and fact-based situations. Multiply a three or four-digit number by a single-digit multiplier to find the correct product.

Multi-digit Word Problems: Multiplying Large Numbers

Sharpen your skills by solving these engaging multi-digit word problems for grade 5. Apply long multiplication method to solve the problems. Use the answer key to check your answers.

Related Worksheets

» Addition Word Problems

» Subtraction Word Problems

» Division Word Problems

» Word Problems

» Multiplication

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Chapter 8, Lesson 8.2 Problem Solving - Use Multiplication

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8.2: Multiplication

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Julie Harland
MiraCosta College

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You will need : Positive and Negative Counters (Material Cards 18A and 18B)

Now, we'll explore how to multiply positive and negative numbers using the counters. Let's look again at a definition of multiplication for whole numbers.

Definition: Multiplication of Whole Numbers using the Repeated-Addition Approach

If $m$ and $n$ are whole numbers, then \[m \times n = n + n + n + n + ... + n, \nonumber \] where there are $m$ add ends of $n$ in this sum.

This definition makes sense as long as $m$ and $n$ are positive numbers. In fact, we can even make sense of and modify this definition using counters as long as m is positive by rewording the definition slightly, as stated below:

Definition: Multiplication of a Whole Number times an Integer using the Repeated-Addition Approach, using positive and negative counters

If $m$ is a whole number and $n$ is any integer, $ m \times n$ is obtained by combining $m$ subsets of a collection of counters representing $n$. The number that the resulting collection represents is the answer to the problem $ m \times n$.

This exercise shows you one way to use the above definition to multiply $3 \times -4$. In this problem, the definition can be used because 3 is a whole number and -4 is an integer. We need to combine 3 subsets of a collection of counters that represent -4.

Use your positive and negative counters to represent a collection of counters that represent -4. For this exercise, choose a collection of 5 negatives and 1 positive. Show what your collection looks like below:
Now, form two more collections (for a total of 3 subsets) of counters that you had for part a. Combine the counters together and show what the large collection looks like below:
After removing any red-green pairs (zero) from your collection in part b, show the collection that remains below. What number does this represent? _____

Do $3 \times -4$ again, using a different collection of counters to represent -4.

Use your positive and negative counters to represent a collection of counters that represent -4. This time, choose a collection of 6 negatives and 2 positives. Show what your collection looks like below:

Okay, let's do $3 \times -4$ one more time, choosing the easiest way to represent -4.

Form a collection of counters to represent -4. Do it the easy, natural way, using the least number of counters possible. Show what your collection looks like below:
What number does the collection in part b represent? _____

Well, I hope you got the answer of -12 for exercises 1, 2 and 3, since $3 \times -4 = -12$! This illustrates that it doesn't matter exactly which collection of counters you use to represent -4, as long as the collection really is -4. To compute $3 \times -4$, you could combine 3 subsets of a collection of 8 reds and 4 greens, or you could combine 3 subsets of a collection of 7 reds and 3 greens, etc. You'll always end up with a collection that represents -12. For exercise 3, did you choose 4 negatives as your representation? If so, did you notice you didn't have to remove any red-green pairs to answer part c? From now on, let's do it the easy way, using the simplest collection possible.

Use your counters to do each of the following multiplication problems using the definition of multiplying a whole number by an integer. Then, explain what the multiplication problem given means in terms of the counters, and explain and show the individual steps. Use the following example as a model.

Multiply $\bf 2 \times -6$.

Multiplying $2 \times -6$ means to combine 2 subsets of 6 red counters. The number that the resulting collection represents is the product (answer). $2 \times -6$ = RRRRRR + RRRRRR = RRRRRRRRRRRR = -12

a. Multiply $4 \times -2$

This means to

b. Multiply $3 \times 5$

This means to

c. Multiply $5 \times -3$

This means to

d. Multiply $7 \times 2$

This means to

e. Multiply $0 \times -3$

This means to

Okay, now that you've mastered how to multiply a whole number by an integer, let's work on how we can use the counters to multiply a negative integer by an integer. Let's look once more at the definition for multiplying $m \times n$, when m is a whole number.

If m is a whole number and n is any integer, $m \times n$ is obtained by combining m subsets of a collection of counters representing n. The number that the resulting collection represents is the answer to the problem $m \times n$.

If m is negative, this definition doesn't make sense since you certainly can't combine a negative number of subsets! The way we'll revise this definition to include the possibility that m may be negative is to agree that if m is negative, we REMOVE $m$ subsets of a collection of counters representing $n$. The trick to doing this is to remove the subsets from a collection of counters representing zero. So, here is the comprehensive definition for multiplying any two integers , using positive and negative counters.

Multiplication of two Integers, using positive and negative counters

Case 1: If $m$ is a whole number and $n$ is any integer, $m \times n$ is obtained by combining $m$ subsets of a collection of counters representing $n$. The product of m and $n$, $m \times n$, is the number that the resulting collection represents.
Case 2: If $m$ is negative and $n$ is any integer, $m \times n$ is obtained by removing |m| subsets of a collection of counters representing $n$ from a collection of counters representing zero. The product of $m$ and $n$, $m \times n$, is the number that the resulting collection represents.

This exercise shows you how to use the above definition to multiply $-4 \times 3$. For this problem, we need to remove 4 subsets of a collection of counters that represents 3 from a collection of counters representing zero. The simplest collection to represent 3 is 3 positives, or 3 green counters. (We could use a more complicated collection and still arrive at the same answer. We did this kind of an exercise in exercises 1 - 3. Convince yourself it wouldn't matter here, either.)

We first need to form a collection of counters that represents zero so that it will be possible to remove 4 subsets of 3 green counters. For this example, make a collection of 14 red and 14 green counters. Write down what your collection looks like here:
From your collection, remove a subset of 3 green counters. Then, remove 3 more subsets of 3 green counters. You have just removed 4 subsets of 3 green counters from zero. To show it on paper, circle a subset of 3 green counters in the collection above in part a. Then, circle 3 more subsets of 3 green counters so that four separate subsets are circled. After you remove the counters (which are shown by what you circled in part a), show what is left in your collection below.
Remove any red-green pairs (zero) from your remaining collection. Show this on paper by crossing off or circling any red-green pairs (zero) from your collection shown in part b. Show the collection that remains below. What number does this collection of counters represent?

Use the definition again to multiply $-4 \times 3$. Remember, you need to remove 4 subsets of a collection of counters that represents 3.

We first need to form a collection of counters that represents zero so that it will be possible to remove 4 subsets of 3 green counters. This time, put in the smallest collection of counters possible so that you'll be able to remove 4 subsets of 3 green counters. Write down what your collection looks like here:
From your collection, remove four subsets of 3 green counters (take out one subset of 3 green counters at a time). You have just removed 4 subsets of 3 green counters from zero. To show it on paper, circle 4 different subsets of 3 green counters in the collection shown in part a. After you remove the counters (which are shown by what you circled in part a), show what is left in your collection below.
What number does the above collection represent?

Did you notice that if you start out with a minimal collection to represent zero, you don't have to remove any red-green pairs when you get to part c? That is the easiest way to do it because you know how to calculate what to take out before you start the problem. However, if you were teaching this to someone who couldn't figure that out ahead of time, you might always start out with zero being 20 (or some other agreed upon number) of each counter.

On the next page, the steps are shown for the example below– how to use your counters to do a multiplication problem when the first number is a negative integer. It's necessary to explain what the multiplication problem given means in terms of the counters, and then explain and show the individual steps. Use the example as a model for the exercises that follow.

Multiply $-4 \times -3$ by using the definition of multiplying integers.

Multiplying $-4 \times -3$ means to remove 4 subsets of 3 red counters from a representation of zero. The number that the resulting collection represents is the answer.

Since there are 12 greens remaining, the answer is +12. Didn't you always wonder why a negative number times a negative number equaled a positive number? Using the definition of multiplying integers with counters, you can really see why it's true. After you do a few more problems, feel free to go out and show all of your friends who still don't understand it or just memorized the rules because someone told them that's the way it is and to just accept it. Okay, enough of that unbridled enthusiasm from me for now.

It's time for you to work a few problems. Some have negative numbers before the multiplication sign (start with a representation of zero and remove subsets as in the last example) and some have whole numbers before the multiplication sign (so just combine subsets together like you did in the earlier exercises of this exercise set). It's the number before the multiplication sign that will indicate which case of the definition you will use.

Use your counters to do each of the following multiplication problems using the definition of multiplying two integers with positive and negative counters. Then, explain what the multiplication problem given means in terms of the counters, and explain and show each of the individual steps. Use the example above as a model when the first number is negative.

a. $-5 \times 3$ ____ This means to ____________________________________________________

Show work and all steps below. Then, state the answer to the problem.

b. $-3 \times 2$ ____ This means to ____________________________________________________

c. $2 \times -3$ ____ This means to ____________________________________________________

NOTE : Although the answer to part b is the same as part c due to the commutative property of multiplication, the problems mean different things, the steps are not alike and the problems are done differently.

d. $-2 \times 3$ ____ This means to _______________________________________________________

e. $3 \times 2$ ____ This means to _______________________________________________________

f. $0 \times -4$ ____ This means to _______________________________________________________

g. $-4 \times 0$ (this means something different than $0 \times -4$) ____ This means to _____________________________

Let's do some more problems when the first integer is negative, using a chart to keep track of the counters. The first column will be the multiplication problem, the second will show what representation of zero is being used, the third will explain the meaning of the multiplication problem (what has to be done in all of these cases, subsets are being removed from the representation of zero), the fourth will show how many of each of the counters are left after the removal of the subsets, and the last column will be the answer, obtained from the representation shown in the fourth column.

Fill in all of the blanks. FILL IN THE ENTIRE TABLE ALL THE WAY TO THE BOTTOM!! You should be using your real manipulatives (red and green counters) as you do (most of) these problems. I've done the first one for you to use as a model.

problem	Counters for Zero		counters remaining	answer
$-3 \times 6$	20G 20R	remove 3 sets of 6 G from zero	2G 20R	-18
$-3 \times 6$	23G 23R
$-3 \times 6$	18G 18R
$-4 \times 4$	18G 18R
$-4 \times -4$	18G 18R
$-5 \times 2$	14G 14R
$-2 \times 5$	13G 13R
$-5 \times -2$	11G 11R
$-2 \times -5$
$-3 \times 3$	10G 10R
$-3 \times -3$	12G 12R
$-7 \times 2$
$-2 \times 8$	18G 18R
$-2 \times -8$	18G 18R

After doing all of the exercises in this Exercise Set, the rule for multiplication of integers should make sense.

Rule for Multiplying Two Integers Together:

To multiply two integers, first multiply the absolute values of the integers. To determine the sign of the product: it is positive if both integers have the same sign (both positive or both negative); otherwise it is negative (if one of the integers is positive and the other integer is negative). If one of the integers is zero, the answer is zero.

If you are multiplying more than two integers together, the sign of the product can be determinined by how many negative numbers are being multiplied. For every two negative numbers being multiplied together, the answer is positive. Therefore, if there are an even number of negative numbers being multiplied, the sign of the product is positive. If there are an odd number of negative numbers being multiplied, the sign of the product is negative. If one of the integers is zero, the answer is zero.

Although we haven't covered division in this exercise set, the rule for determining the sign of a quotient is the same as the rule for determining the sign of a product.

Determine if each product is negative (–), positive (+) or zero (0). Do not compute

Remember that for a set to be closed under multiplication, the product of any two elements in the set must be in the set. To prove a set is not closed under multiplication, you need to provide a counterexample.

Exercise 10

For each of the following sets, determine if the set is closed under multiplication. Provide a counterexample if it is not closed.

Positive Integers
Negative Integers

Less than (<) and Greater than (>) signs are used to order numbers. ](a < b\) if $a$ is to the left of $b$ on the number line. $a < b$ (read "a is less than b") can also be written as $b > a$ (read "b is greater than a.)

Exercise 11

Decide which of the following are true if a, b and c are any integers, p is a positive integer and n is a negative integer. Provide a counterexample if it is false.

If a < b and b < c, then a < c
If a < b, then a + c < b + c
If a < b, then ap < bp
If a < b, then ap > bp
If a < b, then an > bn
If a < b, then an < bn

Exercise 11a, 11b, 11c, and 11e are the four properties of Ordering for Integers. 11a is called the Transitive Property for Less Than. 11b is called the Property of Less Than and Addition. 11c is the Property of Less Than and Multiplication by a Positive 11e. is the Property of Less Than and Multiplication by a Negative. If the less than symbols in 11a, 11b and 11c were replaced with greater than symbols, you would have the corresponding properties of greater than. For part 11e, if both signs were switched, you would have the Property of Greater Than and Multiplication by a Negative.

Exercise 12

Fill in the following properties, if a, b and c are any integers, p is a positive integer and n is a negative integer.

Transitive Property for Greater Than:
Property of Greater Than and Addition:
Property of Greater Than and Multiplication by a Positive:
Property of Greater Than and Multiplication by a Negative:

11.a,b and c are similar to properties of equality. The difference between equalities and inequalities (whether there is a less than or greater than symbol) if that when both sides of an inequality are multiplied by a negative number, the inequality sign changes directions.

Word Problems on Multiplication

Word problems on multiplication for fourth grade students are solved here step by step.

Problem Sums Involving Multiplication: 1. 24 folders each has 56 sheets of paper inside them. How many sheets of paper are there altogether?

We can add 56 sheets 24 times

Since multiplication is repeated addition we can multiply 56 and 24 to get the answer.

[Sometime, more than one calculation is required.] Therefore, altogether there are 1344 sheets.

2. A carton holds 24 packets of biscuits. Each packet has 12 biscuits. How many biscuits can be packed in 45 cartons?

In one carton we can pack 24 × 12 biscuits.

In 45 cartons, we can pack 24 × 12 × 45 biscuits.

24 × 12 = 288

→ 40 + 5

Multiply by 5

Multiply by 40

Therefore, altogether there are 12,960 biscuits.

3. There are 226 pencils in a packet. How many pencils are there in 212 such packets?

Number of pencils in 1 packet = 226

Number of packets = 212

Total number of pencils = 226 × 212

= 47912

4. A bag contains 289 apples. How many apples A will 72 such bags have?

Solution: 1 bag contains = 289 apples

72 bags contain = 289 × 72 apples

2 8 9

× 7 2

5 7 8

+ 2 0 2 3 0

2 0 8 0 8

Hence, 72 bags will contain 20,808 apples.

5. A car travels a distance of 345 km every day. What distance will it travel in a year?

Distance travelled by the car in one day = 345 km

There are 365 days in a year.

Distance travelled by the car in 365 days = 345 km × 365

3 4 5 × 3 6 5

1 7 2 5

2 0 7 0 0

+ 1 0 3 5 0 0

1 2 5 9 2 5

Hence, the car will travel 1,25,925 km in a year.

Consider the following Examples on Word Problems Involving Multiplication:

1. A book costs $ 67. How much will be paid for 102 such books? Solution:

The cost of one book = $ 6 7 6 7 Number of books = 1 0 2 × 1 0 2 The cost of 102 books = $ 67 × 102 1 3 4 = $ 6834 + 6 7 0 0 6 8 3 4

Therefore, cost of 102 books = $ 6834

2. A bicycle costs $ 215. How much will be paid for 87 such bicycles?

Solution:

The cost of one bicycle = $ 2 1 5 2 1 5 Number of bicycle = 8 7 × 8 7 The cost of 87 bicycles = $ 2 1 5 × 8 7 1 5 0 5 = $ 6834 + 1 7 2 0 0 1 8 7 0 5 Therefore, cost of 87 bicycles = $ 18705

3. The monthly salary of a man is $ 2,625. What is his annual income by salary?

Monthly income = $2,625 2 6 2 5 Annual income = $2,625 × 12 × 1 2 = $31,500 5 2 5 0 + 2 6 2 5 0 3 1 5 0 0

Therefore, annual income = $ 31,500

4. A chair costs $ 452 and a table costs $ 1750. What will be cost of 15 chairs and 30 tables?

(i) Cost of one chair = $ 452 Cost of 15 chairs = $ 452 × 15 = $ 6,780 (ii) Cost of one table = $ 1,750 Cost of 30 tables = $ 1,750 × 30 = $ 52,500 Therefore, cost of 15 chairs and 30 tables = $ 6,780 + $ 52,500

$Word Problems on Multiplication$

Worksheet on Word Problems on Multiplication:

1. Each student of class IV $ 75 for the flood victims. If there are 368 students in class IV, what is the total amount of money collected?

Answer: $ 27600

2. An orchard has 46 rows of mango trees. If there are 150 trees in each row. What is the total number of mango trees in the orchard?

Answer: 6900

3. A showroom has 165 bicycles. Each bicycle costs $ 4500. What is the total cost of all the bicycles?

Answer: $ 742500

4. The teller in the bank received 814 notes today. If the value of each note is $ 500, what is the total amount of money collected by the teller?

Answer: $ 407000

5. A car factory manufactures 75 cars each month. How many cars will be manufactured in the factory in one year?

Answer: 900

6. The National Library has 502 book shelves. In each shelf there are 44 books. What is the total number of books in the library?

Answer: 22088

7. Our heart beats about 72 times in a minute. How many times will it beat in an hour?

Answer: 4320

8. Shyam works for 10 hours in a day and Ram works for 9 hours in a day. Ram works for 6 days in a week and Sham works for 5 days in a week. Who works for more hours in a week and by how much?

Answer: Ram, 4 hours

9. There are 100 baskets of fruit. Each basket has 24 kg of fruit. If half of the baskets are kept on the weighing machine, then what weight will be shown by the weighing machine?

Answer: 1200

10. A truck has 673 boxes of candies. Each box has a dozen candies in it. What is the total number of candies on the truck?

Answer: 8076

11. A packet consists of 600 chocolates. How many chocolates are there in 248 such packets?

Answer: 148800

12. A book contains 543 pages. How many pages are there in 22 such books?

Answer: 11946

13. A boat can carry 635 people. How many people can travel in 240 such boats?

Answer: 152400

14. A farmer produced 735 quintals of rice. He told it at the rate of 1,525 per quintal How much money did he get?

15. A transistor costs 2,492. Find the cost of 64 such transistors.

16. A rack can hold 1,850 books. How many books can be kept in 82 such racks.

17. A cartoon can hold 15 dozen of oranges. How many oranges are there in 924 cartons.

18. The cost of a doll is $ 524. What is the east of 680 such dolls?

19. The capacity of a water tank is 6450 litres. In a city, there are 250 such tanks. What is the storage capacity of the city?

20. A weaving machine makes 4148 m of cloth in a week. How much cloth will it in 48 weeks?

21. The water capacity of a tank is 1325 litres. Find the total capacity of such 174 tanks

22. In a village, there are 1265 farmers. Each farmer has 329 sheep. How many shees are there in all? 23. Nairitee reads 12 pages of a book in one hour How many pages are there in that book if she reads 5 hours in a day and finishes the book in 30 days?

24. A bus can carry 52 passengers in one tip. How many passengers will it carry in the month of July if it makes 5 trips in a day?

25. The monthly fee of a student a Rs. 530. There are 142 students in a class. How much fee is collected from that class?

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Formation of Greatest and Smallest Numbers | Arranging the Numbers

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number increases its place value. So the greatest digit should be placed at the

$We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the smallest number then the numbers are arranged in descending order.$

Arranging Numbers | Ascending Order | Descending Order |Compare Digits

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the smallest number then the numbers are arranged in descending order.

$The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know that the position of a digit in a number determines its corresponding value$

Place Value | Place, Place Value and Face Value | Grouping the Digits

The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know that the position of a digit in a number determines its corresponding value

$In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.$

Formation of Numbers with the Given Digits |Making Numbers with Digits

In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.

$We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and ‘-‘ signs. We find the sum of the numbers with ‘+’ sign and similarly the sum$

Addition & Subtraction Together |Combination of addition & subtraction

We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and ‘-‘ signs. We find the sum of the numbers with ‘+’ sign and similarly the sum

$Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) VII (b) IX (c) XI (d) XIV (e) XIX (f) XXVII (g) XXIX (h) XII$

Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) VII (b) IX (c) XI (d) XIV (e) XIX (f) XXVII (g) XXIX (h) XII

$In International place-value system, there are three periods namely Ones, thousands and millions for the nine places from right to left. Ones period is made up of three place-values. Ones, tens, and hundreds. The next period thousands is made up of one, ten and hundred-thous$

International Place-value Chart | International Place-value System

In International place-value system, there are three periods namely Ones, thousands and millions for the nine places from right to left. Ones period is made up of three place-values. Ones, tens, and hundreds. The next period thousands is made up of one, ten and hundred-thous

$In worksheet on formation of numbers, four grade students can practice the questions on formation of numbers without the repetition of the given digits. This sheet can be practiced by students$

Worksheet on Formation of Numbers | Questions on Formation of Numbers

In worksheet on formation of numbers, four grade students can practice the questions on formation of numbers without the repetition of the given digits. This sheet can be practiced by students

$Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits from left most place until we come across unequal digits. To learn$

Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits from left most place until we come across unequal digits. To learn

$In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging the numbers etc…. Find the greatest number:$

Worksheets on Comparison of Numbers | Find the Greatest Number

In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging the numbers etc…. Find the greatest number:

$Dividing 3-Digit by 1-Digit Numbers are discussed here step-by-step. How to divide 3-digit numbers by single-digit numbers? Let us follow the examples to learn to divide 3-digit number by one-digit number. I: Dividing 3-digit Number by 1-Digit Number without Remainder:$

Dividing 3-Digit by 1-Digit Number | Long Division |Worksheet Answer

Dividing 3-Digit by 1-Digit Numbers are discussed here step-by-step. How to divide 3-digit numbers by single-digit numbers? Let us follow the examples to learn to divide 3-digit number by one-digit number. I: Dividing 3-digit Number by 1-Digit Number without Remainder:

Related Concept

● Word Problems on Addition

● Subtraction

● Check for Subtraction and Addition

● Word Problems Involving Addition and Subtraction

● Estimating Sums and Differences

● Find the Missing Digits

● Multiplication

● Multiply a Number by a 2-Digit Number

● Multiplication of a Number by a 3-Digit Number

● Multiply a Number

● Estimating Products

● Word Problems on Multiplication

● Multiplication and Division

● Terms Used in Division

● Division of Two-Digit by a One-Digit Numbers

● Division of Four-Digit by a One-Digit Numbers

● Division by 10 and 100 and 1000

● Dividing Numbers

● Estimating the Quotient

● Division by Two-Digit Numbers

● Word Problems on Division

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Multiplication word problems for grade 3

Simple multiplication.

These worksheets contain simple multiplication word problems. Students derive a multiplication equation from the word problem, solve the equation by mental multiplication and express the answer in appropriate units. Students should understand the meaning of multiplication before attempting these worksheets.

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How to Solve a Multiplication Problem

Do you want to know how to solve a multiplication problem? Have you already learned how to multiply? Did you know that solving problems is the best way to learn multiplication?

That’s why we are going to look at the different steps that we need to follow in order to solve a multiplication problem.

Let’s get to it and look at a multiplication problem:

The witch Malitch made 10 bottles of potion to take to the annual Witches of the World convention. At this convention, all of the witches present new magic potions and the best one wins the Flying Broom Prize. To make each potion, she used 3 boxes of magic herbs that were 5 pounds each. How many pounds of magic herbs did she use in total?

1) The first thing we need to do is to read the problem carefully . In order to make sure that we understand it, we can ask ourselves questions about the problem, for example:

What did the witch Malitch make? She made 10 bottles of potion.
Why did she make them? S he made them for a magic potion contest.

2) Once we understand what the problem said, we continue reading the question and analyze it by asking ourselves more questions:

What is the question asking me? The question is asking me how many pounds of magic herbs Malitch used in total, in all of the potions.
Do I need to do a math operation in order to solve the problem? Yes, because I only know how many pounds of magic herbs that each box had.
Ok, so what information do I need to use? ( T his last question is extremely important. You won’t always use all of the information that is given to you in a problem). I need to use the number of pounds that each box had (5), the number of boxes that she used for each potion (3) and lastly, the number of bottles of potions that she made (10).

3) Now, we can move on to think about the operation that we need to carry out:

We want to know how many pounds she used in total. We know that she used 3 boxes for each potion and that each box weighed 5 pound s, so:

For each potion she used 5 + 5 + 5 pounds . Or, expressed in a different way: 3 x 5 = 15 pounds.

Now we know that she used 15 pounds of magic herbs for each potion and we know that she made 10 bottles of potion, so:

In total, to make all of the potions, she used 15 x 10 = 150 pounds of magic herbs.

4) This last step is very important. We’ve gotten an answer, but now we need to critically reflect on the number that we got:

Finally, does it make sense that the answer (150) is greater than the numbers given in the problem (10, 3, 5)? Yes, it makes sense because these numbers referred to each potion or each box. The answer refers to the total amount of potions and the total amount of boxes.

Let’s solve the problem mentally using approximations: does it make sense that the number we got is 150? Yes. For example, it wouldn’t make sense if we got an answer of 30 because it’s too small of a number to be the answer of 10 x 3 x 5. It wouldn’t make sense either if we got 150,000 because it’s too big of a number.

So we have the final answer:

The witch Malitch used 150 pounds of magic herbs in total.

See? In order to solve a multiplication problem correctly, it’s not enough to just multiply all of the numbers, rather, we need to understand, analyze and reflect on what the problem says before we go ahead with the operation. We also need to check the answer.

Remember this for the next time that you have to solve a multiplication problem or any other problem for that matter!

Meanwhile, you can learn more about multiplication by clicking on the following links:

Multiplication tables
Singapore Model for Multiplication
How to Multiply 2 and 3 Digit Numbers

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How to Apply the Associative Property in a Problem
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Compound Rule of 3: When to Use It and Some Problems
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Multiplication Problem Solving

Keisha Thompson

Readind, understanding and solving multiplication problems using the 2 to 5 times tables.

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Multiplication Facts Worksheets

Welcome to the multiplication facts worksheets page at Math-Drills.com! On this page, you will find Multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats. This is our most popular page due to the wide variety of worksheets for multiplication available. Or it could be that learning multiplication facts and multiplication strategies are essential to many topics in mathematics beyond third grade math.

Learning multiplication facts to the point of quick recall should be a goal for all students and will serve them well in their math studies. Multiplication facts are actually easier to learn than you might think. First of all, it is only essential to learn the facts from 1 to 9. Somewhere along the way students can learn that anything multiplied by zero is zero. Hopefully, that is an easy one. Students also need to learn to multiply by ten as a precursor to learning how to multiply other powers of ten. After those three skills are learned, everything else is long multiplication. Multiplying by 11 is actually two-digit multiplication. Now, learning fact tables of 11 and beyond will do no harm to those students who are keen and able to learn these things quickly, and it might help them figure out how many eggs are in a gross faster than anyone else, but keep it simple for those students who struggle a bit more.

Most Popular Multiplication Facts Worksheets this Week

$Multiplying (1 to 12) by 3 (100 Questions)$

Multiplication Facts Tables

$problem solving use multiplication 8 2$

The multiplication tables with individual questions include a separate box for each number. In each box, the single number is multiplied by every other number with each question on one line. The tables may be used for various purposes such as introducing the multiplication tables, skip counting, as a lookup table, patterning activities, and memorizing.

Multiplication Facts Tables from 1 to 12 Multiplication Facts Tables in Gray 1 to 12 Multiplication Facts Tables in Gray 1 to 12 (Answers Omitted) Multiplication Facts Tables in Color 1 to 12 Multiplication Facts Tables in Color 1 to 12 (Answers Omitted) Multiplication Facts Tables in Montessori Colors 1 to 12 Multiplication Facts Tables in Montessori Colors 1 to 12 (Answers Omitted)
Multiplication Facts Tables from 0 to 11 Multiplication Facts Tables in Gray 0 to 11 Multiplication Facts Tables in Gray 0 to 11 (Answers Omitted) Multiplication Facts Tables in Color 0 to 11 Multiplication Facts Tables in Color 0 to 11 (Answers Omitted) Multiplication Facts Tables in Montessori Colors 0 to 11 Multiplication Facts Tables in Montessori Colors 0 to 11 (Answers Omitted)
Multiplication Facts Tables from 13 to 24 Multiplication Facts Tables in Gray 13 to 24 Multiplication Facts Tables in Gray 13 to 24 (Answers Omitted) Multiplication Facts Tables in Color 13 to 24 Multiplication Facts Tables in Color 13 to 24 (Answers Omitted)

The compact multiplication tables are basically lookup charts. To look up a multiplication fact, find the first factor in the column header and the second factor in the row headers; then use straight edges, your fingers or your eyes to find where the column and row intersect to get the product. These tables are better than the previous tables for finding patterns, but they can be used in similar ways. Each PDF includes a filled out table page and a blank table page. The blank tables can be used for practice or assessment. You might also make a game out of it, such as "Pin the Fact on the Table" (a play on Pin the Tail on the Donkey). Students are given a product (answer) and they pin it on an enlarged version or the table (photocopier enlargement, interactive whiteboard, overhead projector, etc.). Paper-saving versions with multiple tables per page are included. The left-handed versions of the multiplication tables recognize that students who use their left hands might block the row headings on the right-handed versions.

Compact Multiplication Facts Tables from 1 to 7 Multiplication Table to 49 (1 Filled and 1 Blank) Multiplication Table to 49 (9 Filled and 9 Blank) Left-Handed Multiplication Table to 49 (1 Filled and 1 Blank) Left-Handed Multiplication Table to 49 (9 Filled and 9 Blank)
Compact Multiplication Facts Tables from 1 to 9 Multiplication Table to 81 (1 Filled and 1 Blank) Multiplication Table to 81 (6 Filled and 6 Blank) Left-Handed Multiplication Table to 81 (1 Filled and 1 Blank) Left-Handed Multiplication Table to 81 (6 Filled and 6 Blank)
Compact Multiplication Facts Tables from 1 to 10 Multiplication Table to 100 (1 Filled and 1 Blank) Multiplication Table to 100 (6 Filled and 6 Blank) Left-Handed Multiplication Table to 100 (1 Filled and 1 Blank) Left-Handed Multiplication Table to 100 (6 Filled and 6 Blank)
Compact Multiplication Facts Tables from 1 to 12 Multiplication Table to 144 (1 Filled and 1 Blank) Multiplication Table to 144 (4 Filled and 4 Blank) Left-Handed Multiplication Table to 144 (1 Filled and 1 Blank) Left-Handed Multiplication Table to 144 (4 Filled and 4 Blank)

Five Minute Multiplication Frenzies

$problem solving use multiplication 8 2$

Five minute frenzy charts are 10 by 10 grids that are used for multiplication fact practice (up to 12 x 12) and improving recall speed. They are very much like compact multiplication tables, but all the numbers are mixed up, so students are unable to use skip counting to fill them out. In each square, students write the product of the column number and the row number. They try to complete the chart in a set time with an accuracy goal (such as less than five minutes and score 98 percent or better).

It is important to note here that you should NOT have students complete five minute frenzies if they don't already know all of the multiplication facts that appear on them. If you want them to participate with the rest of the class, cross off the rows and columns that they don't know and have them complete a modified version. Remember, these charts are for practice and improving recall, not a teaching tool by itself.

Students who write with their left hands may cover the row headings on the right-handed versions, so the left-handed versions have the row headings on the other side.

Multiplication Frenzies from 0 to 9 Multiplication Frenzy with Factors from 0 to 9 ( 1 Chart Per Page) Multiplication Frenzy with Factors from 0 to 9 ( 4 Charts Per Page) Left-Handed Multiplication Frenzy with Factors from 0 to 9 ( 1 Chart Per Page) Left-Handed Multiplication Frenzy with Factors from 0 to 9 ( 4 Charts Per Page)
Multiplication Frenzies from 1 to 10 Multiplication Frenzy with Factors from 1 to 10 ( 1 Chart Per Page) Multiplication Frenzy with Factors from 1 to 10 ( 4 Charts Per Page) Left-Handed Multiplication Frenzy with Factors from 1 to 10 ( 1 Chart Per Page) Left-Handed Multiplication Frenzy with Factors from 1 to 10 ( 4 Charts Per Page)
Multiplication Frenzies from 2 to 12 Multiplication Frenzy with Factors from 2 to 12 ( 1 Chart Per Page) Multiplication Frenzy with Factors from 2 to 12 ( 4 Charts Per Page) Left-Handed Multiplication Frenzy with Factors from 2 to 12 ( 1 Chart Per Page) Left-Handed Multiplication Frenzy with Factors from 2 to 12 ( 4 Charts Per Page)
Multiplication Frenzies from 5 to 15 Multiplication Frenzy with Factors from 5 to 15 ( 1 Chart Per Page) Multiplication Frenzy with Factors from 5 to 15 ( 4 Charts Per Page) Left-Handed Multiplication Frenzy with Factors from 5 to 15 ( 1 Chart Per Page) Left-Handed Multiplication Frenzy with Factors from 5 to 15 ( 4 Charts Per Page)

Multiplication Facts up to the 7 Times Table

$problem solving use multiplication 8 2$

This section includes math worksheets for practicing multiplication facts to from 0 to 49. There are two worksheets in this section that include all of the possible questions exactly once on each page: the 49 question worksheet with no zeros and the 64 question worksheet with zeros. All others either contain all the possible questions plus some repeats or a unique subset of the possible questions.

Multiplication Facts up to the 7 Times Table (No Zeros) Multiplication Facts to 49 ( 100 Questions) ( No Zeros ) ✎ Multiplication Facts to 49 ( 50 Questions ) ( No Zeros ) ✎ Multiplication Facts to 49 ( 49 Questions) ( No Zeros ) ✎ Multiplication Facts to 49 ( 25 Questions ) ( No Zeros ) ✎
Multiplication Facts up to the 7 Times Table (With Zeros) Multiplication Facts to 49 ( 100 Questions) ( With Zeros ) ✎ Multiplication Facts to 49 ( 64 Questions) ( With Zeros ) ✎ Multiplication Facts to 49 ( 50 Questions ) ( With Zeros ) ✎ Multiplication Facts to 49 ( 25 Questions ) ( With Zeros ) ✎
Horizontally Arranged Multiplication Facts up to the 5 Times Table Horizontally Arranged Multiplication Facts with Products to 25 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts with Products to 25 ( 50 Questions ) ✎ Horizontally Arranged Multiplication Facts with Products to 25 ( 25 Questions ; Large Print) ✎
Horizontally Arranged Multiplication Facts up to the 6 Times Table Horizontally Arranged Multiplication Facts with Products to 36 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts with Products to 36 ( 50 Questions ) ✎ Horizontally Arranged Multiplication Facts with Products to 36 ( 25 Questions ; Large Print) ✎
Horizontally Arranged Multiplication Facts up to the 7 Times Table Horizontally Arranged Multiplication Facts with Products to 49 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts with Products to 49 ( 50 Questions ) ✎ Horizontally Arranged Multiplication Facts with Products to 49 ( 25 Questions ; Large Print) ✎

When a student first learns multiplication facts, try not to overwhelm them with the entire multiplication table. The following worksheets include one row of the facts in order with the target digit on the bottom and one row with the target digit on the top. The remaining rows include each of the facts once, but the target digit is randomly placed on the top or the bottom and the facts are randomly mixed on each row.

Multiplying (1 to 7) by Individual Facts Multiplying (1 to 7) by 1 ✎ Multiplying (1 to 7) by 2 ✎ Multiplying (1 to 7) by 3 ✎ Multiplying (1 to 7) by 4 ✎ Multiplying (1 to 7) by 5 ✎ Multiplying (1 to 7) by 6 ✎ Multiplying (1 to 7) by 7 ✎
Multiplying (0 to 7) by Individual Facts Multiplying (0 to 7) by 0 ✎ Multiplying (0 to 7) by 1 ✎ Multiplying (0 to 7) by 2 ✎ Multiplying (0 to 7) by 3 ✎ Multiplying (0 to 7) by 4 ✎ Multiplying (0 to 7) by 5 ✎ Multiplying (0 to 7) by 6 ✎ Multiplying (0 to 7) by 7 ✎
Horizontally Arranged Multiplying (1 to 7) by Individual Facts (100 Questions per page) Horizontally Arranged Multiplying (1 to 7) by 1 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 2 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 3 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 4 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 5 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 6 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 7 ( 100 Questions ) ✎
Horizontally Arranged Multiplying (1 to 7) by Individual Facts (50 Questions per page) Horizontally Arranged Multiplying (1 to 7) by 1 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 2 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 3 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 4 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 5 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 6 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 7 ( 50 Questions ) ✎
Horizontally Arranged Multiplying (1 to 7) by Individual Facts (25 Questions per page) Horizontally Arranged Multiplying (1 to 7) by 1 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 2 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 3 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 4 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 5 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 6 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 7 ( 25 Questions ; Large Print) ✎
Multiplying Doubles Multiplying Doubles up to 7 x 7

Multiplication Facts up to the 9 Times Table

$problem solving use multiplication 8 2$

This section includes math worksheets for practicing multiplication facts from 0 to 81. There are three worksheets (marked with *) in this section that include all of the possible questions in the specified range exactly once on each page: the 64 question worksheet with no zeros or ones, the 81 question worksheet with no zeros, and the 100 question worksheet with zeros. All others either contain all the possible questions plus some repeats or a unique subset of the possible questions.

Multiplication Facts up to the 9 Times Table (No Zeros or Ones) Multiplication Facts to 81 ( 100 Questions) ( No Zeros or Ones ) ✎ Multiplication Facts to 81 ( 81 Questions) ( No Zeros or Ones ) ✎ *Multiplication Facts to 81 ( 64 Questions) ( No Zeros or Ones ) ✎ Multiplication Facts to 81 ( 50 Questions ) ( No Zeros or Ones ) ✎ Multiplication Facts to 81 ( 25 Questions ) ( No Zeros or Ones ) ✎
Multiplication Facts up to the 9 Times Table (No Zeros) Multiplication Facts to 81 ( 100 Questions) ( No Zeros ) ✎ *Multiplication Facts to 81 ( 81 Questions) ( No Zeros ) ✎ Multiplication Facts to 81 ( 50 Questions ) ( No Zeros ) ✎ Multiplication Facts to 81 ( 25 Questions ) ( No Zeros ) ✎
Multiplication Facts up to the 9 Times Table (With Zeros) *Multiplication Facts to 81 ( 100 Questions) ( With Zeros ) ✎ Multiplication Facts to 81 ( 81 Questions) ( With Zeros ) ✎ Multiplication Facts to 81 ( 50 Questions ) ( With Zeros ) ✎ Multiplication Facts to 81 ( 25 Questions ) ( With Zeros ) ✎
Horizontally Arranged Multiplication Facts up to the 8 Times Table Horizontally Arranged Multiplication Facts with Products to 64 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts with Products to 64 ( 50 Questions ) ✎ Horizontally Arranged Multiplication Facts with Products to 64 ( 25 Questions ; Large Print) ✎
Horizontally Arranged Multiplication Facts up to the 9 Times Table Horizontally Arranged Multiplication Facts with Products to 81 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts with Products to 81 ( 50 Questions ) ✎ Horizontally Arranged Multiplication Facts with Products to 81 ( 25 Questions ; Large Print) ✎

When learning multiplication facts, it is useful to have each fact isolated on a set of practice questions to help reinforce the individual fact. The following worksheets isolate each fact. These worksheets can be used as practice sheets, assessment sheets, or in conjunction with another teaching strategy such as manipulative use.

Multiplying (1 to 9) by Individual Facts (81 Questions per Page) Multiplying (1 to 9) by 0 ( 81 Questions) ✎ Multiplying (1 to 9) by 1 ( 81 Questions) ✎ Multiplying (1 to 9) by 2 ( 81 Questions) ✎ Multiplying (1 to 9) by 3 ( 81 Questions) ✎ Multiplying (1 to 9) by 4 ( 81 Questions) ✎ Multiplying (1 to 9) by 5 ( 81 Questions) ✎ Multiplying (1 to 9) by 6 ( 81 Questions) ✎ Multiplying (1 to 9) by 7 ( 81 Questions) ✎ Multiplying (1 to 9) by 8 ( 81 Questions) ✎ Multiplying (1 to 9) by 9 ( 81 Questions) ✎ Multiplying (1 to 9) by (3 and 4) ( 81 Questions) ✎ Multiplying (1 to 9) by (4 and 5) ( 81 Questions) ✎ Multiplying (1 to 9) by (5 and 6) ( 81 Questions) ✎ Multiplying (1 to 9) by (6 and 7) ( 81 Questions) ✎ Multiplying (1 to 9) by (7 and 8) ( 81 Questions) ✎ Multiplying (1 to 9) by (8 and 9) ( 81 Questions) ✎ Multiplying (1 to 9) by (6 to 8) ( 81 Questions) ✎ Multiplying (1 to 9) by (7 to 9) ( 81 Questions) ✎ Multiplying (1 to 9) by (6 to 9) ( 81 Questions) ✎
Multiplying (2 to 9) by Individual Facts (100 Questions per Page) Multiplying (2 to 9) by (6 to 8) ( 100 Questions) ✎ Multiplying (2 to 9) by (7 to 9) ( 100 Questions) ✎
Multiplying (1 to 9) by Individual Facts (36 Questions per Page; Large Print) Multiplying (1 to 9) by 0 ( 36 Questions) ✎ Multiplying (1 to 9) by 1 ( 36 Questions) ✎ Multiplying (1 to 9) by 2 ( 36 Questions) ✎ Multiplying (1 to 9) by 3 ( 36 Questions) ✎ Multiplying (1 to 9) by 4 ( 36 Questions) ✎ Multiplying (1 to 9) by 5 ( 36 Questions) ✎ Multiplying (1 to 9) by 6 ( 36 Questions) ✎ Multiplying (1 to 9) by 7 ( 36 Questions) ✎ Multiplying (1 to 9) by 8 ( 36 Questions) ✎ Multiplying (1 to 9) by 9 ( 36 Questions) ✎ Multiplying (1 to 9) by (6 and 7) ( 36 Questions) ✎ Multiplying (1 to 9) by (7 and 8) ( 36 Questions) ✎ Multiplying (1 to 9) by (8 and 9) ( 36 Questions) ✎ Multiplying (1 to 9) by (6 to 8) ( 36 Questions) ✎ Multiplying (1 to 9) by (7 to 9) ( 36 Questions) ✎ Multiplying (1 to 9) by (6 to 9) ( 36 Questions) ✎
Horizontally Arranged Multiplying (0 to 9) by Individual Facts (100 Questions per Page) Horizontally Arranged Multiplying ( 0 to 9 ) by 0 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 1 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 2 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 3 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 4 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 5 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 6 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 7 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 8 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 9 ( 100 Questions) ✎
Horizontally Arranged Multiplying (0 to 9) by Individual Facts (50 Questions per Page) Horizontally Arranged Multiplying ( 0 to 9 ) by 0 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 1 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 2 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 3 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 4 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 5 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 6 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 7 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 8 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 9 ( 50 Questions ) ✎
Horizontally Arranged Multiplying (0 to 9) by Individual Facts (25 Questions per Page; Large Print) Horizontally Arranged Multiplying ( 0 to 9 ) by 0 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 1 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 2 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 3 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 4 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 5 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 6 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 8 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 9 ( 25 Questions ; Large Print) ✎
Multiplying Doubles Multiplying Doubles up to 9 x 9

Some students are a little more motivated when learning is turned into a game. Multiplication bingo encourages students to recall multiplication facts in an environment of competition.

Multiplication Bingo Game Multiplication Bingo Cards for Facts 1 to 9 Multiplication Bingo Facts 1 to 9 Teacher Call Cards

Multiplication Facts up to the 10 Times Table

$problem solving use multiplication 8 2$

Multiplying by 10 is often a lesson itself, but here we have included it with the other facts. Students usually learn how to multiply by 10 fairly quickly, so this section really is not a whole lot more difficult than the multiplication facts to 81 section.

Multiplication Facts up to the 10 Times Table (No Zeros or Ones) Multiplication Facts to 100 ( 100 Questions) ( No Zeros or Ones ) ✎ *Multiplication Facts to 100 ( 81 Questions) ( No Zeros or Ones ) ✎ Multiplication Facts to 100 ( 50 Questions ) ( No Zeros or Ones ) ✎ Multiplication Facts to 100 ( 25 Questions ) ( No Zeros or Ones ) ✎
Multiplication Facts up to the 10 Times Table (No Zeros) *Multiplication Facts to 100 ( 100 Questions) ( No Zeros ) ✎ Multiplication Facts to 100 ( 50 Questions ) ( No Zeros ) ✎ Multiplication Facts to 100 ( 25 Questions ) ( No Zeros ) ✎
Multiplication Facts up to the 10 Times Table (With Zeros) Multiplication Facts to 100 ( 100 Questions) ( With Zeros ) ✎ Multiplication Facts to 100 ( 50 Questions ) ( With Zeros ) ✎ Multiplication Facts to 100 ( 25 Questions ) ( With Zeros ) ✎
Horizontally Arranged Multiplication Facts up to the 10 Times Table Horizontally Arranged Multiplication Facts to 10 × 10 = 100 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts to 10 × 10 = 100 ( 50 Questions ) ✎

Some students find it easier to focus on one multiplication fact at a time. These multiplication worksheets include some repetition, of course, as there is only one thing to multiply by. Once students practice a few times, these facts will probably get stuck in their heads for life. Some of the later versions include a range of focus numbers. In those cases, each question will randomly have one of the focus numbers in question. For example, if the range is 6 to 8, the question might include a 6, 7 or 8 or more than one depending on which other factor was chosen for the second factor.

Multiplying (1 to 10) by Individual Facts (100 Questions per Page) Multiplying (1 to 10) by 0 ( 100 Questions) ✎ Multiplying (1 to 10) by 1 ( 100 Questions) ✎ Multiplying (1 to 10) by 2 ( 100 Questions) ✎ Multiplying (1 to 10) by 3 ( 100 Questions) ✎ Multiplying (1 to 10) by 4 ( 100 Questions) ✎ Multiplying (1 to 10) by 5 ( 100 Questions) ✎ Multiplying (1 to 10) by 6 ( 100 Questions) ✎ Multiplying (1 to 10) by 7 ( 100 Questions) ✎ Multiplying (1 to 10) by 8 ( 100 Questions) ✎ Multiplying (1 to 10) by 9 ( 100 Questions) ✎ Multiplying (1 to 10) by 10 ( 100 Questions) ✎
Multiplying (1 to 10) by Ranges Individual Facts (100 Questions per Page) Multiplying (1 to 10) by (6 and 7) ( 100 Questions) ✎ Multiplying (1 to 10) by (7 and 8) ( 100 Questions) ✎ Multiplying (1 to 10) by (8 and 9) ( 100 Questions) ✎ Multiplying (1 to 10) by (9 and 10) ( 100 Questions) ✎ Multiplying (1 to 10) by (6 to 8) ( 100 Questions) ✎ Multiplying (1 to 10) by (7 to 9) ( 100 Questions) ✎ Multiplying (1 to 10) by (8 to 10) ( 100 Questions) ✎ Multiplying Doubles (aka Squares) from (1 to 10) ( 100 Questions)
Multiplying (1 to 10) by Individual Facts (50 Questions per Page) Multiplying (1 to 10) by 0 ( 50 Questions ) ✎ Multiplying (1 to 10) by 1 ( 50 Questions ) ✎ Multiplying (1 to 10) by 2 ( 50 Questions ) ✎ Multiplying (1 to 10) by 3 ( 50 Questions ) ✎ Multiplying (1 to 10) by 4 ( 50 Questions ) ✎ Multiplying (1 to 10) by 5 ( 50 Questions ) ✎ Multiplying (1 to 10) by 6 ( 50 Questions ) ✎ Multiplying (1 to 10) by 7 ( 50 Questions ) ✎ Multiplying (1 to 10) by 8 ( 50 Questions ) ✎ Multiplying (1 to 10) by 9 ( 50 Questions ) ✎ Multiplying (1 to 10) by 10 ( 50 Questions ) ✎
Multiplying (1 to 10) by Ranges of Individual Facts (50 Questions per Page) Multiplying (1 to 10) by (6 and 7) ( 50 Questions ) ✎ Multiplying (1 to 10) by (7 and 8) ( 50 Questions ) ✎ Multiplying (1 to 10) by (8 and 9) ( 50 Questions ) ✎ Multiplying (1 to 10) by (9 and 10) ( 50 Questions ) ✎ Multiplying (1 to 10) by (6 to 8) ( 50 Questions ) ✎ Multiplying (1 to 10) by (7 to 9) ( 50 Questions ) ✎ Multiplying (1 to 10) by (8 to 10) ( 50 Questions ) ✎
Multiplying (1 to 10) by Individual Facts (36 Questions per Page) Multiplying (1 to 10) by 0 ( 36 Questions) ✎ Multiplying (1 to 10) by 1 ( 36 Questions) ✎ Multiplying (1 to 10) by 2 ( 36 Questions) ✎ Multiplying (1 to 10) by 3 ( 36 Questions) ✎ Multiplying (1 to 10) by 4 ( 36 Questions) ✎ Multiplying (1 to 10) by 5 ( 36 Questions) ✎ Multiplying (1 to 10) by 6 ( 36 Questions) ✎ Multiplying (1 to 10) by 7 ( 36 Questions) ✎ Multiplying (1 to 10) by 8 ( 36 Questions) ✎ Multiplying (1 to 10) by 9 ( 36 Questions) ✎ Multiplying (1 to 10) by 10 ( 36 Questions) ✎
Multiplying (1 to 10) by Ranges of Individual Facts (42 Questions per Page) Multiplying (1 to 10) by (6 and 7) ( 42 Questions) ✎ Multiplying (1 to 10) by (7 and 8) ( 42 Questions) ✎ Multiplying (1 to 10) by (8 and 9) ( 42 Questions) ✎ Multiplying (1 to 10) by (9 and 10) ( 42 Questions) ✎ Multiplying (1 to 10) by (6 to 8) ( 42 Questions) ✎ Multiplying (1 to 10) by (7 to 9) ( 42 Questions) ✎ Multiplying (1 to 10) by (8 to 10) ( 42 Questions) ✎
Horizontally Arranged Multiplying (1 to 10) by Individual Facts (100 Questions per Page) Horizontally Arranged Multiplying (1 to 10) by 1 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 2 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 3 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 4 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 5 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 6 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 7 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 8 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 9 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 10 ( 100 Questions ) ✎
Horizontally Arranged Multiplying (1 to 10) by Individual Facts (50 Questions per Page) Horizontally Arranged Multiplying (1 to 10) by 1 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 2 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 3 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 4 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 5 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 6 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 7 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 8 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 9 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 10 ( 50 Questions ) ✎
Horizontally Arranged Multiplying (1 to 10) by Individual Facts (25 Questions per Page; Large Print) Horizontally Arranged Multiplying (1 to 10) by 1 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 2 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 3 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 4 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 5 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 6 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 8 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 10 ( 25 Questions ; Large Print) ✎

If a student is learning their times tables one at a time, these worksheets will help with practice and assessment along the way. Each one increases the range for the second factor.

Multiplying (1 to 10) by Increasing Ranges of Individual Facts (100 Questions per Page) Multiplying (1 to 10) by (1 and 2) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 3) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 4) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 5) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 6) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 7) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 8) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 9) ( 100 Questions) ✎
Multiplying (1 to 10) by Increasing Ranges of Individual Facts (50 Questions per Page) Multiplying (1 to 10) by (1 and 2) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 3) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 4) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 5) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 6) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 7) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 8) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 9) ( 50 Questions ) ✎
Multiplying Doubles Multiplying Doubles up to 10 x 10

Multiplication Facts up to the 12 Times Table

$problem solving use multiplication 8 2$

The Holy Grail of elementary mathematics. Once you learn your twelve times table, it is smooth sailing from now on, right? Well, not exactly, but having a good mental recall of the multiplication facts up to 144 will certainly set you on the right path for future success in your math studies.

Multiplication Facts up to the 12 Times Table (No Zeros or Ones) Multiplication Facts to 144 ( 100 Questions) ( No Zeros or Ones ) ✎ Multiplication Facts to 144 ( 50 Questions ) ( No Zeros or Ones ) ✎ Multiplication Facts to 144 ( 25 Questions ) ( No Zeros or Ones ) ✎
Multiplication Facts up to the 12 Times Table (No Zeros) Multiplication Facts to 144 ( 100 Questions) ( No Zeros ) ✎ Multiplication Facts to 144 ( 50 Questions ) ( No Zeros ) ✎ Multiplication Facts to 144 ( 25 Questions ) ( No Zeros ) ✎
Multiplication Facts up to the 12 Times Table (With Zeros) Multiplication Facts to 144 ( 100 Questions) ( With Zeros ) ✎ Multiplication Facts to 144 ( 50 Questions ) ( With Zeros ) ✎ Multiplication Facts to 144 ( 25 Questions ) ( With Zeros ) ✎
Horizontally Arranged Multiplication Facts up to the 11 Times Table Horizontally Arranged Multiplication Facts to 11 × 11 = 121 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts to 11 × 11 = 121 ( 50 Questions ) ✎
Horizontally Arranged Multiplication Facts up to the 12 Times Table Horizontally Arranged Multiplication Facts to 12 × 12 = 144 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts to 12 × 12 = 144 ( 50 Questions ) ✎

With one, two or three target numbers at a time, students are able to practice just the multiplication facts they need.

Multiplying (1 to 12) by Individual Facts (100 Questions per Page) Multiplying (1 to 12) By 0 ( 100 Questions) ✎ Multiplying (1 to 12) By 1 ( 100 Questions) ✎ Multiplying (1 to 12) By 2 ( 100 Questions) ✎ Multiplying (1 to 12) By 3 ( 100 Questions) ✎ Multiplying (1 to 12) By 4 ( 100 Questions) ✎ Multiplying (1 to 12) By 5 ( 100 Questions) ✎ Multiplying (1 to 12) By 6 ( 100 Questions) ✎ Multiplying (1 to 12) By 7 ( 100 Questions) ✎ Multiplying (1 to 12) By 8 ( 100 Questions) ✎ Multiplying (1 to 12) By 9 ( 100 Questions) ✎ Multiplying (1 to 12) By 10 ( 100 Questions) ✎ Multiplying (1 to 12) By 11 ( 100 Questions) ✎ Multiplying (1 to 12) By 12 ( 100 Questions) ✎
Multiplying (1 to 12) by RAnges of Individual Facts (100 Questions per Page) Multiplying (1 to 12) By (0 and 1) ( 100 Questions) ✎ Multiplying (1 to 12) By (6 and 7) ( 100 Questions) Multiplying (1 to 12) By (7 and 8) ( 100 Questions) ✎ Multiplying (1 to 12) By (8 and 9) ( 100 Questions) ✎ Multiplying (1 to 12) By (9 and 10) ( 100 Questions) ✎ Multiplying (1 to 12) By (10 and 11) ( 100 Questions) ✎ Multiplying (1 to 12) By (11 and 12) ( 100 Questions) ✎ Multiplying (1 to 12) By (6, 7 and 8) ( 100 Questions) ✎ Multiplying (1 to 12) By (7, 8 and 9) ( 100 Questions) ✎ Multiplying (1 to 12) By (8, 9 and 10) ( 100 Questions) ✎ Multiplying (1 to 12) By (9, 10 and 11) ( 100 Questions) ✎ Multiplying (1 to 12) By (10, 11 and 12) ( 100 Questions) ✎
Multiplying (1 to 12) by Individual Facts (50 Questions per Page) Multiplying (1 to 12) By 0 ( 50 Questions ) ✎ Multiplying (1 to 12) By 1 ( 50 Questions ) ✎ Multiplying (1 to 12) By 2 ( 50 Questions ) ✎ Multiplying (1 to 12) By 3 ( 50 Questions ) ✎ Multiplying (1 to 12) By 4 ( 50 Questions ) ✎ Multiplying (1 to 12) By 5 ( 50 Questions ) ✎ Multiplying (1 to 12) By 6 ( 50 Questions ) ✎ Multiplying (1 to 12) By 7 ( 50 Questions ) ✎ Multiplying (1 to 12) By 8 ( 50 Questions ) ✎ Multiplying (1 to 12) By 9 ( 50 Questions ) ✎ Multiplying (1 to 12) By 10 ( 50 Questions ) ✎ Multiplying (1 to 12) By 11 ( 50 Questions ) ✎ Multiplying (1 to 12) By 12 ( 50 Questions ) ✎
Multiplying (1 to 12) by Ranges of Individual Facts (50 Questions per Page) Multiplying (1 to 12) By (6 and 7) ( 50 Questions ) ✎ Multiplying (1 to 12) By (7 and 8) ( 50 Questions ) ✎ Multiplying (1 to 12) By (8 and 9) ( 50 Questions ) ✎ Multiplying (1 to 12) By (9 and 10) ( 50 Questions ) ✎ Multiplying (1 to 12) By (10 and 11) ( 50 Questions ) ✎ Multiplying (1 to 12) By (11 and 12) ( 50 Questions ) ✎ Multiplying (1 to 12) By (6, 7 and 8) ( 50 Questions ) ✎ Multiplying (1 to 12) By (7, 8 and 9) ( 50 Questions ) ✎ Multiplying (1 to 12) By (8, 9 and 10) ( 50 Questions ) ✎ Multiplying (1 to 12) By (9, 10 and 11) ( 50 Questions ) ✎ Multiplying (1 to 12) By (10, 11 and 12) ( 50 Questions ) ✎
Horizontally Arranged Multiplying (0 to 12) by Individual Facts (100 Questions per Page) Horizontally Arranged Multiplying ( 0 to 12 ) by 0 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 1 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 2 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 3 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 4 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 5 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 6 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 7 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 8 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 9 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 10 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 11 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 12 ( 100 Questions) ✎
Horizontally Arranged Multiplying (0 to 12) by Individual Facts (50 Questions per Page) Horizontally Arranged Multiplying ( 0 to 12 ) by 0 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 1 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 2 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 3 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 4 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 5 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 6 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 7 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 8 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 9 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 10 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 11 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 12 ( 50 Questions ) ✎
Horizontally Arranged Multiplying (0 to 12) by Individual Facts (25 Questions per Page; Large Print) Horizontally Arranged Multiplying ( 0 to 12 ) by 0 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 1 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 2 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 3 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 4 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 5 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 6 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 8 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 11 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 12 ( 25 Questions ; Large Print) ✎

In the following multiplication worksheets, the facts are grouped into anchor groups.

Multiplying (1 to 12) by Anchor Facts (Commonly Grouped Facts) Multiplying by Anchor Facts 0, 1, 2, 5 and 10 Multiplying by Facts 3, 4 and 6 Multiplying by Facts 7, 8 and 9 Multiplying by Facts 11 and 12 Multiplying by Facts 0 to 5 and 10 Multiplying by Facts 0 to 7 and 10 Multiplying by Facts 0 to 10
Multiplying (1 to 12) by Increasing Ranges of Individual Facts (100 Questions per Page) Multiplying (1 to 12) by (1 to 5) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 6) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 7) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 8) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 9) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 10) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 11) ( 100 Questions) ✎
Multiplying (1 to 12) by Increasing Ranges of Individual Facts (50 Questions per Page) Multiplying (1 to 12) by (1 to 5) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 6) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 7) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 8) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 9) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 10) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 11) ( 50 Questions ) ✎

On the following multiplication worksheets, the questions are in order and might be useful for students to remember their times tables or to help them with skip counting.

Repetitive Multiplying of Individual Facts by (1 to 12) Repetitive Multiplying of 1 by (1 to 12) Repetitive Multiplying of 2 by (1 to 12) Repetitive Multiplying of 3 by (1 to 12) Repetitive Multiplying of 4 by (1 to 12) Repetitive Multiplying of 5 by (1 to 12) Repetitive Multiplying of 6 by (1 to 12) Repetitive Multiplying of 7 by (1 to 12) Repetitive Multiplying of 8 by (1 to 12) Repetitive Multiplying of 9 by (1 to 12) Repetitive Multiplying of 10 by (1 to 12) Repetitive Multiplying of 11 by (1 to 12) Repetitive Multiplying of 12 by (1 to 12)
Multiplying Doubles Multiplying Doubles up to 12 x 12

Multiplication Facts beyond the 12 Times Table

$problem solving use multiplication 8 2$

It is quite likely that there are students who have mastered all of the multiplication facts up to the 12 times tables. In case they want/need an extra challenge, this sections includes multiplication facts worksheets above 12 with the expectation that students will use mental math or recall to calculate the answers.

Multiplying with Increasing Upper Range Factors from 13 to 20 Multiplying with Factors 2 to 13 (100 Questions) ✎ Multiplying with Factors 2 to 14 (100 Questions) ✎ Multiplying with Factors 2 to 15 (100 Questions) ✎ Multiplying with Factors 5 to 15 (100 Questions) ✎ Multiplying with Factors 5 to 16 (100 Questions) ✎ Multiplying with Factors 5 to 17 (100 Questions) ✎ Multiplying with Factors 5 to 18 (100 Questions) ✎ Multiplying with Factors 5 to 19 (100 Questions) ✎ Multiplying with Factors 5 to 20 (100 Questions) ✎
Multiplying by Individual Facts from 13 to 25 Multiplying by 13 (49 Questions) ✎ Multiplying by 14 (49 Questions) ✎ Multiplying by 15 (49 Questions) ✎ Multiplying by 16 (49 Questions) ✎ Multiplying by 17 (49 Questions) ✎ Multiplying by 18 (49 Questions) ✎ Multiplying by 19 (49 Questions) ✎ Multiplying by 20 (49 Questions) ✎ Multiplying by 21 (49 Questions) ✎ Multiplying by 22 (49 Questions) ✎ Multiplying by 23 (49 Questions) ✎ Multiplying by 24 (49 Questions) ✎ Multiplying by 25 (49 Questions) ✎

Expand your mental math abilities by learning multiplication facts beyond the twelve times tables with these worksheets. They are horizontally arranged, so you won't be tempted to use an algorithm. Even if you can't recall all these facts yet, you can still figure them out using the distributive property. Let's say you want to multiply 19 by 19, that could be (10 × 19) + (9 × 19). Too hard? How about (10 × 10) + (10 × 9) + (9 × 10) + (9 × 9)! Or just remember that 19 × 19 = 361 :)

Horizontally Arranged Multiplying with Increasing Upper Range Factors from 13 to 25 Horizontally Arranged Multiplying with Factors 1 to 13 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 1 to 14 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 1 to 15 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 2 to 16 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 2 to 17 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 2 to 18 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 2 to 19 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 2 to 20 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 5 to 21 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 5 to 22 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 5 to 23 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 5 to 24 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 5 to 25 (100 Questions) ✎
Horizontally Arranged Multiplying by Individual Facts from 13 to 25 Horizontally Arranged Multiplying (1 to 13) by 13 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 14) by 14 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 15) by 15 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 16) by 16 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 17) by 17 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 18) by 18 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 19) by 19 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 20) by 20 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 21) by 21 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 22) by 22 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 23) by 23 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 24) by 24 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 25) by 25 (100 Questions) ✎
Multiplying Doubles Multiplying Doubles up to 15 x 15 Multiplying Doubles up to 20 x 20

Mind Your Decisions

Math Videos, Math Puzzles, Game Theory. By Presh Talwalkar

$problem solving use multiplication 8 2$

What Is 8 ÷ 2(2 + 2) = ? Mathematician Explains The Correct Answer

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Posted July 31, 2019 By Presh Talwalkar. Read about me , or email me .

As many people have opinions on this problem, I want to share a bit about myself. I run the MindYourDecisions channel on YouTube , which has over 1.5 million subscribers and 245 million views. I studied Economics and Mathematics at Stanford University, and my work has received coverage in the press , including the Shorty Awards, The Telegraph, Freakonomics, and many other popular outlets.

I also have covered similar problems before, including the following videos:

What is 6÷2(1+2) = ? The Correct Answer Explained (over 12 million views)

9 – 3 ÷ (1/3) + 1 = ? The Correct Answer (Viral Problem In Japan) (over 9 million views)

Since there is another problem that’s going viral right now, it’s time for the order of operations to save the day!

What is the correct answer to the following expression?

8÷2(2 + 2) =

(Note: some people write 8/2(2 + 2) = but this has the same answer.)

Watch the video where I explain the correct answer.

What is 8÷2(2 + 2) = ? The Correct Answer Explained

"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon .

(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).

The correct answer is 16 according to the modern interpretation of the order of operations.

The order of operations

The expression can be simplified by the order of operations, often remembered by the acronyms PEMDAS/BODMAS.

First evaluate P arentheses/ B rackets, then evaluate E xponents/ O rders, then evaluate M ultiplication- D ivision, and finally evaluate A ddition- S ubtraction.

Everyone is in agreement about the first step: simplify the addition inside the parentheses.

8÷2(2 + 2) = 8÷2(4)

This is where the debate starts.

The answer is 16

If you type 8÷2(4) into a calculator, the input has to be parsed and then computed. Most calculators will convert the parentheses into an implied multiplication, so we get

8÷2(4) = 8÷2×4

According to the order of operations, division and multiplication have the same precedence, so the correct order is to evaluate from left to right. First take 8 and divide it by 2, and then multiply by 4.

8÷2×4 = 4×4 = 16

This gets to the correct answer of 16.

This is without argument the correct answer of how to evaluate this expression according to current usage.

Some people have a different interpretation. And while it’s not the correct answer today, it would have been regarded as the correct answer 100 years ago. Some people may have learned this other interpretation more recently too, but this is not the way calculators would evaluate the expression today.

The other result of 1

Suppose it was 1917 and you saw 8÷2(4) in a textbook. What would you think the author was trying to write?

Historically the symbol ÷ was used to mean you should divide by the entire product on the right of the symbol (see longer explanation below).

Under that interpretation:

8÷2(4) = 8÷(2(4)) (Important: this is outdated usage!)

From this stage, the rest of the calculation works by the order of operations. First we evaluate the multiplication inside the parentheses. So we multiply 2 by 4 to get 8. And then we divide 8 by 8.

8÷(2(4)) = 8÷8 = 1

This gives the result of 1. This is not the correct answer that calculators will evaluate; rather it is what someone might have interpreted the expression according to older usage.

Binary expression trees

Since some people think the answer is 16, and others think it is 1, many people argue this problem is ambiguous: it is a poorly written expression with no single correct answer.

But here’s my counter-point: a calculator is not going to say “it’s an ambiguous expression.” Just as courts rule about ambiguous legal sentences, calculators evaluate seemingly ambiguous numerical expressions. So if we take the expression as written, what would a calculator evaluate it as?

There are two possible binary expression trees.

$problem solving use multiplication 8 2$

I suggested the binary expression tree on the left is consistent with PEMDAS/BODMAS. But what does a calculator actually do?

If you try Google (see it evaluate 8÷2(2+2) ) you’ll get an answer of 16. Furthermore, the Google output even inserts parentheses to indicate it is using the binary tree on the left of (8/2)*(2 + 2).

Most popular calculators evaluate the expression the same way, and I would argue that is NOT a coincidence, but rather a reflection that calculators are programmed to the same PEMDAS/BODMAS rules we learn in school.

Common topics of discussion

I’m so happy people think of me for these kinds of questions. And I’m proud of everyone that takes the time to explain PEMDAS/BODMAS and why 16 is the correct answer. Along the way I have had the chance to help people clear up common sources of confusion.

— “I learned it a different way.” Please do let us know a textbook or printed reference. Many people remember learning the topic a different way, but in 5 years no one has presented proof of this other way.

— “What about the distributive property?” This is irrelevant to the answer. The distributive property is about how to multiply over a grouped sum, not about a precedence of operations. It is definitely true that:

8÷2(2+2) = 8÷2(4)

The issue is whether to do 8÷2 first or 2(4) first. PEMDAS says to go from left to right.

— “What about implied multiplication?” Most calculators treat it the same way as regular multiplication. Grouped terms are typically grouped with parentheses if they are meant to be evaluated first.

— “The problem is not well-defined.” To someone that says that, I would ask, “what is the sum of angles in a triangle?” If they say 180 degrees, I would point out that answer is only true in plane geometry (Euclidean geometry). In other geometries the answer can be different from 180 degrees. But no one would say “what is the sum of angles in a triangle” is not a well-defined question–we most often work in the plane, or we would specify otherwise.

Similarly you can ask if 0 is a “positive” number. In America, the convention is that 0 is neither positive nor negative. But in France 0 I am told 0 is considered to be positive. You’d have to re-write a lot of math tests in America if you say that “positive” is not a well-defined word.

Ultimately we say things like “a triangles angles sum to 180 degrees, according to the axioms of plane geometry,” and “0 is not positive, according to the definition in America.” Similarly we can say “8÷2(2+2) = 16, according to the modern interpretation of the order of operations.”

Isn’t the answer ambiguous?

Some mathematicians believe the expression is incorrectly written, and therefore can have multiple interpretations. I strongly disagree with this point. The main cause of confusion is the order of operations!

For example, consider the problem 9 – 3 ÷ (1/3) + 1 (over 9 million views). This is an unambiguous expression and has only a single answer. But the problem went viral in Japan after a study found 60 percent of 20 somethings could get the correct answer, down from a rate of 90 percent in the 1980s. It is clear the problem is students do not learn the order of operations.

Mathematicians who say “the answer is ambiguous” overlook that students get unambiguous expressions wrong at an alarming rate. It is our duty as mathematicians to emphasize the order of operations in its modern form so that we can write proper expressions and interpret them correctly. Not a single person who disagrees with me has considered why students get the wrong answer to 9 – 3 ÷ (1/3) + 1.

The symbol ÷ historical use

Textbooks often used ÷ to denote the divisor was the whole expression to the right of the symbol. For example, a textbook would have written:

9 a 2 ÷3 a = 3 a

This indicates that the divisor is the entire product on the right of the symbol. In other words, the problem is evaluated:

9 a 2 ÷3 a = 9 a 2 ÷(3 a ) (Important: this is outdated usage!)

I suspect the custom was out of practical considerations. The in-line expression would have been easier to typeset, and it takes up less space compared to writing a fraction as a numerator over a denominator:

$fraction-9a2-over-3a$

The in-line expression also omits the parentheses of the divisor. This is like how trigonometry books commonly write sin 2θ to mean sin (2θ) because the argument of the function is understood, and writing parentheses every time would be cumbersome.

However, that practice of the division symbol was confusing, and it went against the order of operations. It was something of a well-accepted exception to the rule.

Today this practice is discouraged, and I have never seen a mathematician write an ambiguous expression using the division symbol. Textbooks always have proper parentheses, or they explain what is to be divided. Because mathematical typesetting is much easier today, we almost never see ÷ as a symbol, and instead fractions are written with the numerator vertically above the denominator.

*Note: I get many, many emails arguing with me about these order of operations problems, and most of the time people have misunderstood my point, not read the post fully, or not read the sources. If you send an email on this problem, I may not have time to reply.

0. Google evaluation https://www.google.com/#q=8÷2(2%2B2)

1. Web archive of Matthew Compher’s Arguing Semantics: the obelus, or division symbol: ÷

2. In 2013, Slate explained this problem and provided a bit about the history of the division symbol.

http://www.slate.com/articles/health_and_science/science/2013/03/facebook_math_problem_why_pemdas_doesn_t_always_give_a_clear_answer.html

3. The historical usage of ÷ is documented the following journal article from 1917. Notice the author points out this was an “exception” to the order of operations which did cause confusion. With modern typesetting we can avoid confusing expressions altogether.

Lennes, N. J. “Discussions: Relating to the Order of Operations in Algebra.” The American Mathematical Monthly 24.2 (1917): 93-95. Web. http://www.jstor.org/stable/2972726?seq=1#page_scan_tab_contents

4. In Plus magazine, David Linkletter writes a differing perspective that the problem is not well-defined (and see his longer article too). I do not agree with the portrayal of what “mathematicians” say, as many mathematicians are happy for the articles I have written. The article also does not address why students incorrectly answer the unambiguous problem 9 – 3 ÷ (1/3) + 1 .

PEMDAS Paradox (Plus magazine)

PEMDAS Paradox (longer article)

5. Harvard mathematician Oliver Knill also has a differing perspective that the only wrong answer is saying there is a single correct answer. I strongly disagree and the article does not address why students incorrectly answer the unambiguous problem 9 – 3 ÷ (1/3) + 1 .

Ambiguous PEMDAS

6. I have also read many articles from people who disagree with me and allude to my video, but then they do not link to my work. Academic disagreements should be kind spirited and fair minded. If you see an article, please let them know to link to my video or blog post.

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41 thoughts on “What Is 8 ÷ 2(2 + 2) = ? Mathematician Explains The Correct Answer”

I’m curious, would you still think the answer is 16 if the question was 8÷2x and x=4?

It feels to me like doing it that way would make a significant amount of common notation calculus problems go horribly wrong. But it’s hard to be sure because usually those things are of the form 2x^2 + 4x – 12 (where giving the implicit multiply the same precedence as an explicit one makes no difference).

But for me personally, I would interpret the implicit unmentioned multiply as a higher precedence than the explicit multiply and divide operators. Google clearly disagrees – even if you do bring in a letter, Google treats 8/2x as 4x. https://www.google.com/search?q=8%2F2x&oq=8%2F2x

@Raven Black: As we live in a world where coding is very important, programmers should never type 8÷2x = 4x if they mean 8÷(2x) = 8/(2x). I am pretty sure all computer languages would parse 8÷2x as equal to 4x–and I don’t think that is a coincidence.

@Presh Talwalkar: Almost no computer languages would parse 8÷2x (or 8/2x since ÷ isn’t an operator either) at all. If you want to multiply things you have to use a multiply symbol, so it’s not ambiguous in programming.

@Raven, try it in Mathematica. It evaluates the formula as (8/2)x. Also, here is an online algebra engine’s evaluation of the equation: https://www.mathpapa.com/algebra-calculator.html?q=8%2F2x%20%40%20x%3D6

As they should, these programs apply the same, consistent parsing rules described in the article.

If you try 8/(2x) you’ll get a different answer. As Presh notes, the best practice is write the equation in an unambiguous form.

@Argon: Nicely said. I didn’t know about MathPapa–I will check out, thanks.

I will solve this 8÷2(2+2) Solve 8÷2=4, 4(2+2)=16 This is correct answer

The right answer is 16

It’s a confusion for many of us because it’s the way we were taught. I know i can’t name any reference but our answers were never wrong when we calculated it the way we do it. I suppose we were wrong but the teacher never taught us the correct modern usage. I asked many friends what their answers would be and they all replied 1.

The answer is 1.

According to the American Physical Society style and notation guide ( https://cdn.journals.aps.org/files/styleguide-pr.pdf ) first published in July 1983, multiplication by juxtaposition is given preference over division (Section IV–E–2–e).

Without that, you get all kinds of unintended effects. Consider:

8 / 8 = 1, to which we all agree. 8 = 1(8), also true. Then, with simple substitution, does 8 / 1(8) still equal 1 or does it now magically equal 64?

@888Jay: Thanks for the reference. That is not how I would interpret the style guide which emphasizes putting parentheses and writing clear expressions (like I said too). I’ll let people judge:

***quote from APS style guide*** (e) When slashing fractions, respect the following conventions. In mathematical formulas this is the accepted order of operations: (1) raising to a power, (2) multiplication, (3) division, (4) addition and subtraction. According to the same conventions, parentheses indicate that the operations within them are to be performed before what they contain is operated upon. Insert parentheses in ambiguous situations. For example, do not write a/b/c; write in an unambiguous form, such as (a/b)/c or a/(b/c), as appropriate.

1, ONE! is the correct answer.

let’s use algebra please.

x = 8 ÷ 2 (2+2)

please go ahead and solve this equation with the result 16.

you can’t, result will always be 1.

Haha, just a google calculator bug.

Google says, 2π ÷ 2π = 9.86960440109. https://imgur.com/a/Vyj0TXA

When I read the equation, I see the 2(2+2) as a group. 2 outside the parenthesis is a multiplier for the group (2+2) and therefore should be resolved prior calculating from left to right following the order of operations.

@Presh: You are spot on about writing clear expressions precisely because of ambiguities such as this one!

As you state above, 8÷2(2+2) = 8÷2(4). If the “÷” symbol is slashing the fraction, then the guide says we should multiply 2(4) first.

Also, I would always assume that 2(a+b) = (2a + 2b) because of the juxtaposition. Some would argue that it’s just shorthand for a missing multiplication symbol – but there is a difference.

2(a+b) is a single term with a coefficient and a variable. 2 x (a+b) is an expression with two terms. The constant 2 and the variable (a+b).

In which case, Two terms: 8 ÷ 2(2+2) = 1 Three terms: 8 ÷ 2 x (2+2) = 16.

In your explanation, you wrote that “a calculator is not going to say… ” …. that’s the problem right there! So many people rely on an object like a calculator, internet, etc for answers rather than using their brain/knowledge and working out the problem themselves! Stop! Put the calculator down and get your pen and paper out. Lord Jesus….

Can we frame this as an algebraic formula?

8/2(2+2) 8/2(a+b) 8/(2a+2b) a=b=2 8/((2*2)+(2*2)) 8/(4+4) 8/(8) 1

I don’t think the use of algebra has changed over time.

Please solve these equations:

8:x(2+2)=16

Best regards, I like your videos very much!

P.S. Wolfram Alpha says this:

http://m.wolframalpha.com/input/?i=8%3A2%282%2B2%29

@Jochen: Your WolframAlpha used a : symbol. If you use the ÷ symbol the answer is 16. See: https://www.wolframalpha.com/input/?i=8%C3%B72(2%2B2)

8/2(4) isn’t much of a debate. At this point you haven’t solve the parenthesis. To continue solving the parenthesis you would multiply 2 int (4) giving you 8. Therefore 8/8.

Thanks for your reply – I‘ve found out this „mystery“ also.

Until today I was shure that „:“ and „÷“ are equal. Aren‘t they?

What about my equations?

@Jochen: Actually I was very surprised : and ÷ gave different answers–so thanks for pointing that out. Per your equations, I don’t know the convention for : symbol in equations–would need to see a textbook and its examples. Old typesetting did have some different conventions, as I pointed out in the post.

Thanks again for your answer! I just used „:“ instead of „÷“ in my equations, because I didn‘t know howto type „÷“ (now I‘ve just copied it from your post )

So please replace it:

8÷x(2+2)=16

DO NOT TRUST WolframAlpha.

WolframAlpha says,

8÷a(2+2) is 8 ÷ ( a×(2+2) ) 8÷b(2+2) is (8÷b) × (2+2)

It’s broken.

https://www.wolframalpha.com/input/?i=8%C3%B7a(2%2B2) https://www.wolframalpha.com/input/?i=8%C3%B7b(2%2B2)

ab ÷ ab = 1. right?

We can remove × between a and b. but we can not insert × between ab. Therefore 8÷2×(2+2) is wrong, do not insert ×. 2(2+2) is a chunk. It can not be disassembled.

I really don’t get how you get 16 from the formula 8/2(2+2) Don’t matter what order of operations you use You need to get rid of the brackets just solving 2+2 still leaves the brackets (4) so you can not do work on the 8/2 as you will be braking all the order of operation rules 8/2(4) You still have to sort out the brackets by getting the 4 out of the brackets the only way you can do that is by multiplication of 2 as it is the closest number outside the brackets so 2x(4) = 8 now the equation is 8/8 so using the order of operations there are no more brackets no exponents just a division 8/8=1

@kkkk: Haha, that is an interesting example. I’ve sent feedback to WolframAlpha about the apparent inconsistency. I love how this problem has made people engage with mathematics, and I always said this will help mathematics. You might have found a bug in their parser–which does happen–and we’ll see if they fix/change it, or if they have some reason for parsing like that.

In physics research papers the convention “1/2a, means 1/(2a) and not (1/2)a” is still commonly used, see for instance the current StyleGuide of the American Physical Society (APS):

https://journals.aps.org/prl/authors#notations-and-mathematical-material

Taking a random university level math text book from my shelf (it happened to be Analysis II by Fields Medalist Terrence Tao), I found the same convention used, when ε/nm was meant as ε / (n*m).

Being a physicist who had to abide by these rules when publishing in APS journals, I’d interpret 8/2(2+2) as 8 / (2*(2+2)) = 1 because the omitted multiplaction dot signals 2(2+2) is meant to be seen as a term that belongs together.

When reading the expression 8÷2*(2 + 2) I would interpret it as (8/2)*(2+2) = 16 however, because the ÷ is untypical for mathematicians what signals the expression to be interpreted like a garden variety calculator would.

8÷2(2+2) confuses be because signals for both interpretations are present…

8 ÷ 2(2 ×2) = 8 ÷ 2 × 4 = 8 × 1/2 × 4 –>> 8 × 1/2 × 4 = (8 × 1/2) × 4 = 4 × 4 = 16 8 × 1/2 × 4 = = 8 × (1/2 × 4) = 8 × 2 = 16

so.. correct answer is 16!!

You have to simplify the parenthesis first using distribution, the 2(2+2) is an expression that needs to be resolved first before you use order of operations (PEMDAS/BOMDAS). 16 is incorrect as it is assumes that it is 8/2*(2+2) which it is not. It is 8 divided by the simplification of 2(2+2), you can’t break that apart. The answer is 1.

The people above saying you need to break the 4 out of the parenthesis are correct this is why you distribute and simplify the expression. If you don’t you still have the 4 in parenthesis which means in 8÷2(4), you must solve the 2(4) first. Honestly why are people forgetting this? They get to stuck on putting an x between the 2 and 4 that they are dismissing the parenthesis without resolving. This is a calculator glitch that has encouraged the wrong answer.

Those who are saying the answer is 16, So… is 2a ÷ 2a = a^2 ? because 2a ÷ 2a is the same thing as 2 × a ÷ 2 × a, and of course you have to solve it from the left to right, which goes like: 2 × a ÷ 2 × a = 2a ÷ 2 × a = a × a = a^2 Hmmm I don’t think so

@Sebastian: It’s funny since mathematicians often criticize the “hand-wavy” proof methods of physics…but now people are saying a Physics style guide is supposed to be the standard for mathematical notation!

Can you provide a page number for Tao’s book? (Or email me a screen capture?) Modern math textbooks almost always use proper typesetting.

I also think the appeal to authority is interesting in this problem. It’s like everyone forgot Paul Erdos said Monty Hall was 1/2, or that Leibniz (co-inventor of calculus) thought thought that two dice will have a sum of 12 the same as 11. See: https://www.oreilly.com/library/view/classic-problems-of/9781118314333/chapter15.html

Mathematicians can make mistakes! And that’s totally fine!

For years I’ve heard from people/math professors how this problem is a waste of time, and that no mathematician would talk about it. Now these same people are trying to tell everyone what the right answer is. I wish they would have researched the problem and its history carefully like I did. Please do share my videos with them–many times they realize their mistake.

Math teachers around the world struggle to teach the order of operations. They are cringing at ow the confusion caused by people who didn’t properly research this problem.

So how would this equation work:

8 ———– = ? 2 ( 2+2)

if we say 16 is the answer the following should work:

8÷2(2+2)=16 x=8 X÷2(2+2)=16 |*2(2+2) X=16*2(2+2)

And now either way x cant be 8..

8÷2(2+2)=1 x=8 X÷2(2+2)=1 |*2(2+2) X=1*2(2+2) And now however you do it x is 8 😉

Referring back to my earlier explanation, I learned math long before all of this PEDMAS business. The order of operations was defined as the precedence of the interaction of “terms” of an expression. A term can be a signed number, a variable, or a function.

In the case of y ÷ x(a + b), “y” is a term and “x(a + b)” is a term because of the juxtaposition – function “x” with argument “(a + b)”. So, two terms, 8 ÷ 2(2+2) = 1. At least that’s how the old Casio calculators did it.

And, as I recall, the APS style guide published in 1983 was intended to formalize LaTeX markup for consistent use in all scientific disciplines, including mathematics. 🙂

Sorry, but there is a huge difference between putting × symbol and not putting it.

8 ÷ 2 × (2 + 2) = 8 ÷ 2 × (4) = 4 × (4) = 16

But, if you don’t explicitly put the × symbol, we take that as one term. 8 ÷ 2(2 + 2) = 8 ÷ 2(4) = 8 ÷ 8 = 1

Think of this: 2π ÷ 2π According to your solution, 2π ÷ 2π = 2 × π ÷ 2 × π = 2 × 3.14 ÷ 2 × 3.14 = 6.28 ÷ 2 × 3.14 = 3.14 × 3.14 = (3.14)^2

But we all know that 2π ÷ 2π is simply 1. Why? Because we are treating 2π as one term, not like 2 × π. If you still think 2π ÷ 2π = (3.14)^2, I’m done talking.

The reference to the current APS style guide was not meant to to to present a binding standard for mathematical notation but to challenge your claim that the convention according to which 9a^2 / 3a = 3a (to use the example from the Lennes paper) is purely a relict of past.

No, this convention is demonstrably still used by a substantial number of people when they and write and interpret inline fractions in scientific texts. For them, 8/2(2+2) is by convention simply the inline rendering of 8 ——— 2(2+2)

Note that even with today’s better typesetting abilities, using the slashed form of a fraction might be advisable e.g. to avoid too small symbols or to save space.

The people using this convention for written text aimed at people with sufficient mathematical maturity have of course no problem to interpret 8/2(2+2) as yielding 16 when they program their computers or when tutoring to a neighbor child on the order of operations.

Context matters for this question. And without a context the expression 8/2(2+2) is ambiguous.

The best approach is certainly to avoid the ambiguity altogether, as recommended succinctly on the Wolfram site: “Special care is needed when interpreting the meaning of a solidus in in-line math because of the notational ambiguity in expressions such as a/bc. Whereas in many textbooks, “a/bc” is intended to denote a/(bc), taken literally or evaluated in a symbolic mathematics languages such as the Wolfram Language, it means (a/b)×c. For clarity, parentheses should therefore always be used when delineating compound denominators.” ( http://mathworld.wolfram.com/Solidus.html )

P.S.: The reference you were asking for is Terence Tao, Analysis II, Springer 2015, p. 140.

I have to admit that Tao’s book was not really that random a choice: it is the only math book in my shelf that is – written in English, – not written for physicists, – not on category theory, algebraic topology or similar topics too abstract to contain such concrete things as fractions of numbers. At least that should exonerate me from the criticism that I was appealing to authority…

@Sebastian: Thanks for the thoughts and the reference to Tao’s book. I am geniuinely interested in such examples, as I will try to incorporate into my next video. (Such problems go viral each year–I’ve been making videos since 2015 that have tens of millions of views. I have a feeling this kind of problem will go viral again.)

As you can imagine I’m getting hundreds of comments/feedback, so I kind of put many thoughts in the same reply to you. The “appeal to authority” was more directed as some other professors have entered the fray and caused extra confusion.

8÷2(2+2)=1 not 16.

Example: If 8 oranges are to be shared by x boys. How many oranges will each of them get.

8÷1(x)=8÷1x=8/x=8/x. The one in the equation takes whatever that’s in the brackets after it. Each of the boys will get 8/x. 8/x is correct for any number of boys.

Note Not: 8÷1(x)=8(x)=8x. 8x is only correct for 1 boy. It’s never correct for ‘more or less’ than a boy.

Therefore, 8÷2(2+2)=1 is correct and not 16.

You should be able to reverse the equation and get 8 using 16. Show proof.

By reverse, I mean inverse the equation.

Comments are closed.

Grades 6-12
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50 Fun Hands-On Activities and Games To Teach Multiplication

Making it fun makes it stick!

Examples of multiplication activities like LEGO football game and triangle fact families worksheet.

Multiplication is a basic skill students need to master before they can move on to more advanced math. Memorizing multiplication tables is one option, but it’s important for kids to understand exactly what it means to multiply. This list of fun and engaging ways to teach multiplication has so many options. You’re sure to find a way to resonate with every one of your students!

1. Play a game of Scoot

A math lesson set up with task cards and worksheet laid out on a table

This is a fun way to break up the routine of worksheets. One at a time, you will post one of the multiplication task cards and your students will work to find the answer. After a set amount of time (up to you), say “Scoot.” Students will leave their answer sheet on their desk and move one seat to their left. Post another task card. Again, say “Scoot” and have students rotate.

2. Practice skip-counting with a song

For many of us, setting information to music helps us memorize it. This series of videos from HeavenSentHorse features common tunes that your students will quickly catch on to like Jingle Bells, This Old Man and more.

3. Solve multiplication puzzles

Teach multiplication with these puzzles printed on a colorful piece of paper

Puzzles are a great way to engage students and build their problem-solving skills. These puzzles help students put together the pieces to get the whole picture and really understand how to solve a multiplication problem.

4. Play Four in a Row

A worksheet with many circles with multiplication problems in them, a few covered with penguin stickers

This fun game challenges kids to practice their math facts. Partners will take turns choosing a circle and solving the math fact. If they get it right, they place a marker over it (here, a penguin stamp). The first player to connect four wins.

5. Solve Mystery Pictures

An array of colorful puzzles created by solving multiplication problems

Students will solve the one-digit multiplication problems, then use the key to color in the boxes and create the mystery picture.

6. Play multiplication tic-tac-toe

Teach multiplication using tic tac toe frames filled with multiplication problems

Playing with partners, each player chooses a multiplication problem to solve. If they get it right, they mark it with their dot marker. If not, it’s the next person’s turn. Play goes back and forth until someone gets three in a row.

7. Build multiplication skills with Minecraft

A colorful math game for students with the theme of Minecraft

Your kids will flip for this fun version of Minecraft multiplication. Download the game and instructions for free!

8. Deal a hand of Spiral

Playing cards laid out on a table in a spiral

Players take turns rolling the dice and moving around the game board with this fun multiplication card game.

9. Sweeten up multiplication practice

$Teach multiplication using cupcake liners with multiplication problems written on them$

Write multiplication problems on the bottom of small cupcake paper liners. On the inside, write the product. Two players take turns picking a liner, finding the answer, and flipping it over to check.

10. Take a whirl at fidget spinner math

$A math worksheet using a fidget spinner as a tool$

The object of the game is simple: Spin the spinner and complete as many problems as possible.

11. Make multiplication pool noodles

Pool noodles turned into math manipulatives for teaching multiplication

Pick up some pool noodles and use our easy tutorial to turn them into the ultimate multiplication manipulatives ! This is such a unique way for kids to practice their math facts.

12. Match wits at Array Capture

Teach multiplication using this printable worksheet of an Array Capture multiplication game

You can use dice-in-dice or just a regular pair of dice for this game. Players roll the dice and use the numbers to block off space on the grid, writing in the math sentence too. At the end of the game, the player with the most spaces colored in wins.

13. Punch holes to make arrays

Student using a hole punch to make multiplication arrays on rectangles of construction paper

Arrays introduce multiplication in a way that kids can easily understand. This activity is great for active learners who will love punching holes as they create multiplication arrays for basic facts.

14. Fold a multiplication cootie catcher

Colorful paper cootie catchers decorated with multiplication facts

We love finding new and clever ways to practice math facts! Get these free printables , then let kids color and fold them up. Now they’ve got self-checking practice at their fingertips.

15. Visit the Multiplication Shop

Table with array of small items marked with prices

How fun is this? Set up a “store” with small items for sale. Kids choose a number of items from each section to “buy” and write out the multiplication sentences as their receipt!

16. Ask a partner, “Do You Have …?”

Teach multiplication using an old Guess Who game repurposed to play Do You Have... with multiplication facts

Got an old “Guess Who?” game lying around? Turn it into a multiplication game instead!

17. Pull out the base-10 blocks

Base 10 blocks being used to teach array model multiplication

Base-10 blocks are one of our favorite manipulatives, and they’re a terrific tool to help you teach multiplication. Build arrays with them to let kids visualize the problems and their answers.

18. Color in Emoji Mystery pages

Printable Emoji Mystery page for learning multiplication

Here’s a twist on color-by-number. First, kids have to answer the multiplication problems in each square. Then they get to color! Get a free set of these pages at Artsy Fartsy Mama .

19. Multiply with dice-in-dice

Student using dice-in-dice to practice multiplication facts as a fun example of how to teach multiplication

Something about dice-in-dice just makes learning more fun! If you don’t have a set, you can use a pair of regular dice for this activity. Mix things up with polyhedral dice with higher numbers too.

20. Pick sticks to play Kaboom!

Popsicle sticks labeled with multiplication facts

So easy and so fun! Write multiplication facts at the end of a variety of wood craft sticks. On a few, write “Kaboom!” instead. To play, kids draw sticks from a cup and answer the problem. If they get it right, they can keep pulling sticks. But if they get a Kaboom! stick, they have to put their whole collection back!

21. Match Multiplication memory cards

Memory cards with multiplication facts and answers

Practice facts with a memory game. Make your own cards by writing facts and answers, then lay them all face down. Turn over a card and try to find its matching answer or problem. Your turn continues as long as you’re able to make matches.

22. Find it first

Random numbers written on a whiteboard, labeled

Write a series of products on the whiteboard, and mix in a few random numbers too. Send two students up to the board and call out a multiplication problem. The first one to find and point to the correct answer wins a point.

23. Draw Waldorf multiplication flowers

A drawing of a colorful flower with a number written in the middle and a multiplication equation written in each petal

This is a creative way to teach multiplication facts. Draw a flower with 12 petals and a circle in the center. In the circle, write the multiplicand; on the petals, the numbers 1 to 12. Now, draw larger petals outside, and fill in the product of each fact. Add some color to make fun classroom decorations!

24. Play multiplication war

All you need for this is a deck of cards, plus paper and a pencil for each player. Split the deck between the players. Each player flips two cards, then writes out the multiplication sentence and the answer. The player with the higher product takes all the cards. Play until the deck is gone. The player with the most cards wins!

25. Compete at multiplication bingo

Printable multiplication bingo cards are a fun way to teach multiplication

Grab these free printable bingo cards at the link and provide one to each student along with some chips or beans to use as counters. Call out multiplication facts and have students cover the answers if they have them. When they get five in a row, it’s a bingo!

26. Put a twist on Rock, Paper, Scissors

Three hands against a white background, each hand showing a different choice in a game or rock, paper, scissors

Chances are your students already know how to play Rock, Paper, Scissors. This is similar, but instead, each player holds out a random number of fingers. The first one to correctly multiply them together and call out the answer wins a point. Play to 5, 10, or any number you choose.

27. Do some egg carton multiplication

A green egg carton with the numbers 1-12 written in the bottom of the cups used to teach multiplication

Number the cups of an egg carton from 1 to 12. Drop in two marbles or beans, then close the carton and shake it up. Open it up and have students write out the multiplication number sentence based on where the marbles landed. This is an easy tool parents can make for kids at home too.

28. Try interactive flash cards

Multiplication flash cards to print out for student math practice

These aren’t your ordinary flash cards! These free printables are a cool way to teach multiplication since the answer side includes a dot array to help kids visualize the solution. You can use sticky-note flags to cover the answers while kids use the arrays for help too.

29. Teach multiplication facts with a paper plate wheel

A multiplication game made with two paper plates

All it takes is paper plates, glue, and a marker to help your students learn their multiplication tables. Let kids have fun decorating their plates, and this doubles as a math craft!

30. Practice with fact family triangles

Triangular fact family cards made from card stock used to teach multiplication

Tie together multiplication and division facts with triangle flash cards. Learn how to use them and buy a printable set at Primary Flourish . You can also have kids make their own.

31. Make LEGO arrays

Multi-colored LEGO bricks laid out on a table

LEGO bricks are one of our favorite ways to teach math! You can use multiple bricks to make arrays or just look at the bumps on the top of a single brick as an array in itself.

32. Try the finger trick

An illustration of two hands spread out with each finger labeled with a number from 1-10

This cute craft also teaches kids a clever multiplication trick that can help them if they’re stuck with multiplication “times nine.” Learn the easy trick at 5-Minute Crafts .

33. Use the Force to teach multiplication

A student Star Wars-themed math worksheet and color dot markers

Sometimes learning multiplication facts just takes practice. Worksheets may not be very exciting, but adding a theme that kids are interested in may motivate your students. This free download from Royal Baloo features homework sheets and practice papers with graphs, mazes, puzzles, and more, all with a Star Wars theme.

34. Watch a multiplication video

Still shot from a video teaching kids multiplication

From Schoolhouse Rock to Animaniacs and beyond, there are lots of fun videos to help you teach multiplication. Find our big list here.

35. Play multiplication checkers

Blue and white checkerboard with multiplication problems written in squares as an example of how to teach multiplication

Turn a thrift store checkerboard into a multiplication game with some stickers and a marker. The play is similar to traditional checkers, but you have to solve the problem before you can leave your checker on a new space.

36. Toss a multiplication soccer ball

A colorful soccer ball with multiplication equations written in the white squares

What better way to appeal to students than to combine math with one of their favorite activities? These fun balls can be used in so many ways to support learning.

37. Flip bottle caps

Bottle caps with multiplication problems written on top to teach multiplication

Here’s a cool alternative to flash cards. You can use metal bottle caps or plastic bottle lids, along with round stickers that fit the caps. It’s a great way to go green while you teach multiplication!

38. Batter up to learn multiplication

A colorful printout of a multiplication baseball game

Sports-loving kids will love this one! Get the free printables and use them along with a 10-sided die to get some multiplication facts practice.

39. Line up dominoes

Dominoes laid out on a worksheet to teach multiplication

Single dominoes turned sideways become multiplication number sentences! Grab a handful and have kids write out the sentences and their answers.

40. Roll to win

Multiplication Dice Game with dice and free printable

This works a bit like Yahtzee. Roll a die, then choose a number from 1 to 6 to multiply it by. Each number can only be used once, so choose carefully to rack up the most points. If you have polyhedral dice, you can play with higher numbers too.

41. Sculpt play dough arrays

Colorful balls of play dough laid out in arrays above multiplication problems

What kid doesn’t love the chance to play with play dough? Use this activity for math centers, and kids will really enjoy practicing their multiplication facts.

42. Connect the dots with Multiplication Squares

A colorful printout of a multiplication squares game used to teach multiplication

This is a math spin on the old Dots and Boxes game. Kids roll two dice and multiply the numbers together. Then they find the answer on the board and connect two dots next to it. The goal is to complete a box, coloring it in with your own color marker. When the board is full, count the squares to see who wins.

43. Cut out and assemble array cities

A colorful poster of a city made from individual buildings made from arrays

Here’s another colorful math craft: multiplication array cities. Most high-rises have their windows arranged to make perfect arrays. Have kids make their own city skylines with buildings showing various multiplication arrays.

44. Stack math power towers

Three Pringles cans covered with a label that says Math Power Towers behind a stack of plastic cups with multiplication problems on them

There’s a universal appeal about making stacks of cups, so don’t be surprised if kids clamor to play this game over and over again. Pull a cup, answer correctly, and stack. See who can get a stack of 10 first, or who can build the highest tower in 2 minutes, and so on.

45. Change your students’ names (temporarily)

Grab some name tags and write multiplication equations on each. Give a tag to each of your students. For the remainder of the day, everyone will refer to each other by the answer to the equation on their tag (e.g., the student with the name tag that says 7 x 6 would be referred to as “42”).

46. Take multiplication to the gridiron

A pair of leg goal posts, a lego football and a pair of dice on top of a worksheet

All you need is poster board, 12-sided dice, and a couple of game pieces to teach multiplication using football. Students move their game piece up the field by rolling the dice and multiplying the two numbers that face up. They get four chances to score a touchdown.

47. Roll and Bump!

A colorful math worksheet with bright circles with numbers inside

Print the free game boards , each with a multiplier in the heading. Roll two dice, add them together, then multiply by the multiplier. Then place your game piece over that answer. If another player also comes up with the same product, they can “bump” your game piece off and replace it with their own. The player with the most markers on the board at the end of the game wins.

48. Weave multiplication patterns

Embroidery hoops with yarn woven into patterns inside of them

Skip-counting provides an introduction to multiplication. We love this hands-on activity where kids skip-count and weave yarn into pretty patterns.

49. Challenge kids with Multiplication Jenga

A jumble of Jenga wooden blocks with multiplication facts written on them used to teach multiplication

Grab an old Jenga game at the thrift store (or pick up the generic version at the dollar store). Write multiplication problems on each block, then stack ’em up. Player one pulls a block and tries to answer the problem. If they get it right, they keep the block. If they miss, their partner gets a chance. But if no one can answer it, the block gets stacked up on top. Keep playing until the tower collapses!

50. Twist and learn

Kids playing Twister on a Twister mat with numbers written on each dot

Your students will love this twisted version of an old favorite! The original Math Twister was designed for addition, but it works for multiplication too. Simply write products on sticky notes and add them to circles. Then call out math problems like “Left foot, 4 x 5!” The player must put their left foot on the number 20—if they can!

Looking for more activities to teach multiplication? Try these Teacher-Tested Tips and Activities for Teaching the Area Model Multiplication Method .

Plus, get all the latest teaching tips and ideas when you sign up for our free newsletters .

Looking for unique ways to teach multiplication so kids will really understand? Try these games, activities, and other engaging ideas!

$Collage of fifth grade math games, including equivalent fractions spoons and build a pool online game$

30 5th Grade Math Games To Teach Fractions, Decimals, and More

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Unit 1: Decimal place value

Unit 2: add decimals, unit 3: subtract decimals, unit 4: add and subtract fractions, unit 5: multi-digit multiplication and division, unit 6: multiply fractions, unit 7: divide fractions, unit 8: multiply decimals, unit 9: divide decimals, unit 10: powers of ten, unit 11: volume, unit 12: coordinate plane, unit 13: algebraic thinking, unit 14: converting units of measure, unit 15: line plots, unit 16: properties of shapes.

8 ÷ 2(2 + 2) = ? The Correct Answer Explained

The Great Math Debate: 8 ÷ 2(2 + 2)

You’ve likely seen it floating around the internet: the infamous equation 8 ÷ 2(2 + 2). It’s a deceptively simple-looking problem that has sparked heated debates and sparked discussions on the order of operations. In this blog post, we’ll explore the different interpretations of the equation and why there isn’t a single, universally agreed-upon answer.

Understanding the Order of Operations

The order of operations, often remembered by the acronym PEMDAS or BODMAS, tells us the sequence in which to perform mathematical operations:

**P**arentheses (or **B**rackets)
**E**xponents (or **O**rders)
**M**ultiplication and **D**ivision (from left to right)
**A**ddition and **S**ubtraction (from left to right)

Interpretation 1: Multiplication Before Division

One common interpretation is to treat multiplication and division as having equal precedence, working from left to right. Following this approach, we’d solve the equation as follows:

Solve the parentheses: 2 + 2 = 4
Divide 8 by 2: 8 ÷ 2 = 4
Multiply the result by 4: 4 x 4 = 16

Therefore, the answer according to this interpretation would be **16**.

Interpretation 2: Multiplication Implied by Parentheses

Another interpretation emphasizes the role of parentheses. Some argue that the expression 2(2 + 2) implies multiplication and should be treated as a single entity. In this case, we’d solve it as:

Multiply 2 by 4: 2 x 4 = 8
Divide 8 by 8: 8 ÷ 8 = 1

This interpretation leads to an answer of **1**.

The Ambiguity of Notation

The crux of the problem lies in the ambiguity of mathematical notation. The use of the ÷ symbol and the lack of explicit parentheses around the entire expression 2(2 + 2) contribute to the confusion. Different textbooks and calculators may interpret these elements differently.

Historical Perspective

Historically, the precedence of multiplication and division has been debated. In some older textbooks, multiplication was often given higher precedence. However, the modern consensus is that they have equal precedence and are solved from left to right.

The Importance of Clarity

The 8 ÷ 2(2 + 2) problem highlights the importance of clear and unambiguous mathematical notation. To avoid confusion, it’s best to use parentheses to explicitly indicate the order of operations, especially when dealing with potentially ambiguous expressions.

The answer to 8 ÷ 2(2 + 2) depends on the interpretation of the equation and the order of operations. Both 16 and 1 are valid answers depending on how the problem is understood. The debate emphasizes the need for clear and consistent notation in mathematics to avoid ambiguity and ensure accurate results.

So, while there’s no single, universally agreed-upon answer, the discussion around this equation provides a valuable lesson in the importance of understanding mathematical notation and its potential for interpretation.

Mathematical Notation

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Lesson 8.2
8-2: Problem Solving (Use Multiplication)
Multiplication Word Problem Solving Worksheet by Teach Simple
Multiplication Problem Solving
problèmes multiplicatifs cm1
$problem solving use multiplication 8 2$
multiplication problem solving nz maths

VIDEO

5th Grade GO Math: Lesson 8.2 Problem Solving-Use Multiplication pages 361-364
8th Class Maths Chapter 2 Exercise 2.2 PTB
8Th Class Math Exercise 2.20 New Book || Solution of Simultaneous Equations
Unit 2 Lesson 8 Practice Problems
Unit 2 Lesson 8 Practice Problems IM® GeometryTM authored by Illustrative Mathematics®
😉 8th Grade, Unit 2, Lesson 12 "Using Equations for Lines" Practice Lesson

COMMENTS

PDF Go Math! Practice Book (TE), G5
PROBLEM SOLVING Name Lesson 8.2 Problem Solving Use Multiplication COMMON CORE STANDARD CC.5.NF.7b Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 1. Sebastian bakes 4 pies and cuts each pie into sixths. How many G-pie slices does he have? To find the total number of sixths in the 4 pies,
Problem Solving Use Multiplication
This lesson uses diagrams to show multiplication and division with fractions and whole numbers.
5th Grade GO Math: Lesson 8.2 Problem Solving-Use Multiplication pages
This video covers Lesson 8.2 Problem Solving-Use Multiplication on pages 361-364 of the 5th grade GO Math textbook.
Go Math 5th Grade Lesson 8.2 Problem Solving Use Multiplication
This Go Math video includes problem solving using multiplication. It covers the topic of dividing a whole number by a fraction and then using multiplication ...
Multiplication Word Problems Worksheets
The printable PDF worksheets presented here involve single-digit multiplication word problems. Each worksheet carries five word problems based on day-to-day scenarios. Multiplication Word Problems: Two-digit times Single-digit. The word problems featured here require a grade 3 learner to find the product by multiplying a two-digit number by a ...
PDF Name Lesson 8.2 Problem Solving • Use Multiplication
2-size piece of watermelon? ____ 6. WRITE Math Draw a diagram and explain how you can use it to find 3 ! 1_ 5. Chapter 8 501 To !nd the total number of sixths in the 4 pies, multiply 4 by the number of sixths in each pie. 4 ! 1_ 6" 4 # 6 " 24 one-sixth-pie slices Name Problem Solving • Use Multiplication Lesson 8.2 COMMON CORE STANDARD—5.NF ...
Chapter 8, Lesson 8.2 Problem Solving
Chapter 8, Lesson 8.2 Problem Solving - Use Multiplication 0 Reviews Details 5 stars 0: 4 stars 0: 3 stars 0: 2 stars ... Big Idea: Using models and multiplication to solve division problems jbaggett 1 Lesson. Subscribe to Julie's Lessons Download Lesson Filed In: DOK: Level 3 Length: 60 minutes Skill/Strategy : Division of ...
Go Math Interactive MImio Lesson 8.2 Problem Solving
Go Math Grade 5 Chapter 8 Lesson 2 Problem Solving - Use Multiplication. Includes all whole group components for the lesson. **Please note: This product is for Mimio boards and NOT for SmartBoards.**. Lesson is completely digital, no need to turn your back on your students to write on the board! Just hook up to your projector and teach!
8.2: Multiplication
Multiplication of two Integers, using positive and negative counters. Case 1: If m is a whole number and n is any integer, m × n is obtained by combining m subsets of a collection of counters representing n. The product of m and n, m × n, is the number that the resulting collection represents.
Multiplication and division
Math; Arithmetic (all content) Unit 3: Multiplication and division. About this unit. In this topic, we will multiply and divide whole numbers. The topic starts with 1-digit multiplication and division and goes through multi-digit problems. ... Multiplication word problem: parking lot (Opens a modal) Division word problem: school building (Opens ...
Word Problems on Multiplication
Word problems on multiplication for fourth grade students are solved here step by step. Problem Sums Involving Multiplication: 1. 24 folders each has 56 sheets of paper inside them. How many sheets of paper are there altogether? ... We will solve the different types of problems involving addition and subtraction together. To show the problem ...
Mathway
Free math problem solver answers your algebra homework questions with step-by-step explanations. Mathway. Visit Mathway on the web. Start 7-day free trial on the app. Start 7-day free trial on the app. Download free on Amazon. Download free in Windows Store. Take a photo of your math problem on the app. get Go. Algebra. Basic Math.
Multiplication Word Problems for Grade 3
These worksheets contain simple multiplication word problems. Students derive a multiplication equation from the word problem, solve the equation by mental multiplication and express the answer in appropriate units. Students should understand the meaning of multiplication before attempting these worksheets. Worksheet #1 Worksheet #2 Worksheet ...
How to Solve a Multiplication Problem
For each potion she used 5 + 5 + 5 pounds. Or, expressed in a different way: 3 x 5 = 15 pounds. Now we know that she used 15 pounds of magic herbs for each potion and we know that she made 10 bottles of potion, so: In total, to make all of the potions, she used 15 x 10 = 150 pounds of magic herbs. 4) This last step is very important.
Go Math 5th Grade Lesson 8.2 Problem Solving Use Multiplication
This video includes problem solving using multiplication. It covers the importance of reading for information and understanding it.
Multiplication Word Problems
Multiplication word problems are multiplication problems laid out in a sentence format that relates to a real-life scenario. Children are asked to read the problem, work out what the multiplication problem is and how to solve it using the clues provided. Examples of multiplication word problems that are included in this resource pack are:
Multiplication Problem Solving worksheet
Multiplication Problem Solving. Keisha Thompson. Member for 4 years 1 month Age: 7-14. Level: Grade 1-2. Language: English (en) ID: 158382. 05/05/2020. Country code: BB. Country: Barbados. School subject: Math (1061955) Main content: Multiplication (2013181) From worksheet author: Readind, understanding and solving multiplication problems using ...
Multiplication Facts Worksheets
Five minute frenzy charts are 10 by 10 grids that are used for multiplication fact practice (up to 12 x 12) and improving recall speed. They are very much like compact multiplication tables, but all the numbers are mixed up, so students are unable to use skip counting to fill them out.
What Is 8 ÷ 2(2 + 2) = ? Mathematician Explains The Correct Answer
8÷2 (2 + 2) = 8÷2 (4) This is where the debate starts. The answer is 16. If you type 8÷2 (4) into a calculator, the input has to be parsed and then computed. Most calculators will convert the parentheses into an implied multiplication, so we get. 8÷2 (4) = 8÷2×4.
50 Fun Hands-On Activities To Teach Multiplication
Students will solve the one-digit multiplication problems, then use the key to color in the boxes and create the mystery picture. 6. Play multiplication tic-tac-toe School Time Snippets/multiplication tic-tac-toe via schooltimesnippets.com. Playing with partners, each player chooses a multiplication problem to solve.
5th grade
Learn fifth grade math—arithmetic with fractions and decimals, volume, unit conversion, graphing points, and more. ... Multi-digit multiplication and division: Quiz 2; Multi-digit multiplication and division: Unit test; Unit 6 Unit 6: ... Add and subtract fractions Adding and subtracting fractions with unlike denominators word problems: Add ...
PDF Year 3 The 8 Times Table Reasoning and Problem Solving
Questions 2, 5 and 8 (Problem Solving) Developing Use digit cards to create pairs of multiplications that have the same answer. Using pictorial support for each question where each digit is represented. Expected Use digit cards to create pairs of multiplications that have the same answer. Some scaffolding support is given.
8-2: Problem Solving (Use Multiplication)
8-2: Problem Solving (Use Multiplication)
Primary Resources Multiplication Word Problems
Looking for a range of primary resources with multiplication word problems to use with your class? This teaching pack can help. From worksheets and challenge cards to PowerPoints and SATs practice questions, these learning resources are designed to help children master solving word problems.Created by our lovely team of teachers, these resources are ideal to use with your primary KS2 maths ...
Problem Solving Using 2, 4 and 8 x Table Worksheet
Problem solving activity where children use their 2, 4 and 8 x table to work out combinations of animals in a room from the number of legs seen. Suitable for KS2. Show more. 2 4 8 times table 2 4 8 times tables problem solving 4 and 8 times table 2 times tables 2 4 and 8 times tables. times tables worksheets place value doubling multiplication ...
Problem Solving Using 2, 4 and 8 x Table Worksheet
Problem solving activity where children use their 2, 4 and 8 x table to work out combinations of animals in a room from the number of legs seen. Suitable for KS2. Show more. 2 4 8 times table 2 4 8 times tables problem solving 4 and 8 times table 2 times tables 2 4 and 8 times tables. times tables worksheets place value doubling multiplication ...
8 ÷ 2(2 + 2) = ? The Correct Answer Explained
Interpretation 1: Multiplication Before Division. One common interpretation is to treat multiplication and division as having equal precedence, working from left to right. Following this approach, we'd solve the equation as follows: Solve the parentheses: 2 + 2 = 4; Divide 8 by 2: 8 ÷ 2 = 4; Multiply the result by 4: 4 x 4 = 16
Sex-Linked Inheritance Problem Set
Instructions: The following problems have multiple choice answers. Correct answers are reinforced with a brief explanation. Incorrect answers are linked to tutorials to help solve the problem. Crossing a white-eyed female and red-eyed male fly; Test cross of a red-eyed female fly; Predicting the offspring of a homozygous red-eyed female fly

Multiplication Word Problem Worksheets

Chapter 8, Lesson 8.2 Problem Solving - Use Multiplication

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Go Math Interactive MImio Lesson 8.2 Problem Solving - Use Multiplication

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8.2: Multiplication

Definition: Multiplication of Whole Numbers using the Repeated-Addition Approach

Multiplication of two Integers, using positive and negative counters

Exercise 10

Exercise 11

Exercise 12

Word Problems on Multiplication

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What Is 8 ÷ 2(2 + 2) = ? Mathematician Explains The Correct Answer

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50 Fun Hands-On Activities and Games To Teach Multiplication

1. Play a game of Scoot

2. Practice skip-counting with a song

3. Solve multiplication puzzles

4. Play Four in a Row

5. Solve Mystery Pictures

6. Play multiplication tic-tac-toe

7. Build multiplication skills with Minecraft

8. Deal a hand of Spiral

9. Sweeten up multiplication practice

10. Take a whirl at fidget spinner math

11. Make multiplication pool noodles

12. Match wits at Array Capture

13. Punch holes to make arrays

14. Fold a multiplication cootie catcher

15. Visit the Multiplication Shop

16. Ask a partner, “Do You Have …?”

17. Pull out the base-10 blocks

18. Color in Emoji Mystery pages

19. Multiply with dice-in-dice

20. Pick sticks to play Kaboom!