ratio problem solving youtube

Algebra: Ratio Word Problems

Related Pages Two-Term Ratio Word Problems More Ratio Word Problems Algebra Lessons

In these lessons, we will learn how to solve ratio word problems that have two-term ratios or three-term ratios.

Ratio problems are word problems that use ratios to relate the different items in the question.

The main things to be aware about for ratio problems are:

• Change the quantities to the same unit if necessary.
• Write the items in the ratio as a fraction .
• Make sure that you have the same items in the numerator and denominator.

Ratio Problems: Two-Term Ratios

Example 1: In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:4. If the bag contains 120 green sweets, how many red sweets are there?

Solution: Step 1: Assign variables: Let x = number of red sweets.

Step 2: Solve the equation. Cross Multiply 3 × 120 = 4 × x 360 = 4 x

Answer: There are 90 red sweets.

Example 2: John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane?

Solution: Step 1: Sentence: Jane has 20 marbles, all of them either red or blue. Assign variables: Let x = number of blue marbles for Jane 20 – x = number red marbles for Jane

Step 2: Solve the equation

Cross Multiply 3 × x = 2 × (20 – x ) 3 x = 40 – 2 x

John has 12 blue marbles. So, he has 12 – 8 = 4 more blue marbles than Jane.

Answer: John has 4 more blue marbles than Jane.

How To Solve Word Problems Using Proportions?

This is another word problem that involves ratio or proportion.

Example: A recipe uses 5 cups of flour for every 2 cups of sugar. If I want to make a recipe using 8 cups of flour. How much sugar should I use?

How To Solve Proportion Word Problems?

When solving proportion word problems remember to have like units in the numerator and denominator of each ratio in the proportion.

• Biologist tagged 900 rabbits in Bryer Lake National Park. At a later date, they found 6 tagged rabbits in a sample of 2000. Estimate the total number of rabbits in Bryer Lake National Park.
• Mel fills his gas tank up with 6 gallons of premium unleaded gas for a cost of $26.58. How much would it costs to fill an 18 gallon tank? 3 If 4 US dollars can be exchanged for 1.75 Euros, how many Euros can be obtained for 144 US dollars?

Ratio problems: Three-term Ratios

Example 1: A special cereal mixture contains rice, wheat and corn in the ratio of 2:3:5. If a bag of the mixture contains 3 pounds of rice, how much corn does it contain?

Solution: Step 1: Assign variables: Let x = amount of corn

Step 2: Solve the equation Cross Multiply 2 × x = 3 × 5 2 x = 15

Answer: The mixture contains 7.5 pounds of corn.

Example 2: Clothing store A sells T-shirts in only three colors: red, blue and green. The colors are in the ratio of 3 to 4 to 5. If the store has 20 blue T-shirts, how many T-shirts does it have altogether?

Solution: Step 1: Assign variables: Let x = number of red shirts and y = number of green shirts

Step 2: Solve the equation Cross Multiply 3 × 20 = x × 4 60 = 4 x x = 15

5 × 20 = y × 4 100 = 4 y y = 25

The total number of shirts would be 15 + 25 + 20 = 60

Answer: There are 60 shirts.

Algebra And Ratios With Three Terms

Let’s study how algebra can help us think about ratios with more than two terms.

Example: There are a total of 42 computers. Each computer runs one of three operating systems: OSX, Windows, Linux. The ratio of the computers running OSX, Windows, Linux is 2:5:7. Find the number of computers that are running each of the operating systems.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

In order to access this I need to be confident with:

This topic is relevant for:

Ratio Problem Solving

Here we will learn about ratio problem solving, including how to set up and solve problems. We will also look at real life ratio problems.

There are also ratio problem solving worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is ratio problem solving?

Ratio problem solving is a collection of word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.

A ratio is a relationship between two or more quantities . They are usually written in the form a:b where a and b are two quantities. When problem solving with a ratio, the key facts that you need to know are,

• What is the ratio involved?
• What order are the quantities in the ratio?
• What is the total amount / what is the part of the total amount known?
• What are you trying to calculate ?

As with all problem solving, there is not one unique method to solve a problem. However, this does not mean that there aren’t similarities between different problems that we can use to help us find an answer. 

The key to any problem solving is being able to draw from prior knowledge and use the correct piece of information to allow you to get to the next step and then the solution.

Let’s look at a couple of methods we can use when given certain pieces of information.

When solving ratio problems it is very important that you are able to use ratios. This includes being able to use ratio notation. 

For example, Charlie and David share some sweets in the ratio of 3:5. This means that for every 3 sweets Charlie gets, David receives 5 sweets.

Charlie and David share 40 sweets, how many sweets do they each get?

We use the ratio to divide 40 sweets into 8 equal parts. 

Then we multiply each part of the ratio by 5.

3 x 5:5 x 5 = 15:25

This means that Charlie will get 15 sweets and David will get 25 sweets.

• Dividing ratios

Step-by-step guide: Dividing ratios (coming soon)

Ratios and fractions (proportion problems)

We also need to consider problems involving fractions. These are usually proportion questions where we are stating the proportion of the total amount as a fraction.

Simplifying and equivalent ratios

• Simplifying ratios

Equivalent ratios

Units and conversions ratio questions

Units and conversions are usually equivalent ratio problems (see above).

• If £1:\$1.37 and we wanted to convert £10 into dollars, we would multiply both sides of the ratio by 10 to get £10 is equivalent to \$13.70.
• The scale on a map is 1:25,000. I measure 12cm on the map. How far is this in real life, in kilometres? After multiplying both parts of the ratio by 12 you must then convert 12 \times 25000=300000 \ cm to km by dividing the solution by 100 \ 000 to get 3km.

Notice that for all three of these examples, the units are important. For example if we write the mapping example as the ratio 4cm:1km, this means that 4cm on the map is 1km in real life.

Top tip: if you are converting units, always write the units in your ratio.

Usually with ratio problem solving questions, the problems are quite wordy . They can involve missing values , calculating ratios , graphs , equivalent fractions , negative numbers , decimals and percentages .

Highlight the important pieces of information from the question, know what you are trying to find or calculate , and use the steps above to help you start practising how to solve problems involving ratios.

How to do ratio problem solving

In order to solve problems including ratios:

Identify key information within the question.

Know what you are trying to calculate.

Use prior knowledge to structure a solution.

Explain how to do ratio problem solving

Ratio problem solving worksheet

Get your free ratio problem solving worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on ratio

Ratio problem solving is part of our series of lessons to support revision on ratio . You may find it helpful to start with the main ratio lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• How to work out ratio  
• Ratio to fraction
• Ratio scale
• Ratio to percentage

Ratio problem solving examples

Example 1: part:part ratio.

Within a school, the number of students who have school dinners to packed lunches is 5:7. If 465 students have a school dinner, how many students have a packed lunch?

Within a school, the number of students who have school dinners to packed lunches is \bf{5:7.} If \bf{465} students have a school dinner , how many students have a packed lunch ?

Here we can see that the ratio is 5:7 where the first part of the ratio represents school dinners (S) and the second part of the ratio represents packed lunches (P).

We could write this as

Where the letter above each part of the ratio links to the question.

We know that 465 students have school dinner.

2 Know what you are trying to calculate.

From the question, we need to calculate the number of students that have a packed lunch, so we can now write a ratio below the ratio 5:7 that shows that we have 465 students who have school dinners, and p students who have a packed lunch.

We need to find the value of p.

3 Use prior knowledge to structure a solution.

We are looking for an equivalent ratio to 5:7. So we need to calculate the multiplier. We do this by dividing the known values on the same side of the ratio by each other.

So the value of p is equal to 7 \times 93=651.

There are 651 students that have a packed lunch.

Example 2: unit conversions

The table below shows the currency conversions on one day.

Use the table above to convert £520 (GBP) to Euros € (EUR).

Use the table above to convert \bf{£520} (GBP) to Euros \bf{€} (EUR).

The two values in the table that are important are GBP and EUR. Writing this as a ratio, we can state

We know that we have £520.

We need to convert GBP to EUR and so we are looking for an equivalent ratio with GBP = £520 and EUR = E.

To get from 1 to 520, we multiply by 520 and so to calculate the number of Euros for £520, we need to multiply 1.17 by 520.

1.17 \times 520=608.4

So £520 = €608.40.

Example 3: writing a ratio 1:n

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the 500ml of concentrated plant food must be diluted into 2l of water. Express the ratio of plant food to water respectively in the ratio 1:n.

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the \bf{500ml} of concentrated plant food must be diluted into \bf{2l} of water . Express the ratio of plant food to water respectively as a ratio in the form 1:n.

Using the information in the question, we can now state the ratio of plant food to water as 500ml:2l. As we can convert litres into millilitres, we could convert 2l into millilitres by multiplying it by 1000.

2l = 2000ml

So we can also express the ratio as 500:2000 which will help us in later steps.

We want to simplify the ratio 500:2000 into the form 1:n.

We need to find an equivalent ratio where the first part of the ratio is equal to 1. We can only do this by dividing both parts of the ratio by 500 (as 500 \div 500=1 ).

So the ratio of plant food to water in the form 1:n is 1:4.

Example 4: forming and solving an equation

Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their age. Kieran is 3 years older than Josh. Luke is twice Josh’s age. If Josh receives £8 pocket money, how much money do the three siblings receive in total?

Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their ages. Kieran is \bf{3} years older than Josh . Luke is twice Josh’s age. If Luke receives \bf{£8} pocket money, how much money do the three siblings receive in total ?

We can represent the ages of the three siblings as a ratio. Taking Josh as x years old, Kieran would therefore be x+3 years old, and Luke would be 2x years old. As a ratio, we have

We also know that Luke receives £8.

We want to calculate the total amount of pocket money for the three siblings.

We need to find the value of x first. As Luke receives £8, we can state the equation 2x=8 and so x=4.

Now we know the value of x, we can substitute this value into the other parts of the ratio to obtain how much money the siblings each receive.

The total amount of pocket money is therefore 4+7+8=£19.

Example 5: simplifying ratios

Below is a bar chart showing the results for the colours of counters in a bag.

Express this data as a ratio in its simplest form.

From the bar chart, we can read the frequencies to create the ratio.

We need to simplify this ratio.

To simplify a ratio, we need to find the highest common factor of all the parts of the ratio. By listing the factors of each number, you can quickly see that the highest common factor is 2.

\begin{aligned} &12 = 1, {\color{red} 2}, 3, 4, 6, 12 \\\\ &16 = 1, {\color{red} 2}, 4, 8, 16 \\\\ &10 = 1, {\color{red} 2}, 5, 10 \end{aligned}

HCF (12,16,10) = 2

Dividing all the parts of the ratio by 2 , we get

Our solution is 6:8:5 .

Example 6: combining two ratios

Glass is made from silica, lime and soda. The ratio of silica to lime is 15:2. The ratio of silica to soda is 5:1. State the ratio of silica:lime:soda.

Glass is made from silica, lime and soda. The ratio of silica to lime is \bf{15:2.} The ratio of silica to soda is \bf{5:1.} State the ratio of silica:lime:soda .

We know the two ratios

We are trying to find the ratio of all 3 components: silica, lime and soda.

Using equivalent ratios we can say that the ratio of silica:soda is equivalent to 15:3 by multiplying the ratio by 3.

We now have the same amount of silica in both ratios and so we can now combine them to get the ratio 15:2:3.

Example 7: using bar modelling

India and Beau share some popcorn in the ratio of 5:2. If India has 75g more popcorn than Beau, what was the original quantity?

India and Beau share some popcorn in the ratio of \bf{5:2.} If India has \bf{75g} more popcorn than Beau , what was the original quantity?

We know that the initial ratio is 5:2 and that India has three more parts than Beau.

We want to find the original quantity.

Drawing a bar model of this problem, we have

Where India has 5 equal shares, and Beau has 2 equal shares.

Each share is the same value and so if we can find out this value, we can then find the total quantity.

From the question, India’s share is 75g more than Beau’s share so we can write this on the bar model.

We can find the value of one share by working out 75 \div 3=25g.

We can fill in each share to be 25g.

Adding up each share, we get

India = 5 \times 25=125g

Beau = 2 \times 25=50g

The total amount of popcorn was 125+50=175g.

Common misconceptions

• Mixing units

Make sure that all the units in the ratio are the same. For example, in example 6 , all the units in the ratio were in millilitres. We did not mix ml and l in the ratio.

• Ratio written in the wrong order

For example the number of dogs to cats is given as the ratio 12:13 but the solution is written as 13:12.

• Ratios and fractions confusion

Take care when writing ratios as fractions and vice-versa. Most ratios we come across are part:part. The ratio here of red:yellow is 1:2. So the fraction which is red is \frac{1}{3} (not \frac{1}{2} ).

• Counting the number of parts in the ratio, not the total number of shares

For example, the ratio 5:4 has 9 shares, and 2 parts. This is because the ratio contains 2 numbers but the sum of these parts (the number of shares) is 5+4=9. You need to find the value per share, so you need to use the 9 shares in your next line of working.

• Ratios of the form \bf{1:n}

The assumption can be incorrectly made that n must be greater than 1 , but n can be any number, including a decimal.

Practice ratio problem solving questions

1. An online shop sells board games and computer games. The ratio of board games to the total number of games sold in one month is 3:8. What is the ratio of board games to computer games?

8-3=5 computer games sold for every 3 board games.

2. The volume of gas is directly proportional to the temperature (in degrees Kelvin). A balloon contains 2.75l of gas and has a temperature of 18^{\circ}K. What is the volume of gas if the temperature increases to 45^{\circ}K?

3. The ratio of prime numbers to non-prime numbers from 1-200 is 45:155. Express this as a ratio in the form 1:n.

4. The angles in a triangle are written as the ratio x:2x:3x. Calculate the size of each angle.

5. A clothing company has a sale on tops, dresses and shoes. \frac{1}{3} of sales were for tops, \frac{1}{5} of sales were for dresses, and the rest were for shoes. Write a ratio of tops to dresses to shoes sold in its simplest form.

6. During one month, the weather was recorded into 3 categories: sunshine, cloud and rain. The ratio of sunshine to cloud was 2:3 and the ratio of cloud to rain was 9:11. State the ratio that compares sunshine:cloud:rain for the month.

Ratio problem solving GCSE questions

1. One mole of water weighs 18 grams and contains 6.02 \times 10^{23} water molecules.

Write this in the form 1gram:n where n represents the number of water molecules in standard form.

2. A plank of wood is sawn into three pieces in the ratio 3:2:5. The first piece is 36cm shorter than the third piece.

Calculate the length of the plank of wood.

5-3=2 \ parts = 36cm so 1 \ part = 18cm

3. (a) Jenny is x years old. Sally is 4 years older than Jenny. Kim is twice Jenny’s age. Write their ages in a ratio J:S:K.

(b) Sally is 16 years younger than Kim. Calculate the sum of their ages.

Learning checklist

You have now learned how to:

• Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
• Make and use connections between different parts of mathematics to solve problems

The next lessons are

• Compound measures
• Best buy maths

Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths tuition programme.

Privacy Overview

Free video lessons for ratios and proportions (6th and 7th grade math/pre-algebra)

Find here free online math videos on ratios, proportions, and related topics: solving proportions, word problems, unit rates, proportional relationships, scaling geometric figures, and maps.

The videos match the lessons in the Blue Series book Math Mammoth Ratios, Proportions, and Problem Solving . As far as the complete curriculum (Light Blue), the lessons on ratios match chapter 4 of Math Mammoth Grade 6 , and the rest match lessons in chapter 6 of Math Mammoth Grade 7 curriculum .

Word problems involving unit rates

Equivalent rates — using equivalent rates to solve problems, and also graphing them (2 videos)

Ratio problems and bar models

Aspect ratio

Using ratios to convert measurement units

Proportions

Solving proportions

Proportion word problems

Unit rates and more about proportions

How to find the unit rate, including with fractions

Proportional relationships / Direct variation

Scaling figures and the scale ratio

Floor plans and scale ratio

How to calculate distances on the map or in reality using the map scale

These videos match the lessons in the book Math Mammoth Ratios, Proportions, and Problem Solving (Blue Series book), and the lessons in chapter 6 of Math Mammoth Grade 7 curriculum . In either of those, you will get MANY more practice exercises, word problems, and puzzles than what are shown in the videos, and also some lessons that are not in covered in this set of videos.

Free Sample pages (PDF) Contents and Introduction Solving Problems Using Equivalent Ratios Scaling Figures 2 Problem Solving with Diagrams, part 1 Ratio Problems & Bar Models 2

=> Learn more!

© 2006-2024 MathMammoth.com

A ratio compares values .

A ratio says how much of one thing there is compared to another thing.

Ratios can be shown in different ways:

A ratio can be scaled up:

Try it Yourself

Using ratios.

The trick with ratios is to always multiply or divide the numbers by the same value .

Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.

So the ratio of flour to milk is 3 : 2

To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4:

3 ×4 : 2 ×4 = 12 : 8

In other words, 12 cups of flour and 8 cups of milk .

The ratio is still the same, so the pancakes should be just as yummy.

"Part-to-Part" and "Part-to-Whole" Ratios

The examples so far have been "part-to-part" (comparing one part to another part).

But a ratio can also show a part compared to the whole lot .

Example: There are 5 pups, 2 are boys, and 3 are girls

Part-to-Part:

The ratio of boys to girls is 2:3 or 2 / 3

The ratio of girls to boys is 3:2 or 3 / 2

Part-to-Whole:

The ratio of boys to all pups is 2:5 or 2 / 5

The ratio of girls to all pups is 3:5 or 3 / 5

Try It Yourself

We can use ratios to scale drawings up or down (by multiplying or dividing).

Example: To draw a horse at 1/10th normal size, multiply all sizes by 1/10th

This horse in real life is 1500 mm high and 2000 mm long, so the ratio of its height to length is

1500 : 2000

What is that ratio when we draw it at 1/10th normal size?

We can make any reduction/enlargement we want that way.

"I must have big feet, my foot is nearly as long as my Mom's!"

But then she thought to measure heights, and found she is 133cm tall, and her Mom is 152cm tall.

In a table this is:

The "foot-to-height" ratio in fraction style is:

We can simplify those fractions like this:

And we get this (please check that the calcs are correct):

"Oh!" she said, "the Ratios are the same".

"So my foot is only as big as it should be for my height, and is not really too big."

You can practice your ratio skills by Making Some Chocolate Crispies

• Skills by Standard
• Skills by Grade
• Skills by Category

Go to profile

• Assignments
• Assessments
• Report Cards
• Our Teachers

Common Core - State Standards Initiative

Understanding ratios is crucial for solving problems relating to proportions and percents. Math Games makes reviewing this higher-level math skill a breeze, with our suite of enjoyable educational games that students won’t want to stop playing!

Our free resources include mobile-compatible game apps, PDF worksheets, an online textbook and more. Students can use these tools to blend study with play as they practice:

• Describing pictures as ratios
• Calculating percents and prices
• Comparing ratios
• Solving proportions
• Finding the slope of a graph

Help the kids in your life look forward to reviewing math! Our games are tailored to a variety of grade levels and become easier or more challenging depending on how well users are playing. Select one of the skills listed above to check them out!

Simplifying Ratios Pixel Picture ( Editable Word | PDF | Answers ​ )

Simplifying Ratios Odd One Out ( Editable Word | PDF | Answers )

Equivalent Ratios Match-Up ( Editable Word | PDF | Answers )

Working with Ratio Practice Strips ( Editable Word | PDF | Answers )

Dividing in a Ratio Practice Strips ( Editable Word | PDF | Answers )

Dividing in a Ratio Fill in the Blanks ( Editable Word | PDF | Answers )

Dividing in a Ratio Crack the Code ( Editable Word | PDF | Answers )

Combining Ratios Practice Strips ( Editable Word | PDF | Answers )

Sharing and Combining Ratios Practice Strips ( Editable Word | PDF | Answers )

Solving Ratio Problems Practice Strips ( Editable Word | PDF | Answers )

Solving Ratio Problems Practice Grid ( Editable Word | PDF | Answers )

Harder Ratio Problems Practice Strips ( Editable Word | PDF | Answers )

Fractions and Ratio Worded Problems Practice Strips ( Editable Word | PDF | Answers )

Unitary Method Practice Strips ( Editable Word | PDF | Answers )

Unitary Method Match-Up ( Editable Word | PDF | Answers )

Best Buys Practice Strips ( Editable Word | PDF | Answers )

Currency Conversions Practice Strips ( Editable Word | PDF | Answers )

Proportion Worded Problems Practice Strips ( Editable Word | PDF | Answers )

Proportion Worded Problems Practice Grid ( Editable Word | PDF | Answers )

Mixed Ratio and Proportion Revision Practice Grid ( Editable Word | PDF | Answers ​ )

• Number Charts
• Multiplication
• Long division
• Basic operations
• Telling time
• Place value
• Roman numerals
• Fractions & related
• Add, subtract, multiply,   and divide fractions
• Mixed numbers vs. fractions
• Equivalent fractions
• Prime factorization & factors
• Fraction Calculator
• Decimals & Percent
• Add, subtract, multiply,   and divide decimals
• Fractions to decimals
• Percents to decimals
• Percentage of a number
• Percent word problems
• Classify triangles
• Classify quadrilaterals
• Circle worksheets
• Area & perimeter of rectangles
• Area of triangles & polygons
• Coordinate grid, including   moves & reflections
• Volume & surface area
• Pre-algebra
• Square Roots
• Order of operations
• Scientific notation
• Proportions
• Ratio word problems
• Write expressions
• Evaluate expressions
• Simplify expressions
• Linear equations
• Linear inequalities
• Graphing & slope
• Equation calculator
• Equation editor
• Elementary Math Games
• Addition and subtraction
• Math facts practice
• The four operations
• Factoring and number theory
• Geometry topics
• Middle/High School
• Statistics & Graphs
• Probability
• Trigonometry
• Logic and proof
• For all levels
• Favorite math puzzles
• Favorite challenging puzzles
• Math in real world
• Problem solving & projects
• For gifted children
• Math history
• Math games and fun websites
• Interactive math tutorials
• Math help & online tutoring
• Assessment, review & test prep
• Online math curricula

Use the generator to make customized ratio worksheets. Experiment with the options to see what their effect is.

Primary Grade Challenge Math by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

Can Economic Growth Help Solve Our Debt Problem?

The U.S. is among the most indebted countries in the world—and the problem is only getting worse.

The federal government’s debt is currently $33 trillion and annual deficits just reached the highest in U.S. history outside of the pandemic years (at nearly $2 trillion ). Not only are we spending more than we’re taking in, but the long-run growth in our spending is outpacing the growth in our revenue.

If the lessons from other countries dealing with similar problems are any indication, fixing this problem is going to require a combination of spending cuts and tax hikes. But there’s a third factor that could help alleviate some of the pain involved: economic growth .

Economic Growth, Deficits, and Debt

The faster the economy grows, the less pressure there is to raise taxes and cut spending.

With more businesses and workers, the tax base The tax base is the total amount of income, property, assets, consumption, transactions, or other economic activity subject to taxation by a tax authority. A narrow tax base is non-neutral and inefficient. A broad tax base reduces tax administration costs and allows more revenue to be raised at lower rates. expands, meaning the government can collect more tax revenue without raising rates.

To illustrate, suppose we have an economy with a GDP of $1 trillion and an average tax rate The average tax rate is the total tax paid divided by taxable income . While marginal tax rates show the amount of tax paid on the next dollar earned, average tax rates show the overall share of income paid in taxes. of 20 percent. Total tax revenue would be $200 billion. Let’s say the economy grows by 5 percent, bringing the new GDP to $1.05 trillion. With the tax rate unchanged at 20 percent, the new tax revenue would be $210 billion—a $10 billion increase without touching the tax rate.

A growing economy brings in more tax revenue, which reduces the relative debt burden. This gives lawmakers some breathing room to address fiscal imbalances (think gradual tweaks, not drastic measures).

What Is the Debt-to-GDP Ratio and Why Does It Matter?

The debt-to-GDP ratio is a measure of how much debt the federal government holds compared to how much it produces (i.e., the size of its economy) in a year. For example, say you borrowed $10,000 to start a business and you sold $50,000 worth of products. Your personal “debt-to-GDP” ratio would be 20 percent.

But what would happen if your debt-to-GDP ratio was 115 percent (like the U.S. in 2021)? You’d owe more than you produced in a year.

This ratio gives valuable insight into the sustainability of a country’s economy. If it gets too high, a country might struggle to pay back its debts, leading to a host of undesirable consequences. For example, interest costs to service the debt would become a bigger part of the budget, taking resources away from other priorities. And sometimes governments are tempted to print money to deal with the problem, which causes inflation Inflation is when the general price of goods and services increases across the economy, reducing the purchasing power of a currency and the value of certain assets. The same paycheck covers less goods, services, and bills. It is sometimes referred to as a “ hidden tax ,” as it leaves taxpayers less well-off due to higher costs and “bracket creep,” while increasing the government’s spending power. . While there’s disagreement about how high is too high, a debt-to-GDP ratio of 100 percent is a common milestone economists look out for.

How Taxes Affect Economic Growth

One way policymakers can promote economic growth is through tax policies that encourage people to work, save , and invest .

For example, allowing businesses to write off investments in the year they occur rather than over time (which decreases their value) makes investments more profitable. This, in turn, encourages more investments, which boosts productivity and can lead to more jobs and higher wages.

To be sure, some of these tax policies would decrease revenue, but the growing economy could help partially offset the reduction.

The Way Forward

With much of the 2017 tax reform law expiring in less than two years, Congress will get the chance to rewrite the tax code. And while a sustainable approach will require addressing the underlying drivers of the debt—i.e., mandatory spending programs like Social Security and Medicare—lawmakers should prioritize policies that lower the country’s debt-to-GDP ratio the most.

The bottom line: improving the country’s fiscal situation won’t be comfortable, but economic growth can help cushion the blow.

Level-up your tax knowledge with free educational resources—primers, glossary terms, videos, and more—delivered monthly.