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Solving Proportions Worksheets
Learn how to solve proportions with this set of printer-friendly worksheets that are specially designed for students of grade 6 through high school. A series of multi-level worksheets require students to solve proportions using the cross product method and the answers so derived will be in the form of whole numbers, fractions or decimals. Also, solve worksheets that contain the variables in algebraic expressions. A variety of authentic word problems that incorporate real-life scenarios are also featured here. Check out some of these handouts for free!

Solve the Proportion: Level 1
Each set of proportions rendred in these 6th grade pdfs contains a variable. Cross-multiply the ratios to determine the value of the unknown. Answers derived will comprise only whole numbers.

Solve the Proportion: Level 2
Use the cross product method to solve each proportion in these printable worksheets for grade 7. The value of the missing variables will be in the form of either proper fractions or mixed fractions.

Solve the Proportion - Decimals
Students in grade 8 need to determine the product of extremes and the product of means to solve the equations that contain decimals and eventually evaluate the unknown. The answer key is available in the next page of each worksheet.

Level 1: Solve the Proportion - Algebraic Expression
Evaluate the proportions involving algebraic expressions with two terms. Use the proportionality rule and solve the equations to obtain the value of the missing variable.

Level 2: Solve the Proportion - Algebraic Expression
Use the cross product rule to obtain the equation that involves the rational expression on both sides. There are eight problems in each worksheet for 8th grade and high school students.

Proportion Word Problems
Observe the proportional relationships in real world with this series of word problems pdf worksheets; set up the proportionality with the given values and solve for the unknown.
Related Worksheets
» Constant of Proportionality
» Unit Rate
» Proportions
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» Ratio Word Problems
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Proportions word problems

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Math worksheets: Proportions word problems
Below are grade 6 math worksheets with proportions word problems.

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Proportions Word Problems Worksheet: Answers and Explanations
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A proportion is a set of 2 fractions that equal each other. This article focuses on how to use proportions to solve real life problems.
Real World Uses of Proportions
- Modifying a budget for a restaurant chain that is expanding from 3 locations to 20 locations
- Creating a skyscraper from blueprints
- Calculating tips, commissions, and sales tax
Modifying a Recipe
On Monday, you are cooking enough white rice to serve exactly 3 people. The recipe calls for 2 cups of water and 1 cup of dry rice. On Sunday, you are going to serve rice to 12 people. How would the recipe change? If you’ve ever made rice, you know that this ratio—1 part dry rice and 2 parts water—is important. Mess it up, and you’ll be scooping a gummy mess on top of your guests' crawfish étouffée.
Because you are quadrupling your guest list (3 people * 4 = 12 people), you must quadruple your recipe. Cook 8 cups of water and 4 cups of dry rice. These shifts in a recipe demonstrate the heart of proportions: using a ratio to accommodate life's greater and smaller changes.
Algebra and Proportions 1
Sure, with the right numbers, you can forgo setting up an algebraic equation to determine the amounts of dry rice and water. What happens when the numbers are not so friendly, however? On Thanksgiving, you'll be serving rice to 25 people. How much water do you need?
Because the ratio of 2 parts water and 1 part dry rice applies to cooking 25 servings of rice, use a proportion to determine the quantity of ingredients.
Note : Translating a word problem into an equation is super important. Yes, you can solve an incorrectly set up equation and find an answer. You can also mix rice and water together to create "food" to serve at Thanksgiving. Whether the answer or food is palatable depends on the equation.
Think about what you know:
- 3 servings of cooked rice = 2 cups of water; 1 cup of dry rice 25 servings of cooked rice = ? cups of water; ? cup of dry rice
- 3 servings of cooked rice/25 servings of cooked rice = 2 cups of water/ x cups of water
- 3/25 = 2/ x
Cross multiply. Hint : Write these fractions vertically to get the full understanding of cross multiplying. To cross multiply, take the first fraction's numerator and multiply it by the second fraction's denominator. Then take the second fraction's numerator and multiply it by the first fraction's denominator.
3 * x = 2 * 25 3 x = 50 Divide both sides of the equation by 3 to solve for x . 3 x /3 = 50/3 x = 16.6667 cups of water Freeze- verify that the answer is correct. Is 3/25 = 2/16.6667? 3/25 = .12 2/16.6667= .12 Whoo hoo! The answer 16.6667 cups of water is correct.
Ratio and Proportions Word Problem 1: The Brownie Recipe
Damian is making brownies to serve at the family picnic. If the recipe calls for 2 ½ cups of cocoa to serve 4 people, how many cups will he need if there will be 60 people at the picnic? 37.5 cups
What do you know? 2 ½ cups = 4 people ? cups = 60 people 2 ½ cups/ x cups = 4 people/60 people 2 ½/ x = 4/60 Cross Multiply. 2 ½ * 60 = 4 * x 150 = 4 x Divide both sides by 4 to solve for x . 150/4 = 4 x /4 37.5 = x 37.5 cups
Use common sense to verify that the answer is correct. The initial recipe serves 4 people and is modified to serve 60 people. Of course, the new recipe has to serve 15 times more people. Therefore, the amount of cocoa has to be multiplied by 15. Is 2 ½ * 15 = 37.5? Yes.
Ratio and Proportions Word Problem 2: Growing Little Piglets
A piglet can gain 3 pounds in 36 hours. If this rate continues, the pig will reach 18 pounds in 216 hours.
What do you know? 3 pounds = 36 hours 18 pounds = ? hours 3 pounds/18 pounds = 36 hours/ ? hours 3/18 = 36/ x
Cross Multiply. 3 * x = 36 * 18 3 x = 648
Divide both sides by 3 to solve for x . 3 x /3 = 648/3 x = 216 216 hours
Use common sense to verify that the answer is correct. A piglet can gain 3 pounds in 36 hours, which is a rate of 1 pound for every 12 hours. That means that for every pound a piglet gains, 12 hours will pass. Therefore 18 *12, or 216 pounds, is the correct answer.
Ratio and Proportions Word Problem 3: The Hungry Rabbit
Denise’s rabbit can eat 70 pounds of food in 80 days. How long will it take the rabbit to eat 87.5 pounds? 100 days
What do you know? 70 pounds = 80 days 87.5 pounds = ? days 70 pounds/87.5 pounds = 80 days/ x days 70/87.5 = 80/ x
Cross Multiply. 70 * x = 80 * 87.5 70 x = 7000
Divide both sides by 70 to solve for x . 70 x /70 = 7000/70 x = 100
Use Algebra to verify the answer. Is 70/87.5 = 80/100? 70/87.5 = .8 80/100 = .8
Ratio and Proportions Word Problem 4: The Long Road Trip
Jessica drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles? 15.38 hours
What do you know? 130 miles = 2 hours 1,000 miles = ? hours 130 miles/1,000 miles = 2 hours/? hours 130/1000 = 2/ x
Cross Multiply. 130 * x = 2 * 1000 130 x = 2000
Divide both sides of the equation by 130 to solve for x . 130 x /130 = 2000/130 x = 15.38 hours
Use Algebra to verify the answer. Does 130/1000 = 2/15.38? 130/1000 = .13 2/15.38 is approximately .13
- Proportions Word Problems Worksheet 1
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Solving Proportions
How do you solve a proportion? Let this seventh-grade math worksheet help! This one-page practice page begins with an example problem that illustrates how cross products and inverse operations can be used to solve for a variable in two equivalent ratios. Learners will then apply what they've learned to solve for the variable in nine practice problems. Each problem includes variables in either the numerator or denominator of a ratio set equal to ratios made up of two- and three-digit numbers. Solving proportions is an important foundational skill for reasoning with proportions in real-world scenarios.
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Check out these awesome Simplified Ratios Word Problem Worksheets . You’ll practice writing ratios and simplifying the ratios while seeing how useful math is in everyday life. There are some twists in some of the problems, so make sure to read carefully!
Simplified Ratios Word Problem Worksheet 1 – With this 10 problem worksheet, you will practice writing and simplifying simple ratios while looking at how ratios are used in real-life. Simplified Ratios Word Problem Worksheet 1 RTF Simplified Ratios Word Problem Worksheet 1 PDF View Answers
Simplified Ratios Word Problem Worksheet 2 – With this 10 problem worksheet, you will practice writing and simplifying simple ratios while looking at how ratios are used in real-life. Simplified Ratios Word Problem Worksheet 2 RTF Simplified Ratios Word Problem Worksheet 2 PDF View Answers

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Unit: Ratios and rates
Intro to ratios.
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Solving proportion word problems worksheet
This is a set of 2 solving proportions word problems RIDDLE worksheets.Worksheet 1: Most problems can be done mentally to show students

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Worksheet by Kuta Software LLC. Kuta Software - Infinite Pre-Algebra Proportion Word Problems. Answer each question and round your answer to the nearest
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Proportions word problems
Create proportion worksheets to solve proportions or word problems (e.g. speed/distance or cost/amount problems). Available both as PDF and html files.
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Ratio/Proportion Word Problems. Name_______________________. Set up a proportion to solve each problem, show all work, and label all answers.
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Proportion word problems.
A worksheet on solving basic proportions. Story (word) problems are included for students to set up and solve the proportion.
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Algebra 1 Worksheet: Proportions & Word Problems Oct.
Here the the steps to follow to solve this proportion word problem. Step 1: Let x be the distance you are looking for. Step 2: Write down two ratios. You can do
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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.

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Proportion Word Problems Worksheets
Word problems are essential in math lessons because they show students how math is applied in real life and how to gain the skills they will use for the rest of their life! For this reason, there should be a way to make mastering this skill as fun as possible so that students are engaged enough to learn and understand the concept! A proportion word problem worksheet that shows that two ratios are equal can help.
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Proportion Word Problems Worksheet Answers

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Proportions Worksheet Word Problems
Finding Your Way around the Proportion Word Problem Worksheet
With this worksheet, students will solve word problems that involve searching for proportions and finding values when given a ratio. They will compare the two ratios to determine which is higher. Students will fill in the blanks to complete the word-based section.
There’s a surefire way to solve the problems in the worksheets. Create an illustration of the situation: this can be a diagram or picture. Describe the numbers’ relationship through proportions. Don’t forget to read the question part of the problem as some students gloss over it and make mistakes.
1:1 Math Lessons
The section with the proportion word problems worksheet answers explains how to solve proportions from word problems. After completing this worksheet, students will be able to solve word problems that involve balance. Sample exercises are solved, and only then practice problems are presented.
Why Is the Word Problem Sheet Important?
One of the unique features of the proportion word problem worksheet is that it allows students to be more creative in their problem-solving approach. Downloading and solving proportion word problems worksheet with answers PDF will enable them to make more sense in life and solve exercises effectively.
Proportion Word Problems Worksheets PDF
Proportion Word Problems Worksheet
Proportions Word Problems Worksheet
Solving Proportions Word Problems Worksheets
Proportion Word Problems Worksheet With Answers PDF
Visualizing the answers from solving proportions word problems worksheets can make the problem interesting and engaging. Development of these skills through solving proportions and problem worksheets requires step-by-step guidance and practical explanations from experienced tutors. Worksheets develop their ability to be independent thinkers and problem solvers.
More Proportions Worksheets
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Welcome to our Ratio Word Problems page. Here you will find our range of Fifth Grade Ratio Problem worksheets which will help your child apply and practice their Math skills to solve a range of ratio problems.
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Here you will find a range of problem solving worksheets about ratio.
The sheets involve using and applying knowledge to ratios to solve problems.
The sheets have been put in order of difficulty, with the easiest first.
Each problem sheet comes complete with an answer sheet.
Using these sheets will help your child to:
- apply their ratio skills;
- apply their knowledge of fractions;
- solve a range of word problems.
- Ratio Problems 1
- PDF version
- Ratio Problems 2
- Ratio Problems 3
- Ratio Problems 4
Ratio and Probability Problems
- Ration and Probability Problems 1
- Sheet 1 Answers
- Ration and Probability Problems 2
- Sheet 2 Answers
More Recommended Math Worksheets
Take a look at some more of our worksheets similar to these.
More Ratio Worksheets
These sheets are a great way to introduce ratio of one object to another using visual aids.
The sheets in this section are at a more basic level than those on this page.
We also have some ratio and proportion worksheets to help learn these interrelated concepts.
- Ratio Part to Part Worksheets
- Ratio and Proportion Worksheets
More 5th Grade Math Problems
Here you will find our selection of free 5th grade math word problems.
Each sheet is availabel in both standard and metric units (where applicable).
Each sheet comes complete with a separate answer sheet.
All the problems are based around 'real life' such as the planets, heights of mountains, or length of rivers.
Using these sheet will help your child to:
- apply their addition, subtraction, multiplication and division skills;
- apply their knowledge of rounding and place value;
- solve a range of 'real life' problems.
All the worksheets help to support Elementary math benchmarks.
- 5th Grade Math Problems

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This is our finding all possibilities area where all the worksheets involve finding many different answers to the problem posed.
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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:
Dividing a quantity into a ratio
Scale ratios
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.
Step-by-step guide: Ratios and fractions (coming soon)
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}{5} of sales were for tops, \frac{1}{3} 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 revision programme.
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Ratio and Proportion Worksheets 7th Grade
Ratio and proportion worksheets 7th grade help students in practicing questions on expressing ratios in the simplest form, simplifying ratios, comparing ratios, arranging ratios in the ascending order or descending order, proportion, and also mean proportional between numbers. These worksheets also help students in practicing questions involving tables, graphs, word problems, etc.
Benefits of 7th Grade Ratio and Proportion Worksheets
Ratio and proportion worksheets 7th grade deal with the logical and reasoning aspect of mathematics and help students in real-life scenarios as well. The stepwise approach of these worksheets makes students solve a variety of questions with ease. Students can study at their own pace and can solve problems with a gradually increasing difficulty level. As these worksheets are also interactive, students can rely on visual simulations to promote a better understanding of the topic.
Printable PDFs for Grade 7 Ratio and Proportion Worksheets
7th Grade Ratio and Proportion worksheets are available as PDFs that can be downloaded for free, enabling students to access them offline.
- Math 7th Grade Ratio and Proportion Worksheet
- 7th Grade Ratio and Proportion Math Worksheet
- Seventh Grade Ratio and Proportion Worksheet
- Grade 7 Math Ratio and Proportion Worksheet
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GCSE/KS3 - Ratio and Proportion Problem Worksheets
Subject: Mathematics
Age range: 11-14
Resource type: Worksheet/Activity

Last updated
12 April 2013
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Exactly what I needed for my ratio lesson. I adapted it slightly to suit the needs of this group of children
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Excellent .The best explanation of ratio and proportion that I found on internet.And it is free!Thank you!
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Good, but where are the answers?
A nice collection of exam and test questions on all aspects of ratio and proportion up to grade C
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Home / United States / Math Classes / Worksheets / Ratio and Proportions Worksheets
Ratio and Proportions Worksheets
Ratio and proportions worksheets help students compare two similar quantities deriving a ratio. When both ratios in an e quation are equal, they are determined to be in proportion. Ratio and proportion concepts are crucial to young learners, in both math class and the real world. Printable ratio and proportion worksheets feature problems tied to real world experience. Worksheets may include questions regarding the expression and comparison of rations in simpler forms in relation to height, weight, distance, and time. These problems are presented using real-life scenarios such as adjusting a recipe when cooking or making a business deal. Ratio and proportion worksheets are a great study aid for young learners. ...Read More Read Less
Benefits of Ratio and Proportions Worksheets:
Develop logical reasoning :
Students can further develop their logical reasoning when they practice and solve problems regularly using ratio and proportions worksheets. These skills are beneficial not only in successively solving math problems, but in the real world as well.
Phased approach :
Ratio and proportions worksheets feature problems presented in a graded structure. The step-by-step design allows for students to begin with simple problems and gradually increase in difficulty level. As students move to higher level worksheets, their understanding of the concept can improve.
Self-paced study :
Students are encouraged to work through the different levels of ratio and proportions worksheets at their own pace. Students can repeat worksheets when needed to develop an understanding of difficult concepts.
Interactive formats :
Ratio and proportion worksheets are visually stimulating and interactive, which can keep a student engaged and prevent boredom.
- Interactive Worksheets
- Printable Worksheets

- 7th Grade Ratio And Proportions Worksheets
Choose Math Worksheets by Grade
Choose math worksheets by topic, ratio and proportions worksheets explained:.
Using ratio and proportion worksheets can instill confidence and a deeper understanding of complex math concepts. They can act as a homework aid to assist students needing extra practice.
Ratios are generally expressed in their lowest terms, similar to fractions expressed in their lowest terms. While ratios compare between two quantifiable entities, proportions are equations with the ratios on both sides. Printable ratio and proportions worksheets encourage students to solve expression problems in simpler forms, compare ratios, arrange ratios in ascending or descending orders and find a mean proportional between numbers.
As students progress to the higher grade levels, the printable ratio and proportions worksheets incorporate problems involving tables and graphs. Worksheets feature problems requiring the cross-product method, and problems using algebraic variables.
Ratio and proportion worksheets come in many varieties, including:
- Express ratios in numbers, decimals, and fractions
- Reduce ratios to their simplest terms
- Create equivalent ratios
- Obtain missing terms in ratio and proportions
- Use number sets to create proportions
- Find solutions to ratio and proportion word problems
- Find solutions to real-life ratio and proportion problems
Printable ratio and proportions worksheets are available in a large variety to facilitate extra study time in order to help students understand complex mathematical concepts.
Printable Ratio and Proportions Worksheet PDFs:
Radio and proportions worksheets are available in easily downloadable HTML and PDF formats. They are randomly generated and printable at your convenience. They also come with an answer key that explains the basics needed to solve problems involving ratio and proportion concepts successfully. With regular practice of these worksheets students can enhance their knowledge of ratio and proportions.
What are the ratio and proportions worksheets about?
Ratio and proportions worksheets are free printable fun and interactive worksheets that contain questions based on ratio and proportions. These worksheets have detailed solutions of question that help in better understanding of concept.
What is ratio?
Ratio is the mathematical term to represent the comparison of two numbers and ratio is represented by either a/b or a : b
What is proportions?
Proportion is the equation that tells whether the two ratios are equal or not.
How ratio and proportion are used in daily life?
Ratio and proportions are used in various field as finance, shopping, mathematical modeling. While building houses we use ratio and proportion of instructural material. We can see the basic use of ration and proportion while cooking.
What are equivalent ratios?
The equivalent ratios are the ratios that describe the same relationship between numbers. The value of equivalent ratios is equivalent.
How are the ratio and proportions worksheets benefical for students?
The ratio and proportions worksheets by byju’s math have questions based on ratios and proportions. The solution has been provided using different methods that will help in better understanding the concept and developing self-assessment skills. The worksheet has different difficulty levels that will help in recording the progress. The worksheet has real-life examples that will help in how to apply concepts in real life.

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Proportion Worksheets Create proportion worksheets to solve proportions or word problems (e.g. speed/distance or cost/amount problems) — available both as PDF and html files. These are most useful when students are first learning proportions in 6th, 7th, and 8th grade.
Packed with sets of four numbers, these printable worksheets requires 6th grade and 7th grade students to form two equivalent sets of ratios and create a proportion. Identify the Proportion: Graph Observe the coordinates on each graph to determine if they are proportional.
Level 1: Solve the Proportion - Algebraic Expression Evaluate the proportions involving algebraic expressions with two terms. Use the proportionality rule and solve the equations to obtain the value of the missing variable. Level 2: Solve the Proportion - Algebraic Expression
Solving Proportions Name_____ Date_____ Period____-1-Solve each proportion. 1) n ... Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com. Title: document1 Author: Mike Created Date:
Proportions worksheets Proportions and ratios The use of proportions is a practical math skill that students often struggle with. Our proportions worksheets review whole number and decimal proportions as well as provide simple proportion word problems. Sample Grade 6 Proportions Worksheet What is K5?
©7 m2k0n1 Q2E yKeu6t 6aM 5SQoJfztkw KaArjeu VLsL5CU.2 h TA Bl tl 1 Mrzi Rguh ktOsn PrDe0sAesr Rv oekdK.q C mMYawdEel PwKiXtFhy OIgnef Ki4nUigtbe d RPHrDer- MAWlgXewbur6aE.c Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Proportion Word Problems Date_____ Period____
Below are grade 6 math worksheets with proportions word problems. Worksheet #1 Worksheet #2 Worksheet #3 Similar: Proportions word problems - using decimals Ratio word problems What is K5? K5 Learning offers free worksheets, flashcards and inexpensive workbooks for kids in kindergarten to grade 5.
Proportion word problems Multi-step ratio and percent problems Math > 7th grade > Rates & proportional relationships > Writing & solving proportions Solving proportions CCSS.Math: 7.RP.A.2, 7.RP.A.2c Google Classroom Solve for y y. \dfrac {6} {11} = \dfrac {y} {3} 116 = 3y y = y = Stuck? Review related articles/videos or use a hint.
A proportion is a set of 2 fractions that equal each other. This article focuses on how to use proportions to solve real life problems. Real World Uses of Proportions Modifying a budget for a restaurant chain that is expanding from 3 locations to 20 locations Creating a skyscraper from blueprints Calculating tips, commissions, and sales tax
Solving Proportions. How do you solve a proportion? Let this seventh-grade math worksheet help! This one-page practice page begins with an example problem that illustrates how cross products and inverse operations can be used to solve for a variable in two equivalent ratios. Learners will then apply what they've learned to solve for the ...
Each free worksheet can be customized and comes with an answer key. Simplified Ratios Word Problem Worksheet 1 - With this 10 problem worksheet, you will practice writing and simplifying simple ratios while looking at how ratios are used in real-life. Simplified Ratios Word Problem Worksheet 1 RTF Simplified Ratios Word Problem Worksheet 1 PDF
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Solving Proportions Worksheets Students must first understand the idea of proportion and then proceed step by step to solve the proportion worksheet. These worksheets keep students interested and help them solve some of the most challenging proportion problems.
What types of word problems can we solve with proportions? If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, ... Solving unit rate problem (Opens a modal) Solving unit price problem (Opens a modal) Rate problems (Opens a modal) Comparing rates example (Opens a ...
CHILL 6 Multi Step Problem Solving with percentages. by nduce2. Percent Model - Find the Amount Shaded. by mathistheway. Decimals to Percents. by mrslowik. Tax 1. by Fishcakes. Percentage increase and decrease.
Solving proportion word problems worksheet - Worksheet. In Real-Life Situations. Page 2. Solving Problems using Proportional Reasoning For each problem, set up. ... This is a set of 2 solving proportions word problems RIDDLE worksheets.Worksheet 1: Most problems can be done mentally to show students
Ratio Worksheets Columns: Rows: (These determine the number of problems) Level: Level 1: write a ratio Level 2: write a ratio and simplify it Numbers used (only for levels 1 & 2): Range from to with step Level 3: word problems Page orientation: Portrait Landscape
With this worksheet, students will solve word problems that involve searching for proportions and finding values when given a ratio. They will compare the two ratios to determine which is higher. Students will fill in the blanks to complete the word-based section. There's a surefire way to solve the problems in the worksheets.
Proportions Word Problems: Worksheet And Answers. A proportion is a set of 2 fractions that equal each other. Here's all you need to know about using proportions to solve real life problems. A proportion is a set of 2 fractions th...
Ratio Word Problems. Here you will find a range of problem solving worksheets about ratio. The sheets involve using and applying knowledge to ratios to solve problems. The sheets have been put in order of difficulty, with the easiest first. Each problem sheet comes complete with an answer sheet. solve a range of word problems.
These are usually proportion questions where we are stating the proportion of the total amount as a fraction. Step-by-step guide: Ratios and fractions (coming soon) You have been given. the ratio. And you want to find. one part of the ratio as. a fraction of the total. Step 1: Add the parts of the ratio.
Ratio and proportion worksheets 7th grade deal with the logical and reasoning aspect of mathematics and help students in real-life scenarios as well. The stepwise approach of these worksheets makes students solve a variety of questions with ease. Students can study at their own pace and can solve problems with a gradually increasing difficulty ...
ID: 2652370 Language: English School subject: Math Grade/level: Gr.6 & 7 Age: 11-14 Main content: Problem solving Other contents: Solving Add to my workbooks (3) Embed in my website or blog Add to Google Classroom
rtf, 427.03 KB. doc, 20 KB. Ratio Harvesting Apples: Ratio and Proportion GCSE Problem Worksheets in word document. Tes classic free licence. Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch. Last updated.
Ratio and proportion worksheets come in many varieties, including: Express ratios in numbers, decimals, and fractions. Reduce ratios to their simplest terms. Create equivalent ratios. Obtain missing terms in ratio and proportions. Use number sets to create proportions. Find solutions to ratio and proportion word problems.