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.

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Ratio Word Problems

Here, we will learn to do some practical word problems involving ratios.

Amelia and Mary share $40 in a ratio of 2:3. How much do they get separately?

There is a total reward of $40 given.  Let Amelia get = 2x and Mary get = 3x Then, 2x + 3x = 40 Now, we solve for x => 5x = 40 => x = 8 Thus, Amelia gets = 2x = 2 × 8 = $16 Mary gets = 3x = 3 × 8 = $24

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

Let the total number of blue marbles be x Thus, ${\dfrac{3}{4}=\dfrac{x}{120}}$ x = ${\dfrac{3\times 120}{4}}$ x = 90 So, there are 90 blue marbles in the bag.

Gregory weighs 75.7 kg. If he decreases his weight in the ratio of 5:4, find his reduced weight.

Let the decreased weight of Gregory be = x kg Thus, 5x = 75.7 x = \dfrac{75\cdot 7}{5} = 15.14 Thus his reduced weight is 4 × 15.14 = 60.56 kg

A recipe requires butter and sugar to be in the ratio of 2:3. If we require 8 cups of butter, find how many cups of sugar are required. Write the equivalent fraction.

Thus, for every 2 cups of butter, we use 3 cups of sugar Here we are using 8 cups of butter, or 4 times as much So you need to multiply the amount of sugar by 4 3 × 4 = 12 So, we need to use 12 cups of sugar Thus, the equivalent fraction is ${\dfrac{2}{3}=\dfrac{8}{12}}$

Jerry has 16 students in his class, of which 10 are girls. Write the ratio of girls to boys in his class. Reduce your answer to its simplest form.

Total number of students = 16 Number of girls = 10 Number of boys = 16 – 10 = 6 Thus the ratio of girls to boys is ${\dfrac{10}{6}=\dfrac{5}{3}}$

A bag containing chocolates is divided into a ratio of 5:7. If the larger part contains 84 chocolates, find the total number of chocolates in the bag.

Let the total number of chocolates be x

Then the two parts are:

${\dfrac{5x}{5+7}}$ and ${\dfrac{7x}{5+7}}$

${\dfrac{7x}{5+7}}$ = 84

=> ${\dfrac{7x}{12}}$ = 84

Thus, the total number of chocolates that were present in the bag was 144

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Solving Word Problems with Ratios

Solving Word Problems with Ratios Video

Hey guys! Welcome to this video tutorial on word problems involving ratios .

Ratios are what we use to compare certain number values. People everywhere use ratios. We use, or at least we should, use ratios when we cook. For example, if I were to make macaroni and cheese for a group of 6 people and I knew that a \(\frac{1}{2}\) cup of macaroni would feed one person, then I could multiply 6 times \(\frac{1}{2}\) to get 3. Well, 3 to 6 is my ratio, and this ratio tells me that for every 3 cups of macaroni that I have, I can serve 6 people.

But hang on. What if I told you that 1 cup of macaroni to every 2 persons is the same ratio as 3:6? Well, it’s the same ratio. 3:6 can be reduced to 1:2 because both 3 and 6 are divisible by 3, which is how we get \(\frac{1}{2}\). So, even though these two ratios look different, they are actually the same.

Let’s take a look at a few word problems, and practice working through them.

Example Problem 1

There are 7 kids in a classroom with green shirts, 8 with red shirts, and 10 with yellow shirts. What is the ratio of people with red and yellow shirts? 7:10 8:7 8:10 4:5

Alright, so let’s look at our problem, and see what it is asking us to find, and write out the information that we have been given.

So, there are 7 kids with green shirts; so, let’s write that down. We have Green: 7. We have 8 kids with red shirts, so that is Red: 8, and we have 10 kids with yellow shirts, Yellow: 10.

solving ratios word problems

So now let’s look at each of our options and eliminate. It can’t be 7:10, we don’t care about the green shirts. It can’t be 8:7, because again we don’t care about the green shirts. Option C is correct; that is the exact number ratio we found. Now, look closely at D here. Is 4:5 not the same thing as 8:10? 8 and 10 are both divisible by 2, and when we reduce them both down we get 4:5, so D is also correct!

Great, now let’s look at another word problem.

Example Problem 2

A vegetable tray contains 12 baby carrots, 27 cherry tomatoes, 18 florets of broccoli, and 45 slices of red bell peppers. For every 2 baby carrots, there are 3_____.

Alright, let’s start off the same way that we did our last problem; read through the problem, write down what we know, and find out what is being asked.

So, this vegetable tray contains 12 baby carrots. It contains 27 cherry tomatoes. We have 18 broccoli florets and 45 slices of red bell peppers.

solving ratios word problems

When we look at all of our information written down, we can see that we have 18 broccoli florets; so there is our answer. For every 2 baby carrots, there are 3 broccoli florets.

Another way to check and verify that these two ratios are equal is by setting them up in fraction form and cross multiplying.

\(\frac{2}{3}=\frac{12}{18}\)

When we cross multiply, we get \(36=36\).

You can practice finding ratios anywhere you go, like finding the ratio of boys to girls in your class.

I hope that this video helped you to understand how to solve word problems with ratios.

See you guys next time!

Frequently Asked Questions

How do you figure out ratios.

A ratio is simply a comparison between two amounts. When figuring out ratios, it is important to consider what two values are being compared. This can be expressed in fraction form, in word form, or simply by using a colon.

When writing a ratio that is comparing a “part” to the “whole”, list the “part” first, and the “whole” second. For example, if you eat \(3\) slices of pizza out of \(10\) slices total, you have eaten \(3\) out of \(10\) slices. This can be expressed as \(\frac{3}{10}\) or \(3\):\(10\), where the part is listed first, and the whole is listed second.

Ratios can also be “part” to “part” comparisons. For example, if there are \(7\) boys in a class, and \(9\) girls in a class, the ratio of boys to girls is \(7\):\(9\). Make sure to match the order of the ratio to the order presented in the scenario.

What are basic ratios?

Ratios are used to directly compare two amounts. Basic ratios are used in many real-world situations, which makes it a valuable skill to master. Basic ratios can be expressed as fractions, words, or by using a colon. For example, \(\frac{4}{5}\), “four to five”, and \(4\):\(5\), all represent the same ratio.

What are the 3 ways to write a ratio?

A ratio is the comparison between two quantities. There is more than one way to write a ratio. For example, ratios can be written using a fraction bar, using a colon, or using words.

\(\frac{5}{8}\) \(5\):\(8\) \(\text{five to eight}\)

What are equivalent ratios?

Ratios that have the same value are considered equivalent ratios . For example, if you slice a cake into \(10\) pieces, and you eat \(2\) pieces, you have eaten “\(2\) out of \(10\)” pieces, or \(2\):\(10\). If you had sliced the cake into \(20\) pieces, and eaten \(4\) pieces, you would have eaten the same amount of cake. Eating “4 out of 20” pieces is the same amount as eating “2 out of 10” pieces. Equivalent ratios occur when you multiply or divide both quantities of the ratio by the same amount. \(\frac{50}{100}\) is equivalent to \(\frac{5}{10}\) because when you divide both quantities of the ratio by \(10\), the result is \(\frac{5}{10}\).

How do you find an equivalent ratio?

Equivalent ratios can be thought of as equivalent fractions. Two ratios are equivalent if they represent the same amount. For example \(\frac{1}{2}\) and \(\frac{5}{10}\) are equivalent because they represent the same amount. Equivalent ratios are found by multiplying or dividing the numerator and denominator by the same amount. For example, \(3\):\(4\) and \(15\):\(20\) are equivalent ratios because both values in \(3\):\(4\) can be multiplied by \(5\) in order to create the ratio \(15\):\(20\).

How do you solve ratio word problems?

Ratios have many real-world applications. Word problems that involve ratios will usually require you to find an unknown value by finding an equivalent ratio.

For example, if you made \($170\) washing \(10\) cars, how much money did you make per car? The ratio of dollars earned compared to cars washed is \(\frac{170}{10}\). We can divide both of these values by \(10\) in order to solve for the dollars earned for washing \(1\) car. \(\frac{170\div10}{10\div10}=\frac{17}{1}\). This means that \($17\) was earned per car. Many word problems involving ratios require you to create equivalent ratios. Remember, as long as you multiply or divide both values of a ratio by the same amount, you have not changed the ratio.

How do you write a ratio in words?

Ratios are used to compare two quantities. There are generally two ways to write a ratio in word form. When a ratio is considered a “part-out-of-whole” ratio, the phrase “out of” can be used. For example, if there is a pizza with \(8\) slices, and you eat \(2\) of those slices, you have eaten “\(2\) out of \(8\)” slices. However, some ratios are considered “part-to-part” ratios. For example, when comparing \(3\) green marbles to \(8\) red marbles, the phrase “\(3\) to \(8\)” can be used.

How do you explain ratios and proportions?

Ratios describe the relationship between two amounts. Ratios can be described as part-to-part or part-to-whole. For example, in a new litter of puppies, \(4\) of the pups are female and \(3\) of the pups are male. The part-to-part ratio \(4\):\(3\) would be used to compare female to male pups. When comparing female pups to the whole liter, the part-to-whole ratio \(4\):\(7\) would be used. Similarly, the ratio of male pups to total pups would be \(3\):\(7\). If two ratios are equivalent, they are said to be proportional. For example, if \(50\) meters of rope weighs \(5\) kilograms, and \(150\) meters of rope weighs \(15\) kilograms, the two amounts are proportional. \(50\):\(5\) is equivalent to \(150\):\(15\) because both values of the first ratio are multiplied by \(3\) in order to create the second ratio.

What is a ratio, short answer?

A ratio is a comparison between two amounts. Ratios can be written using a fraction bar \((\frac{3}{4})\), using a colon (\(3\):\(4\)), or using words (“three to four”). Ratios can be “part-to-part” or “part-to-whole”. For example, \(5\) green marbles and \(7\) red marbles would be a “part-to-part” ratio (\(5\):\(7\)). Solving \(95\) problems correctly out of \(100\) on a math test would be a “part-to-whole” ratio (\(95\):\(100\)).

Ratio Word Problems

  Cross multiply in order to determine which pair of ratios are equivalent.

3:5 and 4:9

6:7 and 7:8

7:8 and 35:40

12:25 and 14:17

The correct answer is 7:8 and 35:40. We can use cross multiplication to determine if two ratios are equivalent. Let’s look at the ratios for Choice C, and let’s set these up as fractions: \(\frac{7}{8}\) and \(\frac{35}{40}\)

Now, cross multiply by finding the product of \(8×35\) and \(7×40\). In both cases our product is 280, so we know that the original ratios are equivalent.

  Which ratio is equivalent to \(\frac{36}{45}\)?

The correct answer is 4:5. We can simplify ratios with the same strategy that we use to simplify fractions. In the ratio \(\frac{36}{45}\) we can divide the numerator and denominator by 9. \(\frac{36}{45}\) now becomes \(\frac{4}{5}\) or 4:5.

  James has a bag full of red, blue, and yellow candy. There are 10 red candies, 9 blue candies, and 11 yellow candies. What is the ratio of blue candies to total candies in the bag? Simplify the ratio if possible.

The correct answer is 3:10. The total number of blue candies is 9, and the total number of candies in the bag is 30. If we set this ratio up as a fraction, we have \(\frac{9}{30}\). This fraction can be simplified if we divide the numerator and denominator by 3. Our final answer is \(\frac{3}{10}\) or 3:10.

  Alex is counting the coins in his pocket, and finds that he has 14 quarters, 7 nickels, and 4 dimes. What is the ratio of quarters to nickels? Simplify if possible.

The correct answer is 2:1. We can compare the number of quarters to the number of nickels by setting up a ratio. There are 14 quarters and 7 nickels, so our ratio would be 14:7. Choice B says 14:7, but we should simplify when possible. 14:7 simplifies to 2:1.

  In Mr. Jenkin’s 4th grade class there are 14 boys and 17 girls. What is the ratio of boys to girls? Simplify if possible.

The correct answer is 14:17. We can express this comparison of boys to girls as a ratio. 14 boys and 17 girls can be described as the ratio 14:17, or the fraction \(\frac{14}{17}\). 14 and 17 do not have any factors in common, so 14:17 is in simplest form.

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Word Problems Involving Rates and Ratios

Word Problems Involving Rates and Ratios

The ratio is to compare two numbers. Rate is one type of ratio and is used to measure the variety of one thing or quantity in comparison to other. Word problems involving comparing rates deal with distances, time, rates, wind or water current, money, and age.

A step-by-step guide to solving rates and ratios word problems

To solve the word problems involving rates and ratios, follow these steps: Step 1: Find the known ratio and the unknown ratio. Step 2: Write the proportion. Step 3: Use cross-multiply and solve. Step 4: Plug the result into the unknown ratio to check the answers.

Word Problems Involving Rates and Ratios – Examples 1

If 11 apple pies cost $88, what will 8 apple pies cost? Solution: Write as a rate. \(\frac{88÷11}{11÷11}=\frac{8}{1}\) Write a proportion to know the cost of 8 apple pies. \(\frac{8}{1}=\frac{x}{6}→8×6=1×x→x=48\)

Word Problems Involving Rates and Ratios – Examples 2

If 6 cookbooks cost $120, how much would a dozen cookbooks cost? Solution: Write as a rate. \(\frac{120÷6}{6÷6}=\frac{20}{1}\) Write a proportion to know the cost of 12 cookbooks. \(\frac{20}{1}=\frac{x}{12}→20×12=1×x→x=240\)

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Welcome to our Ratio Word Problems page. Here you will find our range of 6th 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. They are aimed at students in 6th grade.

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

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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
  • Unit Rate Problems 6th Grade

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Take a look at our percentage worksheets for finding the percentage of a number or money amount.

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Ratio word problems

Ratios, Proportions and Problem Solving Workbook

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Use ratios to solve these word problems

Students can use simple ratios to solve these word problems ; the arithmetic is kept simple so as to focus on the understanding of the use of ratios.

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24 Ratio Word Problems for Year 6 to Year 8 With Tips On Supporting Pupils’ Progress

Emma johnson.

Ratio word problems are introduced for the first time in upper Key Stage 2. The earliest mention of ‘Ratio’ in the National Curriculum is in the Year 6 programme of study, where a whole section is dedicated to Ratio and Proportion.

At this early stage, it is essential to concentrate on the language and vocabulary of ratio. Children need to be clear on the meaning of the ratio symbol right from the start of the topic. Word problems really help children understand this concept, as they make it much more relevant and meaningful than a ratio question with no context.

Ratio in KS2

Ratio in ks3, why are word problems important for children’s understanding of ratio, how to teach ratio word problem solving in year 6 and early secondary school , ratio word problems for year 6, ratio word problems for year 7, ratio word problems for year 8, more word problems.

Concrete resources and pictorial representations are key to the success of children’s early understanding of ratio. These resources are often used in word problems for year 3 , word problems for year 4 and word problems for year 5 . There is often a misconception amongst upper Key Stage 2 teachers and students, that mathematical equipment is only for children who struggle in maths. However, all students should be introduced to this new concept through resources, such as two-sided counters and visual representations, such as bar models as this can help with understanding basic mathematical concepts such as addition and subtraction word problems .

All Kinds of Word Problems Four Operations

Download this free pack of mixed word problems covering all four operations. Test your student's problem solving skills over a range of topics.

As pupils progress into Key Stage 3, they continue to build on their knowledge and understanding of ratio. As students move away from the practical and visual resources, word problems continue to be a key element to any lessons involving ratio. As students move into Key Stage 4, they continue to build on this knowledge of ratio and can expect to encounter ratio and proportion word problems in their GCSE maths exams. 

Ratio word problems are an essential component of any lessons on ratio, to help children understand how ratio is used in real-life. To help you with this, we have put together a collection of 24 word problems including multi-step word problems , which can be used by pupils from Year 6 to Year 8.

Ratio word problems in the National Curriculum

Children are first introduced to ratio and ratio problems in Year 6. The National Curriculum expectations for ratio are that students will be able to:

  • solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts
  • solve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison
  • solve problems involving similar shapes where the scale factor is known or can be found
  •  solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

Students in Key Stage 3 continue to build on their knowledge of ratio from primary. The expectations for Years 7 and 8 are that pupils will:

  •  Use scale factors, scale diagrams and maps
  • Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
  •  Use ratio notation, including reduction to simplest form
  •  Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
  •  Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction.
  •  Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions.
  • Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics.

Solving word problems are important for helping children to develop their understanding of ratio and the different ways ratio is used in everyday life. Without this context, ratio can be quite an abstract concept, which children find difficult to understand. Word problems bring ratio to life and enable students to see how they will make use of this skill outside the classroom.

Third Space Learning’s online one-to-one tuition programme relates maths concepts to real life situations to deepen conceptual understanding. Personalised fill the gaps in each individual student’s maths knowledge, our programmes help to build skills and confidence.

It is important children learn the skills needed to solve ratio word problems. As with any maths problem, children need to make sure they have read the questions carefully and thought about exactly what is being asked and whether they have fully understood this. The next step is to identify what they will need to do to solve the problem and whether there are any concrete resources or pictorial representations which will help them. Even older pupils can benefit from drawing a quick sketch to understand what a problem is asking.

Here is an example:

 Jamie has a bag of red and yellow sweets.

For every red sweet there are 2 yellow sweets.

If the bag has 6 red sweets. How many sweets are in the whole bag?

How to solve:

What do you already know?

  • We know that for every red sweet there are 2 yellow sweets.
  • If there are 6 red sweets, we need to work out how many yellow sweets there must be. 
  • If there are 2 yellow sweets for each 1 red sweet, then we must need to multiply 2 by 6, to work out how many yellow sweets there are with 6 red sweets.
  • Once we have worked out the total number of yellow sweets (12), we then need to add this to the 6 red sweets, to work out how many sweets are in the bag altogether.
  • If there are 6 red sweets and 12 yellow sweets, there must be 18 sweets in the bag altogether.

  How can this be represented pictorially?

  • We can use the two-sided counters to represent the red and yellow sweets.
  • If we put down 1 red counter and 2 yellow counters.
  • We then need to repeat this 6 times, until there are 6 red counters and 12 yellow counters.
  • We can now visually see the answer to the word problem and that there are now a total of 18 counters (18 sweets in the bag).

Word problems for year 6 often incorporate multiple skills: a ratio word problem may also include elements from multiplication word problems , division word problems , percentage word problems and fraction word problems .

Sophie was trying to calculate the number of students in her school.

She found the ratio of boys to girls across the school was 3:2

If there were 120 boys in the school

  • How many girls were there?
  • How many students were there altogether?

Answer: a) 80 b) 200

This can be shown as a bar model.

120 ÷ 3 = 40

40 x 2 = 80

  • 200 students altogether

120 boys + 80 girls = 200

Pupils on the Eco Committee in Year 6 wanted to investigate how many worksheets were being printed each week.

They found that there were 160 maths worksheets and 80 English worksheets

What is the ratio of maths to English worksheets?

Answer: 2:1

Ratio of 160:80 

This can be simplified to 2:1 by dividing both 160 and 80 by 80

The Year 6 football club has 30 members. The ratio of boys to girls is 4:1. How many boys and girls are in the club?

Answer: 24 boys and 6 girls

The ratio of 4:1 has 5 parts

Boys: 4 x 6 = 24

Girls 1 x 6 = 6

Yasmine has a necklace with purple and blue beads.

The ratio of purple:blue beads  = 1:3

There are 24 beads on the necklace. How many purple and blue beads are there?

Answer: 6 purple beads and 18 blue beads

The ratio of 1:3 has 4 parts

24 ÷ 4 = 6 beads per part

Purple: 1 x 6 = 6

Blue 3 x 6 = 18

Maisie drives past a field of sheep and cows.

She works out that the ratio of sheep to cows is 3:1

If there are 5 cows in the field, how many sheep are there?

Answer: 15 sheep

If there are 5 cows in the field, the 1 has been multiplied by 5.

We need to also multiply the 3 by 5, which is 15

At a party there is a choice of 3 flavours of jelly – orange, blackcurrant and lemon,

The ratio of the jellies are 3:2:1 (orange: blackcurrant: lemon)

If there are 9 orange jellies. How many blackcurrant and lemon jellies are there?

Answer: 6 blackcurrant and 3 lemon jellies

To get 9 jellies, we need to multiply 3 by 3. This means we need to multiply 2 x 3 = 6 and 1 x 3 = 3

The school photocopier prints out 150 sheets in 3 minutes.

How many sheets can it print out in 15 minutes?

Answer: 750 sheets in 15 minutes

We need to multiply 3 by 5 to get 15 minutes. This means we also need to multiply 150 by 5 = 750

Mason carried out a survey of the favourite sports of children in Year 6.

For every 3 students who chose football, 2 chose swimming and 1 chose basketball.

12 children chose football. How many took part in the survey altogether?

Answer: 24 children took part in the survey.

If we multiply 3 by 4, we get to the 12 students who chose football. 

We need to also multiply the 2 by 4 (8 children chose swimming) and the 1 by 4 (4 children chose swimming)

12 + 8 + 4 = 24

David has 2 grandchildren: Maisie (age 6) and Lottie (age 3)

He decides to share £60 between the 2 children in a ratio of their ages.

How much does each child get?

Answer: Maisie gets £40, Lottie gets £20

Ratio of 2:1 = 3 parts

60 ÷ 3 = £20 per part

Maisie: 2 x 20 = £40

Lottie: 1 x 20 = £20

A rectangle has the ratio of width to length 2:3. If the perimeter of the rectangle is 50cm, what’s the area?

Answer: Area: 150cm^{2}

Width: 10cm

Length: 15cm

Divide 50 by 5 to work out 1 part = 10

The 2 widths must by 2 x 10 = 20

The 2 lengths must be 3 x 10 = 30

To work out the width of 1 side, divide the 20 by 2 = 10

To work out the length of 1 side, divide the 30 by 2 = 15

Area: 10 x 15 = 150cm2

In Bethany’s class there are 20 girls and 12 boys.

Write down the ratio of girls to boys in the simplest form

Answer: 5:3

(Divide both sides by 4 = 5:3)

A piece of ribbon is 45cm long.

It has been cut into 3 smaller pieces in a ratio of 4:3:2

How long is each piece?

Answer: 20cm, 15cm and 10cm

4:3:2 =9 parts: 45 ÷ 9 = 5cm per part

4 x 5 = 20cm

3 x 5 = 15cm

2 x 5 = 10cm

Chloe is making a smoothie for her and her 3 friends.

She has the recipe for making a smoothie for 4 people: 240ml yoghurt, 120 ml milk, 300ml apple juice, 180g strawberries and 1 table spoon of sugar.

  • How much yoghurt would be needed to make a smoothie for 8 people.
  • How many g of strawberries are needed to make the smoothie for 2 people?
  • 480 ml yoghurt 

240ml x 2 = 480

  • 90g strawberries

180 ÷ 2 = 90

The ratio of cups of flour:cups of water in the recipe for making the dough for a pizza base is 7:4.

The pizza restaurant needs to make a large quantity of pizzas  and is using 42 cups of flour. How much water will be needed?

Answer: 24 cups of water

Multiply 7 by 6 to get 42 cups of flour.

We therefore need to also multiply the 4 by 6 to work out how many cups of water are needed.

Ahmed shared £56 between him and Hamza in a ratio of 3:5 (3 for Hamza and 5 for him).

How much did each get?

Answer: Ahmed got £35, his brother got £21

Ratio of 3:5 = 8 parts

56 ÷ 8 = £7 per part

3 x 7 =£ 21

5 x 7 = £35

Amber and Holly share some money in a ratio of 5:7

If Amber gets £30. How much do they have between them to share?

Answer: £72

Amber gets £30 which is 5 parts: 30 ÷ 5 = 6

Holly gets 7 x 6 = £42

£30 + £42 = £72       

Two companies are making an orange coloured paint.

Company A makes the orange paint by mixing red and yellow paint in a ratio of 5:7

Company B makes the orange paint by mixing red and yellow paint in a ratio of 3:4.

Which company uses a higher proportion of red paint to make the orange?

Answer: Company B uses more red paint.

Company A: 5:7 = \frac{5}{12} is red

Company B: 3:4 = \frac{3}{7} is red

We can compare the fractions by giving them the same denominator, to find the equivalent fractions.

Students in a school have to choose one Humanities subject – History or Geography.

The ratio of boys to girls is 5:4 and \frac{3}{5} of the girls study History.

There are 225 students in the year. How many girls study History?

Answer: 60 girls study History

The ratio of 5:4 has 9 parts. Divide 225 by 9 to work out 1 part = 25

There are 5 x 25 boys = 125  and 4 x 24 girls = 100

\frac{3}{5} of 100 = 60

The angles in a triangle are in the ratio of 3:4:5 for angles A, B and C

Calculate the size of each angle.

Angle A: 45°

Angle B: 60°

Angle C: 75°

3:4:5 = 12 parts.   180 ÷ 12 = 15 (each part is worth 15°)

3 x 15 = 45

4 x 15 = 60

5 x 15 = 75

The audience in a theatre has a ratio of 2:1 adults to children.

There are 2,250 people in the audience.

The cost of an adult ticket is £10 and a child ticket is £5

How much money did the theatre make from the ticket sales

Answer: £18,750

2250 ÷ 3 = 750 people per part

Number of adults: 2 x 750 = 1500          Number of children: 1 x 750 = 750

Cost of adult tickets = 1500 x £10 = £15,000    Cost of child tickets = 750 x £5 = £3,750

Total cost: £15,000 + £3,750 = £18,750

Sophia and Jessica collect stickers and stamps.

Altogether they have the same number of stickers as stamps.

The ratio of stickers Sophia has to the stickers Jessica has is 3:7. 

The ratio of stamps Sophia has to stamps Jessica has is 1:4

Show Jessica has more stamps than stickers.

Answer: 

Ratio of stickers to stickers has 10 parts

Ratio of stamps to stamps has 5 parts.

To make the stamps equivalent to the stickers, they need to be doubled – 1:4 becomes 2:8, compared to 3:7 stickers, therefore, Jessica has more stamps than stickers.

A drink is made by mixing pineapple and lemonade in the ratio of 1:4. 

Pineapple costs £1.50 per litre. Lemonade costs £1.30 per litre (Bottles are sold in 1 litre containers)

How much will it cost to make 4 litres of drink?

Answer: £6.70

Ratio of pineapple to lemonade has 5 parts

4l of drink = 4000 ml. 1 part = 4000 ÷ 5 = 800

Pineapple = 1 x 800 = 800ml

Lemonade = 4 x 800 = 3200ml

1 Bottle of pineapple will be needed (£1.50) and 4 bottles of lemonade (4 x £1.30 = £5.20)

Total cost = £1.50 + £5.20 = £6.70

The ratio of Amber’s age to Zymal’s age is 5:7

If Zymal is 12 years older than Amber, how old are both Amber and Zymal

Answer: Amber: 30 years & Zymal: 42 years

Zymal is 12 years older. This means that the 2 parts more in the ratio  of 5:7 must be worth 12 years. Therefore, 1 part = 6 years.

Amber is 5 x 6 = 30 years

Zymal is 7 x 6 = 42 years

Hamza, Jude and Adam are collecting red and yellow leaves for an art project.

In total they collect the same number of red and yellow leaves.

The 3 boys  collect red leaves in a ratio of 4:7:9 and yellow leaves in a ratio of 3:1:5 (Hamza:Jude:Adam)

Did Hamza collect more red leaves or yellow leaves?

Answer: Hamza collected more yellow leaves (60 yellow, compared to 36 red)

Red leaves have a ratio of 20 parts, yellow leaves have a ratio of 9 parts. To make them both equivalent, they both need to have 180 parts (20 x 9 = 180) and (9 x 20 = 180)

4:7:9 = 20 parts red leaves. Multiply each part by 9 36:63:81

3:1:5= 9 parts yellow leaves. Multiply each part by 20 = 60:20:100

Hamza collected more yellow leaves (60 yellow leaves and 36 red leaves)

Looking for word problems on more topics? Take a look at our practice problems for Years 3-6 including money word problems , time word problems , addition word problems and subtraction word problems .

Do you have students who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of students across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to address learning gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary students become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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Course: praxis core math   >   unit 1.

  • Rational number operations | Lesson
  • Rational number operations | Worked example

Ratios and proportions | Lesson

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  • Percentages | Lesson
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  • Rates | Lesson
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  • Naming and ordering numbers | Lesson
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  • Number concepts | Lesson
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  • Counterexamples | Lesson
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  • Pre-algebra word problems | Lesson
  • Pre-algebra word problems | Worked example
  • Unit reasoning | Lesson
  • Unit reasoning | Worked example

What are ratios and proportions?

What skills are tested.

  • Identifying and writing equivalent ratios
  • Solving word problems involving ratios
  • Solving word problems using proportions

How do we write ratios?

  • The ratio of lemon juice to sugar is a part-to-part ratio. It compares the amount of two ingredients.
  • The ratio of lemon juice to lemonade is a part-to-whole ratio. It compares the amount of one ingredient to the sum of all ingredients.
  • Determine whether the ratio is part to part or part to whole.
  • Calculate the parts and the whole if needed.
  • Plug values into the ratio.
  • Simplify the ratio if needed. Integer-to-integer ratios are preferred.

How do we use proportions?

  • Write an equation using equivalent ratios.
  • Plug in known values and use a variable to represent the unknown quantity.
  • If the numeric part of one ratio is a multiple of the corresponding part of the other ratio, we can calculate the unknown quantity by multiplying the other part of the given ratio by the same number.
  • If the relationship between the two ratios is not obvious, solve for the unknown quantity by isolating the variable representing it.
  • (Choice A)   1 : 4 ‍   A 1 : 4 ‍  
  • (Choice B)   1 : 2 ‍   B 1 : 2 ‍  
  • (Choice C)   1 : 1 ‍   C 1 : 1 ‍  
  • (Choice D)   2 : 1 ‍   D 2 : 1 ‍  
  • (Choice E)   4 : 1 ‍   E 4 : 1 ‍  
  • (Choice A)   1 6 ‍   A 1 6 ‍  
  • (Choice B)   1 3 ‍   B 1 3 ‍  
  • (Choice C)   2 5 ‍   C 2 5 ‍  
  • (Choice D)   1 2 ‍   D 1 2 ‍  
  • (Choice E)   2 3 ‍   E 2 3 ‍  
  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

Things to remember

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  2. How to Solve Ratio Problems Easily: Try These Tricks!

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  3. Ratio and Proportion Word Problems

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  4. Free worksheets for ratio word problems

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  5. Ratio and Rates Word Problems worksheets

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VIDEO

  1. 10

  2. Equivalent Ratios Word Problems- Part 2 (2023)

  3. Grade 7

  4. Word problems in ratio

  5. Math II 6.1 Ratios and Proportions

  6. Word Problem

COMMENTS

  1. Ratio Word Problems (video lessons, examples and solutions)

    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 ...

  2. Free worksheets for ratio word problems

    Find here an unlimited supply of worksheets with simple word problems involving ratios, meant for 6th-8th grade math. In level 1, the problems ask for a specific ratio (such as, "Noah drew 9 hearts, 6 stars, and 12 circles. What is the ratio of circles to hearts?"). In level 2, the problems are the same but the ratios are supposed to be simplified.

  3. Ratio Problem Solving

    Ratio problem solving is a collection of ratio and proportion 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. ...

  4. How to Solve Ratio Word Problems

    Solving Ratio Word Problems. To use proportions to solve ratio word problems, we need to follow these steps: Identify the known ratio and the unknown ratio. Set up the proportion.

  5. Ratio Word Problems Solved

    Write the ratio of girls to boys in his class. Reduce your answer to its simplest form. Solution: Total number of students = 16. Number of girls = 10. Number of boys = 16 - 10 = 6. Thus the ratio of girls to boys is 10 6 = 5 3. A bag containing chocolates is divided into a ratio of 5:7. If the larger part contains 84 chocolates, find the ...

  6. Part to whole ratio word problem using tables

    Discover how to solve ratio problems with a real-life example involving indoor and outdoor playtimes. Learn to use ratios to determine the number of indoor and outdoor playtimes in a class with a 2:3 ratio and 30 total playtimes. ... What you need to do in any word problem involving the ratios is exactly the same. Take the entire amount and ...

  7. Equivalent ratio word problems (video)

    Equivalent ratio word problems. Google Classroom. 0 energy points. About About this video Transcript. This video teaches solving ratio word problems, using examples like Yoda Soda for guests, fish ratios in a tank, ice cream sundae ingredients, and dog color ratios at a park. Mastering these techniques helps students tackle real-world math ...

  8. Equivalent ratio word problems (practice)

    Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

  9. Solve Ratio Word Problems

    In this video I'll show you how to solve multiple types of Ratio Word Problems using 5 examples. We'll start simple and work up to solving the most complex p...

  10. Solving Ratio Word Problems (the easy way!)

    This video focuses on how to solve ratio word problems. In particular, I show students the trick of multiplying each term in the ratio by x to help set up an...

  11. Ratios

    Learn all about ratios and solving ratio word problems. Check out all my videos at http://YouTube.com/MathMeeting

  12. Solving Word Problems with Ratios

    A. A ratio is simply a comparison between two amounts. When figuring out ratios, it is important to consider what two values are being compared. This can be expressed in fraction form, in word form, or simply by using a colon. When writing a ratio that is comparing a "part" to the "whole", list the "part" first, and the "whole ...

  13. Word Problems Involving Rates and Ratios

    Word problems involving comparing rates deal with distances, time, rates, wind or water current, money, and age. A step-by-step guide to solving rates and ratios word problems. To solve the word problems involving rates and ratios, follow these steps: Step 1: Find the known ratio and the unknown ratio. Step 2: Write the proportion.

  14. 24 Ratio Word Problems for Grades 5-7

    Ratios in 7th grade. Students in 7th grade continue to build on their knowledge of ratio from 6th grade. Calculate unit rates and solve problems for ratios comparing two fractions. Solve problems involving proportional relationships. Solve problems involving percentage change, including: percentage increase, decrease and original value problems ...

  15. Ratios and rates

    Pre-algebra 15 units · 179 skills. Unit 1 Factors and multiples. Unit 2 Patterns. Unit 3 Ratios and rates. Unit 4 Percentages. Unit 5 Exponents intro and order of operations. Unit 6 Variables & expressions. Unit 7 Equations & inequalities introduction. Unit 8 Percent & rational number word problems.

  16. Ratio Word Problems

    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. They are aimed at students in 6th grade. Each problem sheet comes complete with an answer sheet. Using ...

  17. Ratio word problems

    K5 Learning offers free worksheets, flashcards and inexpensive workbooks for kids in kindergarten to grade 5. Become a member to access additional content and skip ads. Ratio word problems. Students can use simple ratios to solve these word problems; the arithmetic is kept simple so as to focus on the understanding of the use of ratios.

  18. Ratio and Proportion Word Problems

    This math video tutorial provides a basic introduction into ratio and proportion word problems. Here is a list of examples and practice problems:Percentages...

  19. 24 Ratio Word Problems for Year 6 to Year 8

    How to teach ratio word problem solving in Year 6 and early secondary school . It is important children learn the skills needed to solve ratio word problems. As with any maths problem, children need to make sure they have read the questions carefully and thought about exactly what is being asked and whether they have fully understood this.

  20. How to Solve Ratio Word Problems

    http://www.mathtestace.comhttp://www.mathtestace.com/fraction-word-problems/Need help solving word problems with ratios and fractions? This video will walk y...

  21. Solving Ratio Word Problems: A Practical Approach

    Ratio word problems provide real-life scenarios that involve ratios, allowing us to apply mathematical concepts to solve problems in various contexts. In this lesson, we will explore ratio word problems in detail, including definitions, step-by-step processes, relevant formulas, and practical examples.

  22. Ratios and proportions

    Things to remember. A ratio is a comparison of two quantities. A proportion is an equality of two ratios. To write a ratio: Determine whether the ratio is part to part or part to whole. Calculate the parts and the whole if needed. Plug values into the ratio. Simplify the ratio if needed.

  23. Ratio Word Problems

    This video focuses on how to solve ratio word problem in algebra 1. I show how to carefully translate the verbal portions of the problem in algebraic express...