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Ratio Problem Solving
Here we will learn about ratio problem solving, including how to set up and solve problems. We will also look at real life ratio problems.
There are also ratio problem solving worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
What is ratio problem solving?
Ratio problem solving is a collection of word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.
A ratio is a relationship between two or more quantities . They are usually written in the form a:b where a and b are two quantities. When problem solving with a ratio, the key facts that you need to know are,
- What is the ratio involved?
- What order are the quantities in the ratio?
- What is the total amount / what is the part of the total amount known?
- What are you trying to calculate ?
As with all problem solving, there is not one unique method to solve a problem. However, this does not mean that there aren’t similarities between different problems that we can use to help us find an answer.
The key to any problem solving is being able to draw from prior knowledge and use the correct piece of information to allow you to get to the next step and then the solution.
Let’s look at a couple of methods we can use when given certain pieces of information.
When solving ratio problems it is very important that you are able to use ratios. This includes being able to use ratio notation.
For example, Charlie and David share some sweets in the ratio of 3:5. This means that for every 3 sweets Charlie gets, David receives 5 sweets.
Charlie and David share 40 sweets, how many sweets do they each get?
We use the ratio to divide 40 sweets into 8 equal parts.
Then we multiply each part of the ratio by 5.
3 x 5:5 x 5 = 15:25
This means that Charlie will get 15 sweets and David will get 25 sweets.
- Dividing ratios
Step-by-step guide: Dividing ratios (coming soon)
Ratios and fractions (proportion problems)
We also need to consider problems involving fractions. These are usually proportion questions where we are stating the proportion of the total amount as a fraction.
Simplifying and equivalent ratios
- Simplifying ratios
Equivalent ratios
Units and conversions ratio questions
Units and conversions are usually equivalent ratio problems (see above).
- If £1:\$1.37 and we wanted to convert £10 into dollars, we would multiply both sides of the ratio by 10 to get £10 is equivalent to \$13.70.
- The scale on a map is 1:25,000. I measure 12cm on the map. How far is this in real life, in kilometres? After multiplying both parts of the ratio by 12 you must then convert 12 \times 25000=300000 \ cm to km by dividing the solution by 100 \ 000 to get 3km.
Notice that for all three of these examples, the units are important. For example if we write the mapping example as the ratio 4cm:1km, this means that 4cm on the map is 1km in real life.
Top tip: if you are converting units, always write the units in your ratio.
Usually with ratio problem solving questions, the problems are quite wordy . They can involve missing values , calculating ratios , graphs , equivalent fractions , negative numbers , decimals and percentages .
Highlight the important pieces of information from the question, know what you are trying to find or calculate , and use the steps above to help you start practising how to solve problems involving ratios.
How to do ratio problem solving
In order to solve problems including ratios:
Identify key information within the question.
Know what you are trying to calculate.
Use prior knowledge to structure a solution.
Explain how to do ratio problem solving
Ratio problem solving worksheet
Get your free ratio problem solving worksheet of 20+ questions and answers. Includes reasoning and applied questions.
Related lessons on ratio
Ratio problem solving is part of our series of lessons to support revision on ratio . You may find it helpful to start with the main ratio lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
- How to work out ratio
- Ratio to fraction
- Ratio scale
- Ratio to percentage
Ratio problem solving examples
Example 1: part:part ratio.
Within a school, the number of students who have school dinners to packed lunches is 5:7. If 465 students have a school dinner, how many students have a packed lunch?
Within a school, the number of students who have school dinners to packed lunches is \bf{5:7.} If \bf{465} students have a school dinner , how many students have a packed lunch ?
Here we can see that the ratio is 5:7 where the first part of the ratio represents school dinners (S) and the second part of the ratio represents packed lunches (P).
We could write this as
Where the letter above each part of the ratio links to the question.
We know that 465 students have school dinner.
2 Know what you are trying to calculate.
From the question, we need to calculate the number of students that have a packed lunch, so we can now write a ratio below the ratio 5:7 that shows that we have 465 students who have school dinners, and p students who have a packed lunch.
We need to find the value of p.
3 Use prior knowledge to structure a solution.
We are looking for an equivalent ratio to 5:7. So we need to calculate the multiplier. We do this by dividing the known values on the same side of the ratio by each other.
So the value of p is equal to 7 \times 93=651.
There are 651 students that have a packed lunch.
Example 2: unit conversions
The table below shows the currency conversions on one day.
Use the table above to convert £520 (GBP) to Euros € (EUR).
Use the table above to convert \bf{£520} (GBP) to Euros \bf{€} (EUR).
The two values in the table that are important are GBP and EUR. Writing this as a ratio, we can state
We know that we have £520.
We need to convert GBP to EUR and so we are looking for an equivalent ratio with GBP = £520 and EUR = E.
To get from 1 to 520, we multiply by 520 and so to calculate the number of Euros for £520, we need to multiply 1.17 by 520.
1.17 \times 520=608.4
So £520 = €608.40.
Example 3: writing a ratio 1:n
Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the 500ml of concentrated plant food must be diluted into 2l of water. Express the ratio of plant food to water respectively in the ratio 1:n.
Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the \bf{500ml} of concentrated plant food must be diluted into \bf{2l} of water . Express the ratio of plant food to water respectively as a ratio in the form 1:n.
Using the information in the question, we can now state the ratio of plant food to water as 500ml:2l. As we can convert litres into millilitres, we could convert 2l into millilitres by multiplying it by 1000.
2l = 2000ml
So we can also express the ratio as 500:2000 which will help us in later steps.
We want to simplify the ratio 500:2000 into the form 1:n.
We need to find an equivalent ratio where the first part of the ratio is equal to 1. We can only do this by dividing both parts of the ratio by 500 (as 500 \div 500=1 ).
So the ratio of plant food to water in the form 1:n is 1:4.
Example 4: forming and solving an equation
Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their age. Kieran is 3 years older than Josh. Luke is twice Josh’s age. If Josh receives £8 pocket money, how much money do the three siblings receive in total?
Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their ages. Kieran is \bf{3} years older than Josh . Luke is twice Josh’s age. If Luke receives \bf{£8} pocket money, how much money do the three siblings receive in total ?
We can represent the ages of the three siblings as a ratio. Taking Josh as x years old, Kieran would therefore be x+3 years old, and Luke would be 2x years old. As a ratio, we have
We also know that Luke receives £8.
We want to calculate the total amount of pocket money for the three siblings.
We need to find the value of x first. As Luke receives £8, we can state the equation 2x=8 and so x=4.
Now we know the value of x, we can substitute this value into the other parts of the ratio to obtain how much money the siblings each receive.
The total amount of pocket money is therefore 4+7+8=£19.
Example 5: simplifying ratios
Below is a bar chart showing the results for the colours of counters in a bag.
Express this data as a ratio in its simplest form.
From the bar chart, we can read the frequencies to create the ratio.
We need to simplify this ratio.
To simplify a ratio, we need to find the highest common factor of all the parts of the ratio. By listing the factors of each number, you can quickly see that the highest common factor is 2.
\begin{aligned} &12 = 1, {\color{red} 2}, 3, 4, 6, 12 \\\\ &16 = 1, {\color{red} 2}, 4, 8, 16 \\\\ &10 = 1, {\color{red} 2}, 5, 10 \end{aligned}
HCF (12,16,10) = 2
Dividing all the parts of the ratio by 2 , we get
Our solution is 6:8:5 .
Example 6: combining two ratios
Glass is made from silica, lime and soda. The ratio of silica to lime is 15:2. The ratio of silica to soda is 5:1. State the ratio of silica:lime:soda.
Glass is made from silica, lime and soda. The ratio of silica to lime is \bf{15:2.} The ratio of silica to soda is \bf{5:1.} State the ratio of silica:lime:soda .
We know the two ratios
We are trying to find the ratio of all 3 components: silica, lime and soda.
Using equivalent ratios we can say that the ratio of silica:soda is equivalent to 15:3 by multiplying the ratio by 3.
We now have the same amount of silica in both ratios and so we can now combine them to get the ratio 15:2:3.
Example 7: using bar modelling
India and Beau share some popcorn in the ratio of 5:2. If India has 75g more popcorn than Beau, what was the original quantity?
India and Beau share some popcorn in the ratio of \bf{5:2.} If India has \bf{75g} more popcorn than Beau , what was the original quantity?
We know that the initial ratio is 5:2 and that India has three more parts than Beau.
We want to find the original quantity.
Drawing a bar model of this problem, we have
Where India has 5 equal shares, and Beau has 2 equal shares.
Each share is the same value and so if we can find out this value, we can then find the total quantity.
From the question, India’s share is 75g more than Beau’s share so we can write this on the bar model.
We can find the value of one share by working out 75 \div 3=25g.
We can fill in each share to be 25g.
Adding up each share, we get
India = 5 \times 25=125g
Beau = 2 \times 25=50g
The total amount of popcorn was 125+50=175g.
Common misconceptions
- Mixing units
Make sure that all the units in the ratio are the same. For example, in example 6 , all the units in the ratio were in millilitres. We did not mix ml and l in the ratio.
- Ratio written in the wrong order
For example the number of dogs to cats is given as the ratio 12:13 but the solution is written as 13:12.
- Ratios and fractions confusion
Take care when writing ratios as fractions and vice-versa. Most ratios we come across are part:part. The ratio here of red:yellow is 1:2. So the fraction which is red is \frac{1}{3} (not \frac{1}{2} ).
- Counting the number of parts in the ratio, not the total number of shares
For example, the ratio 5:4 has 9 shares, and 2 parts. This is because the ratio contains 2 numbers but the sum of these parts (the number of shares) is 5+4=9. You need to find the value per share, so you need to use the 9 shares in your next line of working.
- Ratios of the form \bf{1:n}
The assumption can be incorrectly made that n must be greater than 1 , but n can be any number, including a decimal.
Practice ratio problem solving questions
1. An online shop sells board games and computer games. The ratio of board games to the total number of games sold in one month is 3:8. What is the ratio of board games to computer games?
8-3=5 computer games sold for every 3 board games.
2. The volume of gas is directly proportional to the temperature (in degrees Kelvin). A balloon contains 2.75l of gas and has a temperature of 18^{\circ}K. What is the volume of gas if the temperature increases to 45^{\circ}K?
3. The ratio of prime numbers to non-prime numbers from 1-200 is 45:155. Express this as a ratio in the form 1:n.
4. The angles in a triangle are written as the ratio x:2x:3x. Calculate the size of each angle.
5. A clothing company has a sale on tops, dresses and shoes. \frac{1}{3} of sales were for tops, \frac{1}{5} of sales were for dresses, and the rest were for shoes. Write a ratio of tops to dresses to shoes sold in its simplest form.
6. During one month, the weather was recorded into 3 categories: sunshine, cloud and rain. The ratio of sunshine to cloud was 2:3 and the ratio of cloud to rain was 9:11. State the ratio that compares sunshine:cloud:rain for the month.
Ratio problem solving GCSE questions
1. One mole of water weighs 18 grams and contains 6.02 \times 10^{23} water molecules.
Write this in the form 1gram:n where n represents the number of water molecules in standard form.
2. A plank of wood is sawn into three pieces in the ratio 3:2:5. The first piece is 36cm shorter than the third piece.
Calculate the length of the plank of wood.
5-3=2 \ parts = 36cm so 1 \ part = 18cm
3. (a) Jenny is x years old. Sally is 4 years older than Jenny. Kim is twice Jenny’s age. Write their ages in a ratio J:S:K.
(b) Sally is 16 years younger than Kim. Calculate the sum of their ages.
Learning checklist
You have now learned how to:
- Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
- Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
- Make and use connections between different parts of mathematics to solve problems
The next lessons are
- Compound measures
- Best buy maths
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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
Take a look at some more of our worksheets similar to these.
More Ratio & Unit Rate 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
- Unit Rate Problems 6th Grade
6th Grade Percentage Worksheets
Take a look at our percentage worksheets for finding the percentage of a number or money amount.
We have a range of percentage sheets from quite a basic level to much harder.
- Percentage of Numbers Worksheets
- Money Percentage Worksheets
- 6th Grade Percent Word Problems
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Ratio problem solving for 9-1 GCSE with answers
Subject: Mathematics
Age range: 14-16
Resource type: Worksheet/Activity
Last updated
27 September 2017
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clareturnertutor
A good set of ratio questions that require problem-solving. Thank you for sharing.
Empty reply does not make any sense for the end user
Nice selection of questions, thank you.
This is an excellent worksheet for the most able students because it focuses on the harder questions that initially cause them problems that are reasonably easy to overcome.
Lovely selection of questions, thank you.
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IMAGES
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The ratio of green sweets to sweets that are not green is 6: 19 Work out the ratio ofred sweets to blue sweets to green sweets. 5 PBPTS 10 6 Q +0 THE OF (Total for question 7 is 3 marks) 8 A football team plays some games in a season. Each game was a win, a draw or a loss. The ratio ofthe games the won to the games they did not win was 9:7
Sharing between a Ratio. Example 1: Abbie and Ben share £120 in the ratio 2:1. Work out how much each of them get. The first step is to work out how many equal parts there are. The ratio is 2:1 so there are 3 (2 + 1) equal parts. We now need to work out how much each of the parts is worth. We divide the £120 between the 3 parts.
Harder GCSE ratio problem questions including combining ratios, converting ratios to fractions solving problems using ratio. For the full list of videos and ...
40 \div 8=5 40 ÷ 8 = 5. Then you multiply each part of the ratio by 5. 5. 3\times 5:5\times 5=15 : 25 3 × 5: 5 × 5 = 15: 25. This means that Charlie will get 15 15 sweets and David will get 25 25 sweets. There can be ratio word problems involving different operations and types of numbers.
Solving One Step Equations: Exam Questions: Solving One Step Equations: Solutions: Angles: Exam Questions: Angles: ... Writing and Simplifying Ratio: Solutions: Ratio: Exam Questions: Sharing Ratio: Solutions: Proportion: Proportion Ingredients Questions: ... Maths Genie Limited is a company registered in England and Wales with company number ...
The Corbettmaths Textbook Exercise on Ratio: Problem Solving. Welcome; Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. Further Maths; GCSE Revision; Revision Cards; Books; Ratio: Problem Solving Textbook Exercise. Click here for Questions. Textbook Exercise. Previous: Ratio: Difference ...
36 litres = 3 parts. Divide both sides by 3. 12 litres = 1 part. The ratio was 3 : 2. Find the volume of white paint, 2 parts. 2 × 12 = 24. 24 litres of white paint. In total there are 5 parts, so the total volume of paint will be. 5 × 12 = 60.
Ratio problem solving GCSE questions. 1. One mole of water weighs 18 18 grams and contains 6.02 \times 10^ {23} 6.02 × 1023 water molecules. Write this in the form 1gram:n 1gram: n where n n represents the number of water molecules in standard form. (3 marks)
To find the value of one part, divide the difference value (6) by the number of parts that make up the difference (3). 6 ÷ 3 = 2. The value of one part is 2. Image caption, Multiply the value of ...
The trick to ratio problems made easy. Essential skills for GCSE maths. Become a maths genius, get the basics of ratio and proportion correct.Designed by www...
Click here for Answers. . answers. Previous: Ratio: Difference Between Textbook Answers. Next: Reflections Textbook Answers. These are the Corbettmaths Textbook Exercise answers to Ratio: Problem Solving.
You can transform word problems into equations to find a more efficient way of solving these problems. ... You can use a proportion to solve this problem by comparing two ratios. One ratio is 2 short hair to 3 long hair, or 2:3. The other ratio is 12 short hair to an unknown number of long hair, or 12:x. Since the ratios are equivalent, you can ...
We can multiply both sides of the C:S ratio by 2, so that both ratios are comparing relative to 6 sheep. C:S = 4:6 and S:P = 6:7. These can now be joined together. C:S:P = 4:6:7. We can now use this to share the 85 animals in the ratio 4:6:7. There are 17 parts in total (4 + 6 + 7 = 17)
Model Answers. 1 2 marks. A pattern of tiles is being created in a bathroom, consisting of black and white tiles. of the tiles are black. (i) Write down the ratio of white tiles to black tiles. [1] (ii) There is a total of 42 tiles.
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.
Previous: Percentages of an Amount (Non Calculator) Practice Questions Next: Rotations Practice Questions GCSE Revision Cards
Proportion Worded Problems Practice Strips ( Editable Word | PDF | Answers) Proportion Worded Problems Practice Grid ( Editable Word | PDF | Answers) Mixed Ratio and Proportion Revision Practice Grid ( Editable Word | PDF | Answers. . )
In 2018, the ratio of the amount each paid in rent was Arjun : Gretal = 5 : 7. In 2019, the ratio of the amount each paid in rent was Arjun : Gretal = 9 : 13. Arjun paid the same amount of rent in both 2018 and 2019. Gretal paid $290 more rent in 2019 than she did in 2018. Work out the amount Arjun paid in rent in 2019.
Subject: Mathematics. Age range: 14-16. Resource type: Worksheet/Activity. File previews. docx, 18.26 KB. Ratio problems that involve a bit of thinking, such as combining ratios. Perfect for practice for the new GCSE. Creative Commons "Sharealike". See more.