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Ratio: Problem Solving Textbook Exercise

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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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Solving ratio problems

Part of Maths Ratio

The ratio of horses to donkeys at an animal sanctuary is 5 : 2. What fraction of the animals are donkeys?

Add the ratio parts (5 and 2) to find the denominator of the fraction. 5 + 2 = 7. The denominator is 7

The numerator of the fraction is the ratio part that is the focus of the question (donkeys). The numerator is 2. The fraction of the animals that are donkeys is 2⁄7

To make pink paint, 2⁄5 red paint is mixed with white paint. How much white paint is needed? What is the ratio of red to white paint?

The numerator of the fraction of red paint is 2. This is the ratio part for red paint. To find the ratio part for the white paint, subtract the numerator from the denominator. 5 – 2 = 3. The ratio part for white paint is 3. 3⁄5 of the paint is white. The ratio of red to white paint is 2 : 3

A farm has sheep and goats in the ratio 7 : 5 (sheep : goats). What fraction of the animals are sheep?

Show answer Hide answer

Add the ratio parts (7 and 5) to find the denominator of the fraction.

7 + 5 = 12. The denominator is 12

The numerator of the fraction is the ratio part that is the focus of the question (sheep). The numerator is 7

The fraction of animals that are sheep is \( \frac{7}{12} \)

A box contains toffees and truffles in the ratio 7 : 6. There are 24 truffles. How many toffees are there?

Draw a bar model and label it to illustrate the problem. The ratio of toffees to truffles is 7 : 6. Draw 7 parts for the toffees and 6 for the truffles. Label the truffle bar with 24. To work out the total number of toffees, the value of one part needs to be found.

To work the value of one part, divide the number of truffles (24) by the number of parts given (6). This gives the value of one part. 24 ÷ 6 = 4

Multiply the value of one part (4) by the number of parts asked for: the toffees (7). 4 × 7 = 28. There are 28 toffees in the box.

A library stocks books for children and books for adults in the ratio 3 : 5. There are 450 books for children. How many books are in the library?

Draw a bar model and label it to illustrate the problem. The ratio of books for children to books for adults is 3 : 5. Draw 3 parts for books for children and 5 parts for books for adults. Label the books for children bar with 450. To work out the total number of books, the value of one part needs to be found.

To find the value of one part, divide the amount of books for children (450) by the number of parts given (3). 450 ÷ 3 = 150. The value of one part is 150

Multiply the value of one part (150) by the number of parts asked for: the number of books in the library. This is the total of books for children parts and the books for adults parts. (3 + 5 = 8). The calculation is 150 × 8. The total number of books in the library is 1200.

The ratio of desserts to pizzas in a supermarket freezer is 4 : 3 There are a total of 620 desserts. How many pizzas are in the freezer?

Draw a bar model to illustrate the problem. The ratio of desserts to pizzas is 4 : 3 . Draw 4 parts for desserts and 3 parts for pizzas.

Label it to illustrate the problem. Label the dessert bar with 620. To find the number of pizzas in the freezer, work out the value of one part.

To find the value of one part, divide the share for desserts (620) by the number of parts (4). 620 ÷ 4 = 155. The value of one part is 155

Multiply the value of one part (155) by the number of parts asked for: pizzas (3). 155 x 3 = 465

The number of pizzas in the freezer is 465

Everyone at a fancy dress party is dressed up as either a vampire or a wizard. The ratio of people dressed as vampires to wizards is 5 : 2. If there are 6 more vampires than wizards, how many people are at the party?

Draw a bar model to illustrate the problem. The ratio of vampires to wizards is 5 : 2. There are 5 parts for the vampires and 2 parts for the wizards.

Label the given information. There are 6 more vampires than wizards. The diagram shows the comparison between the vampires bar and the wizards bar. To work out the total number of people at the party, the value of one part needs to be found.

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

Multiply the value of one part (2) by the number of parts asked for (all the people so all the parts, 7). 2 × 7 = 14. The total number of people at the party is 14

The ratio of the number of tulips to daffodils in a flower display is 3 : 7. There are 96 fewer tulips than daffodils. Find the number of daffodils in the display.

Draw a bar model to illustrate the problem. The ratio of tulips to daffodils is 3 : 7. There are 3 parts for tulips and 7 parts for daffodils.

Label the given information. There are 96 fewer tulips than daffodils. The diagram shoes the comparison between the tulips bar and the daffodils bar. To work out the number of daffodils in the display, the value of one part needs to be found.

To find the value of one part, divide the comparison value (96) by the number of parts that make up the difference (4). 96 ÷ 4 = 24. The value of one part is 24

Multiply the value of one part (24) by the number of parts asked for (all the daffodils, 7 parts). 24 × 7 = 168. The number of daffodils in the display is 168

The ratio of the number of robins to sparrows to blackbirds in a survey of garden birds is 1 : 3 : 8 (robins : sparrows : blackbirds)

There were 70 fewer robins than sparrows. How many birds were observed in this survey?

Draw a bar model to illustrate the problem. The ratio of robins to sparrows to blackbirds is 1 : 3 : 8. There is 1 part for robins, 3 for sparrows and 8 for blackbirds.

Label the given information. There are 70 fewer robins than sparrows. This is the difference between the robins bar and the sparrows bar. To find the total number of birds in the survey, the value of one part needs to be found.

To find the value of one part, divide the difference value (70) by the number of parts that make up the difference (2). 70 ÷ 2 = 35. The value of one part is 35

Multiply the value of one part (35) by the number of parts asked for (all the parts, 12). 35 x 12 = 420

A market stall has 60 T-shirts. The ratio of small, medium and large T-shirts being sold on the stall is 2 : 3 : 1. The stallholder sells 26 medium and 2 large T-shirts. What is the ratio of small, medium and large T-shirts now?

Draw a bar model to illustrate the starting information. Draw 2 parts for small T-shirts, 3 for medium and 1 for large. The total number of T-shirts is 60

Divide 60 in the ratio 2 : 3 : 1. To find the value of one part, divide the total number (60) by the sum of the parts (2 + 3 + 1 = 6). 60 ÷ 6 = 10. The value of one part is 10

2 parts are small, so 2 × 10 = 20 small T-shirts. 3 parts are medium, so 3 × 10 = 30 medium T-shirts. 1 part is large, so 1 × 10 = 10 large T-shirts.

Adjust the shared amounts according to the given information in the question. At the start there were 20 small, 30 medium and 10 large T-shirts. 26 medium and 2 large T-shirts are sold. The remaining T-shirts are 20 small, 4 medium and 8 large T-shirts.

The ratio of small to medium to large T-shirts is now 20 : 4 : 8. This ratio can be simplified.

To simplify the ratio, divide each part by their highest common factor (HCF). The HCF of 20, 4 and 8 is 4. Divide each part by 4. The new simplified ratio of small to medium to large T-shirts is 5 : 1 : 2

There are 55 big cats in a safari park. The ratio of lions to tigers is 3 : 2 12 lion cubs and 5 tiger cubs are born. What is the ratio of lions to tigers now?

A total amount and ratio is given. Draw a bar model to illustrate this starting information. Draw 3 parts for lions and 2 parts for tigers, with a total of 55

Divide the total number of big cats (55) in the ratio 3 : 2. To find the value of one part, divide the amount (55) by the total number of parts (5). 55 ÷ 5 = 11. The value of one part is 11. Multiply one part by the number of parts for each big cat. There are 11 × 3 = 33 lions. There are 11 × 2 = 22 tigers.

Adjust the shared amounts according to given information in the question. After the cubs have been born there are 33 + 12 = 45 lions and 22 + 5 = 27 tigers.

Write the new shares as a ratio and simplify. The new ratio of lions to tigers is 45 : 27. This ratio can be simplified by finding the HCF of 45 and 27. This is 9. Divide each ratio share by 9. The ratio simplifies to 5 : 3

The ratio of lions to tigers is now 5 : 3

Practise solving ratio problems

Practise solving ratio problems in this quiz. You may need a pen and paper to complete these questions.

Real-world maths

More on Ratio

Find out more by working through a topic

Scale drawings

• count 4 of 5

Map scales and ratio

• count 5 of 5

Equivalent ratios and simplifying ratios

• count 1 of 5

Division in a given ratio

• count 2 of 5

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Praxis Core Math

Course: praxis core math   >   unit 1.

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

Ratios and proportions | Lesson

• Ratios and proportions | Worked example
• Percentages | Lesson
• Percentages | Worked example
• Rates | Lesson
• Rates | Worked example
• Naming and ordering numbers | Lesson
• Naming and ordering numbers | Worked example
• Number concepts | Lesson
• Number concepts | Worked example
• Counterexamples | Lesson
• Counterexamples | Worked example
• 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.
• 1 5 ‍   of the students on the varsity soccer team are lower-level students.
• 1 ‍   in 5 ‍   students on the varsity soccer team are lower-level students.

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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Sharing in a Ratio: Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

Mathster keyboard_arrow_up Back to Top

Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers.

Corbett Maths keyboard_arrow_up Back to Top

Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. It really is one of the very best websites around.

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English National Curriculum, Programme Of Study For Year 6 Mathematics

Ratio and proportion.

Pupils should be taught to solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

• Ratio A ratio is a relationship between two numbers of the same kind. In layman's terms a ratio represents, simply, for every amount of one thing, how much there is of another thing. This topic presents a number if different ways pupils can represent ratios and apply their meaning to problem solving situations.

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.

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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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Course Support. Past Paper Questions by Topic. For Free.

Ratio & Basic Proportion (Including Conversions)

Prior Content:  Basic Operations +-x/ , Using a Calculators/ BIDMAS

Possible Next Steps: Direct & Inverse Proportion , Compound Measures , Similar Shapes , Vectors , Pie Charts , Basic Trigonometry

1.1 Simplifying & Equivalent Ratios

1.2.1 basic direct proportion, 1.2.2 converting money & best buys, 1.3.1 metric & imperial units, 1.3.2 conversions (metric), 1.3.3 conversions (non-metric), 1.4 map ratios & scale drawings, 2.1 basic inverse proportion, 3.1 dividing into a ratio, 3.2 dividing when given an amount within a ratio, 3.3 working with changing ratios, 3.4 questions in context (fdpr), 4.1 converting units between dimensions, whole topic summary resources (including past paper questions), teaching videos, exercises & activities, tutorial videos.

Corbett Maths Ratio Simplifying

Corbett Maths Expressing Ratios as 1 to n

Online Platforms (with Videos & Exercises)

Activities & resources.

• Simplifying Ratios Loop Set 1
• Simplifying Ratios Loop Set 2
• Simplifying Ratio ppt
• Simplifying Ratio Pair Task
• Three-Way Ratio Problems ppt
• thewessens.net online ratio simplifying
• Simplifying Ratios Pixel Picture ( Editable Word  |  PDF  |  Answers )
• Simplifying Ratios Odd One Out ( Editable Word  |  PDF  |  Answers )
• Equivalent Ratios Match-Up ( Editable Word  |  PDF  |  Answers )
• Combining Ratios Practice Strips ( Editable Word  |  PDF  |  Answers )
• Simplifying Ratios Worksheet & Solutions
• Simplifying Ratios First Steps
• Simplifying Ratios Strengthen
• Equivalent Ratios (Two Parts) Codebreaker
• Equivalent Ratios (Three Parts) Codebreaker
• Three-Way Ratio Problems

Dr Frost Resources

Dr frost video.

K196:  Write a Ratio in its Simplest Form.

K197:  Write a Ratio in the Form 1:n or n:1.

K695:  Convert an Equation Involving Two Variables into a Ratio.

K206:  Combine Two Ratios to Form One.

Dr Frost Slides & Activities

Dr Frost Slides (1-4 & 10)

Extra Questions

• Dr Frost Questions

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 196 Write a Ratio in its Simplest Form.
• 197 Write a Ratio in the Form 1:n or n:1.
• 695 Convert an Equation Involving Two Variables into a Ratio.
• 206 Combine Two Ratios to Form One.
• 746 Form a Four-Part Ratio.
• Combination of All

Ratio & Proportion Key Skills Section (for selecting more than one)

Extension Materials

Other videos & multimedia.

Corbett Maths Expressing Ratios as Fractions or Percentages

Corbett Maths Writing a Ratio as an Equations

• Ratio: Expressing as a Fraction/Percentage Worksheet & Solutions

Corbett Maths Unitary Method

Corbett Maths Recipes

• Direct Proportion Loop Set 1
• Direct Proportion Loop Set 2
• Recipes ppt
• Recipes Menu
• Unitary Method Practice Strips ( Editable Word  |  PDF  |  Answers )
• Unitary Method Match-Up ( Editable Word  |  PDF  |  Answers )
• Unitary Method Worksheet & Solutions
• Recipes Practice Questions & Solutions
• Recipes Worksheet & Solutions
• Daniel Burke Capture Recapture (TES Account Required)
• Proportion KS2 SATS Questions and Solutions
• Recipes KS2 SATS Questions and Solutions
• Recipes RAG
• Recipes Extension
• Capture-Recapture Exam Questions (Emporium)
• Capture-Recapture Mark Scheme (Emporium)

K230:  Solve Direct Proportion Problems Using a Scaling Method.

K231:  Use Multiplicative Reasoning in a Recipe.

K272:  Use the Capture-Recapture Method to Estimate the Size of a Population.

• 230 Solve Direct Proportion Problems Using a Scaling Method.
• 231 Use Multiplicative Reasoning in a Recipe.
• 272 Use the Capture-Recapture Method to Estimate the Size of a Population.

Data Collection Key Skills Section (for selecting more than one)

Corbett Maths Capture Recapture

• Capture Recapture Worksheet & Solutions

Corbett Maths Exchange Rates

Corbett Maths Best Buys

• Best Buys ppt
• Best Buys Starter
• Best Buys Investigation
• Exchange Rates ppt
• Exchange Rates Extension Task 1
• Exchange Rates Extension Task 2
• Current Exchange Rates
• Best Buys Practice Strips ( Editable Word  |  PDF  |  Answers )
• Currency Conversions Practice Strips ( Editable Word  |  PDF  |  Answers )
• Converting Currency Practice Questions & Solutions
• Exchange Rates Worksheet & Solutions
• Best Buys Practice Questions & Solutions
• Best Buys Worksheet & Solutions
• Linear Proportion GCSE Questions and Solutions
• Best Buys RAG
• Exchange Rates RAG

K234:  Use an Exchange Rate to Calculate an Amount by Multiplying.

K235:  Use an Exchange Rate to Calculate an Amount by Dividing.

K233:  Use Proportion to Solve Best Value Problems.

• 234 Use an Exchange Rate to Calculate an Amount by Multiplying.
• 235 Use an Exchange Rate to Calculate an Amount by Dividing.
• 233 Use Proportion to Solve Best Value Problems.

Compound Measures and Units of Measurement  Key Skills Section (for selecting more than one)

TEACHING VIDEOS, EXERCISES & ACTIVITIES

Corbett Maths Introduction to Metric & Imperial Units

Corbett Maths Reading Scales

Corbett Maths Sensible Estimates

• Metric Units ppt
• Imperial Units ppt
• thechalkface Appropriate Units
• Metric/ Imperial Units Practice Questions & Solutions
• Reading Scales Practice Questions & Solutions
• Reading Scales Worksheet & Solutions
• Sensible Estimates Practice Questions & Solutions
• Sensible Estimates Worksheet & Solutions

Dr Frost resources

Topic tests.

• Standard Test
• Advanced Test

No Key Skills Yet

Further Practice

• Practise Questions

EXTENSION MATERIALS

Other videos.

Khan Academy

Corbettmaths Videos

• Maths Made Easy
• Khan Academy Converting metric units , Converting metric units word problems lessons & main page (including test)
• cimt.org (no video) self contained notes and self checking questions
• Go Teach Maths  treasure trove of activities & ppts
• alutwyche codebreakers (TES Account Required)
• thechalkface interactive excel file illustrating links
• transum matching games
• mathopolis.com multiple choice quiz and numerous other quizzes available in the measurement section here
• rachfenwick metric conversions (TES Account Required)
• DIY (or multiple pre-made) worksheets at homeschoolmath.net
• DIY worksheets also available at math-aids.com
• math-salamanders multiple worksheets (I go for the mixed one at the bottom)
• Converting Units of Length and Mass Practice Strips ( Editable Word  |  PDF  |  Answers )
• Equivalent Lengths Match-Up ( Editable Word  |  PDF  |  Answers )
• Equivalent Mass, Volume and Capacity Match-Up ( Editable Word  |  PDF  |  Answers )
• Converting Units of Area and Volume Practice Strips ( Editable Word  |  PDF  |  Answers )
• Metric Units Practice Questions & Solutions
• Metric Units Worksheet & Solutions
• mathworksheets4kids large selection on individual skills
• Larger to Smaller First Steps
• Larger to Smaller inc. Decimals First Steps
• Larger to Smaller Strengthen
• Small to Larger First Steps
• Small to Larger inc. Decimals First Steps
• Small to Larger Strengthen
• Km, cm & mm First Steps
• Km, cm & mm Strengthen
• Converting Metric Lengths Topic Review
• Capacity KS2 SATS Questions and Solutions
• Mass KS2 SATS Questions and Solutions
• Metric Units RAG

K127:  Convert Metric Units of Length from Smaller Units to Bigger Units.

K128:  Convert Metric Units of Length from Bigger Units to Smaller Units.

K129:  Calculate with Metric Measures of Length.

K130:  Convert Units of Mass by Multiplying.

K131:  Convert Units of Mass by Dividing.

K132:  Convert Units of Capacity by Multiplying.

K133:  Convert Units of Capacity by Dividing.

• 127 Convert Metric Units of Length from Smaller Units to Bigger Units.
• 128 Convert Metric Units of Length from Bigger Units to Smaller Units.
• 129 Calculate with Metric Measures of Length.
• 130 Convert Units of Mass by Multiplying.
• 131 Convert Units of Mass by Dividing.
• 132 Convert Units of Capacity by Multiplying.
• 133 Convert Units of Capacity by Dividing.
• 749  Simplifying Ratios When the Units are Different.

Corbett Maths Videos on Imperial Conversions. Last 3 Converting to Metric.

• Khan Academy Converting US Customary units , Converting US Customary units word problems lessons & main page (including tests). Note this is the same skill as ‘imperial units’, with many of the same units.
• cimt.org (no video) self contained notes and self checking questions and problems in context
• Metric & Imperial Conversion Factors
• math-salamanders conversions table
• transum matching games , miles to km online worksheet
• DIY worksheets at homeschoolmath.net (will need a conversion table to hand)
• Imperial Units Practice Questions & Solutions
• Imperial & Metric Units Practice Questions & Solutions
• thechalkface introduction to imperial units with mini conversion table
• thechalkface context problems
• Imperial Units Cross-Number
• Imperial Units World Record Questions

Whole Topic Video

K64:  Convert From Hours to Minutes.

K65:  Convert From Minutes to Seconds.

K66:  Convert From Years to Months.

K67:  Convert From Weeks to Days.

• Dr Frost Slides
• 64 Convert From Hours to Minutes.
• 65 Convert From Minutes to Seconds.
• 66 Convert From Years to Months.
• 67 Convert From Weeks to Days.
• K42e:  Convert from minutes to hours.
• K42f:  Convert from seconds to minutes.

Time  Key Skills Section (for selecting more than one)

Corbett Maths Maps & Scales

• Scale Drawing ppt
• Kitchen Plan
• Scale Drawing Extension Task
• Using Map Scales Practice Strips ( Editable Word  |  PDF  |  Answers )
• Scale Diagrams Practice Grid ( Editable Word  |  PDF  |  Answers )
• Bearings and Scale Diagrams Practice Strips ( Editable Word  |  PDF  |  Answers )
• Drawing Scale Diagrams Practice Grid ( Editable Word  |  PDF  |  Answers )
• Scales & Maps Practice Questions & Solutions
• Scale Drawing RAG

K543:  Use a Map Scale to Find an Actual Distance.

K544:  Use a Map Scale in the Form 1:n to Find an Actual Distance.

• 543  Use a Map Scale to Find an Actual Distance.
• K3e  GDP TESTING
• 544 Use a Map Scale in the Form 1:n to Find an Actual Distance.

Construction, Loci & Scale Drawings  Key Skills Section (for selecting more than one)

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

K232:  Solve Inverse Proportion Problems Using a Scaling Method.

• 232 Solve Inverse Proportion Problems Using a Scaling Method.

Corbett Maths Ratio Sharing the Total

• Dividing into a Ratio ppt
• Sharing and Combining Ratios Practice Strips ( Editable Word  |  PDF  |  Answers )
• Ratio: Sharing the Total Worksheet & Solutions
• Dividing Into a Ratio RAG

K202:  Share an Amount into a Ratio With 2 Parts.

K203:  Share an Amount into a Ratio With 3 Parts.

• Standard Test (covering all Multiplying and Dividing by Powers of 10)
• 202 Share an Amount into a Ratio With 2 Parts.
• 203 Share an Amount into a Ratio With 3 Parts.

Corbett Maths Ratio When Given One Quantity

Corbett Maths Ratio Questions Involving Differences

• Ratio Sharing Money Loop Set 1
• Ratio Sharing Money Loop Set 2
• maths box Mixed Ratios treasure hunt (free sample activity)
• Working with Ratio Practice Strips ( Editable Word  |  PDF  |  Answers )
• Dividing in a Ratio Practice Strips ( Editable Word  |  PDF  |  Answers )
• Dividing in a Ratio Fill in the Blanks ( Editable Word  |  PDF  |  Answers )
• Dividing in a Ratio Crack the Code ( Editable Word  |  PDF  |  Answers )
• Ratio Practice Questions & Solutions
• Ratio: Given One Quantity Worksheet & Solutions
• Ratio: Difference Between Worksheet & Solutions
• Ratio Topic Review
• Ratio GCSE Questions and Solutions
• Ratio KS2 SATS Questions and Solutions

K204:  Determine a Value in a Ratio When the Difference Between Two Amounts is Given.

K205:  Determine a Value in a Ratio When One Amount is Given.

Dr Frost Slides (4-6)

• 204 Determine a Value in a Ratio When the Difference Between Two Amounts is Given.
• 205 Determine a Value in a Ratio When One Amount is Given.

Corbett Maths Given Two Ratios

• Ratio: Two Ratios Worksheet & Solutions
• Harder Ratio Problems Practice Strips ( Editable Word  |  PDF  |  Answers )

K696:  Determine an Amount Given a Change in a Ratio Where One Part is Changing.

K697:  Determine an Amount Given a Change in a Ratio Where Two Parts are Changing.

Dr Frost Slides (13-16)

• 696 Determine an Amount Given a Change in a Ratio Where One Part is Changing.
• 697 Determine an Amount Given a Change in a Ratio Where Two Parts are Changing.

Ratios, Fractions and Percentage Problems! Common Exam Questions!! | Grade 5+ by The GCSE Maths Tutor

• Goal Free Problems Foundation Q’s (Q4, 14-17) by Peter Mattock
• Problem Solving (Bar Modelling) ppt
• Fractions and Ratio Worded Problems Practice Strips ( Editable Word  |  PDF  |  Answers )
• Fractions, Ratio and Percentages Worded Problems Grid ( Editable Word  |  PDF  |  Answers )
• Problem Solving Worksheet & Solutions
• Fraction word problems with the 4 operations 1 , 2 , 3 , 4 , 5 , 6
• More Mixed Fractions Word Problems 1 , 2 , 3 , 4 , 5 , 6
• Bar Model RAG
• Tannermaths.co.uk  R.U.L.E.R. Exam Question Practice  (Pages 3-19) &  MS

K198:  Determine the Fraction That a Number Within a Ratio Represents.

K199:  Determine the Percentage That a Number Within a Ratio Represents.

• 198 Determine the Fraction That a Number Within a Ratio Represents.
• 199 Determine the Percentage That a Number Within a Ratio Represents.

Corbett Maths Converting Metric Units of Area

Corbett Maths Converting Metric Units of Volume

• Area and Volume Unit Conversions ppt
• Converting Unit Of Length, Area, Volume Codebreaker (TES Account Required)
• Converting Units of Area & Volume Practice Questions & Solutions
• Converting Areas Worksheet & Solutions
• Converting Volumes Worksheet & Solutions
• Converting Length, Area and Volume Topic Review
• Area and Volume Unit Conversions RAG

K529:  Convert Metric Units of Area by Multiplying.

K530:  Convert Metric Units of Area by Dividing.

K531:  Convert Metric Units of Volume by Multiplying.

K532:  Convert Metric Units of Volume by Dividing.

• 134 Convert from Units of Volume to Units of Capacity.
• 135 Convert from Units of Capacity to Units of Volume.
• 529  Convert Metric Units of Area by Multiplying.
• 530  Convert Metric Units of Area by Dividing.
• 531  Convert Metric Units of Volume by Multiplying.
• 532  Convert Metric Units of Volume by Dividing.
• K250d:  Find an actual area given an area on the map.
• K250e:  Find an area on a map given the actual area.

Units of Measurement Key Skills Section (for selecting more than one)

Download Ratio & Basic Proportion PPQs as WW Powerpoint for Edexcel IGCSE , AQA GCSE , Edexcel GCSE or OCR GCSE (or all GCSE together )

Download FDPR Mixed Context PPQs as WW Powerpoint for AQA GCSE , Edexcel GCSE or OCR GCSE (or all GCSE together )

Other Whole Topic Resources

• Solving Ratio Problems Practice Strips ( Editable Word  |  PDF  |  Answers )
• Solving Ratio Problems Practice Grid ( Editable Word  |  PDF  |  Answers )
• Mixed Ratio and Proportion Revision Practice Grid ( Editable Word  |  PDF  |  Answers )

Proportion Questions

Primary Study Cards

• 5-a-day Answers
• Worksheet Answers

Ratio Questions involving Differences - Corbettmaths