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## GCSE Maths (9-1) - Ratio - Problem Solving

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

19 April 2021

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Worksheet with 9 Problem Solving, Exam Style Questions on RATIO

The idea behind the resource is to help students be able to solve problem solving questions. It could be used towards the end of a set of lessons on RATIO or used as revision. I would recommend that the teacher goes through the questions in the first boxes, the students then try the similar questions from the middle boxes and then there is a slightly trickier questions in the third boxes to help stretch and deepen their knowledge. I would suggest printing Page 1 and 2 side by side. Having the answer boxes separate to the questions encourages students to show their working out.

Suggested Grade - 5+

Answers included

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## Not quite what you were looking for? Search by keyword to find the right resource:

Applied Ratio

Lots of applied ratio here!

This new lesson on three-way ratio problem solving looks at using given ratios to create others. Students will need to understand equivalence of ratios and sharing into a ratio.

Recipes is a common exam question and the main task of this lesson is fully differentiated and focuses on the menu for the restaurant Pythagoras' Place. The extension task requires the students to work out ingredients for Shrove Tuesday for the class in question.

Best buys features lots of opportunity for discussion and plenty of relevant maths. Pair work, visual explanations and a differentiated main task with answers.

Exchange rates is another highly relevant topic using current exchange rates (use the given link). Answers will change along with the rates so I have not included answers for this lesson.

## All About Maths

Ratio and proportion (8300 - higher - ratio, proportion and rates of change), specification references (in recommended teaching order).

The subject content (above) matches that set out in the Department for Education’s Mathematics GCSE subject content and assessment objectives document.

• All students will develop confidence and competence with the content identified by standard type
• All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
• Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

## Teaching resources

Diagnostic questions (e-library), activities (e-library), worksheets (e-library), legacy resources that might be useful for this topic, topic tests.

Access thousands of exam questions with Exampro Mathematics

• GCSE Maths (8300) question papers and mark schemes
• GCSE Maths (8300) Mock Exam Analysers
• GCSE Maths (8300) Reports on the Examination

Create, edit, and share assessments quickly and easily with Exampro Mathematics

## Quick links

• AQA exams and results services

## Resourceaholic

Ideas and resources for teaching secondary school mathematics

• Blog Archive

## 20 December 2017

New gcse: ratio.

• Mel from JustMaths collated ratio Higher GCSE questions from sample and specimen papers here , and has written up her solutions here .
• If you subscribe to MathsPad then you'll be pleased to hear that they have lovely resources for ratio including a set of questions for Higher GCSE  with loads of examples like the problems I've featured in this post.
• Don Steward has plenty of ratio tasks  including his set of ' Harder Ratio Questions ' and a really helpful collection of GCSE ratio and proportion questions .
• On MathsBot you can generate ratio questions, revision grids and practice papers. Select 'ratio, proportion and rates of change' at the top.
• There are exam style questions in this collection from Lucy Kilgariff on TES.
• OCR has a 'Calculations with Ratio' Topic Check In  and AQA has a Ratio and Proportion Topic Test .
• David Morse of Maths4Everyone has shared a set of revision exercises and ratio exam style questions .

## 20 comments:

My ratio pages don't get much attention - not sure why since I think they're instructive and easy to use. They don't support the particular type of harder questions described in the post (but I'll look to add something along those lines), but they do help understanding the concept of a ratio and it's utility. Manipulation of ratio quantities: http://thewessens.net/ClassroomApps/Main/ratios.html?topic=number&path=Main&id=7 Introduction to the ratio concept: http://www.thewessens.net/blog/2015/03/19/ratios-the-super-fractions/ Bar model visualisation of ratios: http://thewessens.net/ClassroomApps/Models/BarModels/visualfractionratio.html?topic=models&path=Models&id=17 Multiplicative word problems: http://thewessens.net/ClassroomApps/Models/BarModels/multiplicationwordproblems.html?topic=models&path=Models&id=8 Ken

Fantastic! Thanks Ken.

Thanks so much for your blog on ratio question types. Although I've been a maths teacher/tutor for over 30 year, ratio has always been a bug bear for me. I could wing it with old style gcse because I learnt the types of solutions required, however I have been stressed on the new types. This blog has made me think through ratios and I am certainly a lot happier. Bryan

Excellent, I'm so pleased it helps.

On your fractions approach, a quick trick is to realise that a/c = a/b x b/c. Makes it quite quick to work out (That is, if the students are good with cancelling down when multiplying). However, what I find confuses students about writing ratios as fractions is that it confuses the part:part idea of a ratio with the part:whole idea of a fraction. Perhaps that's why it's somewhat counter-intuitive. Also, final point is that ratios (fractions) and vectors is another application of harder ratio questions that often pops up on the new GCSE. Thanks for the post, Farah

Thanks for the comment!

This is a fabulous resource on work that is missing from the new GCSE texts that I have seen. Lovely challeging questions to make students think.

Thanks! Glad it's helpful.

I've been using equivalent ratios for these type of questions. Find what doesn't change - the total number of sweets. Write ratios as equivalent ratios where the parts that doesn't change are the same. 3:7 has 10 parts, 3:5 has 8 parts LCM of 8 and 10 is 40 Ratios are 12:28 and 15:25 Number of sweets given is 3. Also works for following question Ratio of blue to red counters in a bag is 1:2, I add 12 blue counters and the ratio is 5:7. How many red counters are in the bag? What doesn't change? Red counters LCM of 2 and 7 is 14 Ratios are 7:14 and 10:14 3 parts are 12 counters, 1 part is 4 counters and 14 parts are 56 red counters. Also Jill is 4 times older than Jack. In 14 years time the ratio of Jack's age to Jill is 5:7. How old is Jill now? Ratios are 1:4 and 5:7. What doesn't change? The difference between their ages Find two equivalent ratios where difference between them is the same. 4 - 1 = 3 and 7 - 5 = 2 LCM of 2 and 3 is 6 Equivalent ratios are 2:8 and 15:21 13 parts = 26 years, 1 part is 2 years, Jill is 16.

This is the approach I use. I think it's logical.

Thank you! Yes, this is logical. Same approach as bar modelling (but without the visual).

Oops, my mistake, third example should be .....in 26 years time the ratio of their ages is 5:7 ..... I did try to represent these using bar modelling at first but struggled to find a model that was intuitive and actually helped with the question. I would be grateful if anyone has ideas on this.

Although some bar modelling experts would disagree, I don't think bar modelling is intuitive/helpful for harder ratio questions. Bar modelling is fantastic for easier ratio questions, but when the questions get more complicated it's often really hard to figure out how to draw the scenario - definitely not as easy as some people make out!

Thank you for the post. Brilliant as usual. I actually did the sweets question in my class once. I simply said that Alice fraction of sweets changed from 7/10 to 5/8 when she gave the 3 sweets away. If we just subtract those fractions, the fraction remaining, 7/10 - 5/8 = 3/40. This means that Alice originally had 40 sweets.

Hadnt considered tis method but I love it

Thanks Stephen. I guess it makes sense, as the fraction lost is equivalent to the 3 sweets divided by the total.

Love this! Thanks for sharing.

Hi Jo, thanks for the post which I came across via a tweet you put out a couple of days ago - which also tied in with a question and the same method I saw in my step-daughters book the very next day - freaky! It is a more compact method than I would normally use in my teaching and will be switching to it. I think the only tweak I might make is to write the algebra ratio above the numeric one so the starting fractions are (7x-3)/5 : (3x+3)/3 The reason being that some students might get a little scared seeing algebra as part of the denominator but less so when faced with a number.

Good idea - thank you!

Hi Jo, One method I use when teaching questions like the first one above (Alice gives 3 sweets to Olivia) is the following. To begin with Alice has 7/10 of the sweets and then after giving three to Olivia, her share has reduced to 5/8 of the sweets. So Alice's share has reduced by (7/10 - 5/8=) 3/40 which is equivalent to 3 sweets, therefore there must be 40 sweets in total. Students can then proceed in answering the relevant question. I must admit I only use this method with the top sets.

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This SMILE resource contains two packs of games, investigations, worksheets and practical activities supporting the teaching and learning of ratio and a booklet 'The Golden Rectangle'.

Ratio pack one  contains twelve work cards with a wide variety of activities covering comparing lengths, introducing simple ratio, comparing ratio, converting between units, ratio problems, and similar rectangles.

Ratio pack two  contains nine work cards with activities requiring students to solve problems using ratios, solve problems using rates, investigate standard paper sizes, and explore proportion.

The Golden Rectangle  is a booklet containing a number of activities based upon the Golden Ratio followed by a detailed exploration of the Fibonacci sequence.

SMILE (Secondary Mathematics Individualised Learning Experiment) was initially developed as a series of practical activities for secondary school students by practising teachers in the 1970s. It became a complete individualised scheme based around a network of activity cards and assessments.

Related resources include answers  to all of the cards and test books and answers .

## Show health and safety information

Please be aware that resources have been published on the website in the form that they were originally supplied. This means that procedures reflect general practice and standards applicable at the time resources were produced and cannot be assumed to be acceptable today. Website users are fully responsible for ensuring that any activity, including practical work, which they carry out is in accordance with current regulations related to health and safety and that an appropriate risk assessment has been carried out.

## Show downloads

Share this resource, did you like this resource, lists that tag this content, ratio and scale factors , posted by, ratio , posted by rachel jackson, ratio , posted by, chris 1 problem , posted by.

## Mr Barton Maths Podcast

Long-form conversations about teaching and learning with craig barton.

## Ratio using Bar Modelling – Secondary: TES Maths Resource of the Week

To see all of the work I do for TES Maths, including Resource of the Week, Inspect the Spec, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the TES Maths Blog  here

What is it? The more I visit primary schools and work with their teachers and pupils, the more I become convinced by the power of their bar modelling approach. Likewise, the Year 7s I teach these days seem significantly stronger in all aspects of ratio and multiplicative reasoning than Year 7s in the past. This resource provides a wonderful introduction to the basics of bar modeling for ratio, aimed at secondary teachers. The choice of questions is superb, and really helps illustrate the power of the approach.

Consider the following three approaches:

1) Kallan and Adam share some money in the ratio 5:3. Between them they have £240. How much does each person receive?

2) Kallan and Adam share some money in the ratio 5:3 Adam has £240 How much money did they share?

3) Kallan and Adam share some money in the ratio 5:3 Kallan has £240 more than Adam How much does Adam have?

These three questions all look similar, but have completely different answers and, as the resource demonstrates superbly, setting each of these scenarios up with a bar model can move students away from guessing at half-remembered rules and towards a coherent approach that makes sense.

How can it be used? This resource is really well structured. Students are encouraged to think about how each question is slightly different, “how will this affect your diagram? What will stay the same each time and what will change?”. Students could initially try these problems on their own, and then compare their answers and approaches with their neighbour before the teacher leads a whole-class discussion. Following this, there are a series of scaffolded worksheets for calculating the final solution to these problems, as well as some fresh problems to try. Then to top it all off, there is the kind of tricky exam question where I have certainly seen many students over the years struggle. I am confident that students using this resource will flourish!

Thanks so much for sharing

Download: Ratio using Bar Modelling – Secondary View the author’s other resources

## Key Stage 3 Maths - Lesson Objectives, Keywords and Resources - Year 8 - Number

• Cut-the-knot
• Curriculum Online
• Starter of the Day

## Lesson Objectives

To be able to:

• Reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation;
• Divide a quantity into two or more parts in a given ratio
• Use the unitary method to solve simple word problems involving ratio and direct proportion.
• Compare two ratios.

ratio, unitary method, percentage, fraction, conversion

Home | Year 7 | Year 8 | Year 9 | Starter of the Day | Links

One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

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

This topic is relevant for:

Here we will learn about ratio, including simplifying ratios, dividing a ratio into a quantity, ratios to fractions, and problem solving with ratios.

There are also ratio 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?

Ratio is a relationship between two or more quantities showing the number of times one is contained within the other(s).

Ratios are written in the form a:b , which is said “ a \ to \ b ” where a and b are normally integers, fractions or decimals.

They can also be represented in the form \frac{a}{b} (a fraction).

The order of the quantities in the ratio is important.

If there are 10 boys in a class and 15 girls, we can say that the ratio of boys to girls is 10:15 which we say as “ 10 to 15 ”.

Ratios are used in real life very frequently.

We use ratios to bake cakes, convert currencies when you go on holiday, determine the shutter speed on a camera, draw scale models of buildings, calculate the speed of a car, determine the aspect ratio of television screens, read maps and many many more!

In the GCSE mathematics curriculum, topics that use ratios include the above as well as trigonometry, calculating the gradient of a line, measuring density or pressure of an object, calculating best value for money, speed calculations, and even within sampling techniques.

See also: 15 Ratio questions

## How to use ratios

We can use a variety of methods when interpreting ratios:

## Working out ratio

A ratio can be written as a part to part and a part to whole.

We explore how to write a relationship as a ratio, manipulate ratios and real life ratio problems

30 people attend a fitness class. 23 are female and the rest are male.

Write the part to part ratio of males to females.

Solution 7:23

Step-by-step guide: How to work out ratio

## Simplifying ratios

Writing a ratio in its simplest form allows us to carry out calculations with ratios that are easier mathematically as the numbers we use are smaller.

We explore how to simplify a ratio, equivalent ratios and more real life ratio problems.

Simplify fully the ratio 14:21:35 .

Solution 2:3:5

Step-by-step guide: Simplifying ratios

## Dividing ratios

Dividing a quantity into a ratio can help us find how much the value of one or each part of a ratio is worth.

We explore how to divide a quantity into a ratio and use this to solve real life problems.

Divide £50 into the ratio of 2:3 .

Solution £20:£30

Step-by-step guide: Dividing ratios

## Ratio to fraction

When we express a ratio as a fraction, we need to know either the value of each part of the ratio or the total amount and the value of all but one part of the ratio (of which we need to find).

We explore using ratios to find fractions, and using fractions to find ratios.

The ratio of red to blue counters is 3:4 . What fraction of the counters are blue?

Solution \frac{4}{7}

Step-by-step guide: Ratio to fraction

## Ratio to percentage

Writing a ratio as fractions can be extended to then writing it as percentages.

The ratio of green counters to yellow counters is 1:3 . What percentage of the counters are yellow?

Solution: \frac{3}{4}=75 %. 75 % of the counters are yellow.

Step-by-step guide: Ratio to percentage

## Ratio problem solving

Comprehension and a wide range of subject knowledge is required to solve problems involving ratios.

We explore how to set up and solve problems involving ratios.

Jenny is x years old and Suzie is four times as old as Jenny. If the difference between their ages is 15 , how old is each person? Write your answer as a ratio of Jenny’s age to Suzie’s age.

Solution 5:20

Step-by-step guide: Ratio problem solving

## Ratio scale

Square A has an area of 9cm^2 . Square B has a perimeter of 20cm . Write the ratio of their side lengths in the form 1:n

Solution 1:\frac{5}{3}

Step-by-step guide: Ratio scale

## Ratio worksheet

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

## Write as a ratio

Questions may ask you to write a situation as a ratio. For example, a class has 12 boys and 17 girls, write the number of boys and the number of girls as a ratio. The answer would be 12:17 .

## Use a ratio

You may be given a ratio and asked to use the ratio to solve problems.

For example, a purple paint in made by mixing red and blue paint in the ratio 2:3 . Use the ratio to work out how many litres of red and blue paint are needed to make 40 litres of purple paint.

Red:Blue=2:3 which has 5 parts in total. The total is the amount of purple paint.

We need to scale up the ratio so that there are 40 litres of purple paint by multiplying each part by 8.

Therefore there will be 16 litres of red paint and 24 litres of blue paint needed to make 40 litres of purple paint.

You may be asked to express a ratio in the form “ n:1 ” or “ 1:n ”. This would involve scaling the ratio so that one of the parts is 1.

For example,

Express the ratio 12:4 is the ratio of n:1 . This would mean we have to scale the four so that it becomes 1. We can do this by dividing both parts of the ratio by 4 to become 3:1 , with n= 3 .

## Ratio on a line

Some ratio problems involve points on a straight line and the ratios of the lengths of the different sections.

For example,The points A, B, C and D lie in order on a straight line.

AB:BD=2:5 and AC:CD=3:2

Then we add the ratio parts.

The total for the ratio parts needs to be the same, so we scale up using the lowest common multiple.

If we write the new ratios onto the line, we can then see what the different sections of the line are.

The sections BC will be 21-10=11 .

Or alternatively BC can be calculated by 25-14=11 .

The final answer is

## Ratio to graph

Ratio problems may also involve coordinates.

Points A and B have the coordinates (1,1) and (11,6) respectively.

Point C lies on the line AB such that AC:CB=3:2

Find point C .

The ratio 3:2 has 5 parts. We need to split the line AB into 5 equal parts. AC will be \frac{3}{5} of the line and CB will be \frac{2}{5} of the line.

We can do this by looking at the x -coordinates and the y -coordinates separately.

The distance in the x direction is 11 - 1 = 10

So the x -coordinate will be 1 + \frac{3}{5} ✕ 10 = 7

The distance in the y direction is 6 - 1 = 5

So the x -coordinate will be 1 + \frac{3}{5} ✕ 5 = 4

So point C is at (7,4) .

## Ratio examples

Example 1: how to work out a ratio.

The ratio of people who prefer skiing holidays to beach holidays is expressed as a bar model. State the ratio of people who prefer skiing holidays to the total number of people.

• State the number of shares in the required part of the ratio.

The Beach has 3 parts.

2 State the number of shares in the other part(s) as required.

The total number of parts is 1+3=4

3 Write the ratio using a colon : (and simplify when necessary).

## Example 2: simplifying ratios

Use a bar model to simplify the ratio 12:6

Calculate the highest common factor of the parts of the ratio.

Representing the ratio 12:6 as a bar model, we have

Where purple represents 12 shares, and yellow represents 6 shares.

HCF(12,6)=6

Divide each part of the ratio by the highest common factor.

As the highest common factor is 6 , we divide the bar above into six bars containing the same amount of purple shares, and yellow shares.

Each bar is the ratio 2:1 .

Solution : 2:1

## Example 3: dividing ratios

Shirley wants to make shortbread for a party. The recipe requires flour, butter and sugar in the ratio 3:2:1 .

Shirley has 610g of flour, 450g of butter, and 750g of sugar.

Does she have enough of each ingredient to make 1.2kg of shortbread?

The weight of each ingredient in a shortbread is shown as a bar model below.

Add the parts of the ratio together.

Adding up the number of shares in the bar we have 3+2+1=6

Divide the quantity by the sum of the parts.

1.2kg is equal to 1200g (multiply by 1000 ).

1200 \div 6=200g per share.

Multiply the share value by each part in the ratio.

Looking at each ingredient, we have

Flour = 200 \times 3=600g

Butter = 200 \times 2=400g

Sugar = 200 \times 1=200g

Answer : Yes she has enough of each ingredient.

## Example 4: ratio to fraction

The diagram below shows the days of the month that were above or below 20^{\circ}C on average.

Complete the bar model to show the fraction of days in the month at were above 20^{\circ}C

Add the parts of the ratio for the denominator.

By counting the number of days in the month, there are 31 days.

We therefore need to split the bar into 31 equal shares.

State the required part of the ratio as the numerator.

The first number in the ratio represents the number of days above 20^{\circ}C and so we need to colour in 11 of these shares in red, the rest are blue.

This means that 11 out of the 31 days were warmer than 20^{\circ}C and so the fraction is \frac{11}{31} .

Solution: \frac{11}{31}

## Example 5: problem solving

The ratio of a:b=3:2 . The ratio of b:c=3:5 . What is the ratio of a:c ?

Identify key information within the question.

Drawing these ratios using bar models, we have:

Know what you are trying to calculate.

Instinctively, you may think that the ratio of a:c is 3:5 but this would be incorrect. We need to calculate the ratio of a:c when the number of shares of b are the same for each ratio.

We therefore need to calculate the lowest common multiple of the two values of b, find the equivalent ratios of a:b and b:c when b is the same value, then we can state the ratio a:c.

Use prior knowledge to structure a solution.

The first five multiples of 2 and 3 are:

Multiples of 2 = 2, 4, {\color{red} 6}, 8, 10

Multiples of 3 = 3, {\color{red} 6}, 9, 12, 15

LCM(2,3) = {\color{red} 6}.

We now find the equivalent ratios.

Multiplying both parts of the ratio of a:b by 3 , we get the ratio 9:6 .

Multiplying both parts of the ratio of b:c by 2 , we get the ratio 6:10

As the value of b is the same for both ratios, the ratio for a:c can be stated by counting the number of shares in each part.

This ratio is already in its lowest terms and so cannot be simplified further.

## Example 6: ratio scales

A map has the scale of 1cm:2km . The distance between two points on the map is 3.5cm . Calculate the distance between the two points in real life.

Write down two related quantities from the question / diagram.

Using a bar model, we can show the ratio of the map to the actual distance as

Calculate the scale factor / ratio of the two quantities.

We know that the ratio between the two quantities is 1cm:2km . Remember that these are different units.

Use the scale factor to determine other scaled values.

Every 1cm on the map represents 2km in real life and so by multiplying the number of shares by 3.5 , we will calculate the actual distance

Here, 3.5cm on the map is equal to 7km in real life.

## Common misconceptions

• Ratio written in the wrong order

A common error is to write the parts of the ratio in the wrong order. E.g. The number of dogs to cats is given as the ratio 12:13 but the solution is incorrectly written as 13:12 .

• Ratios and fractions confusion

E.g. The ratio 2:3 is incorrectly expressed as the fraction \frac{2}{3} and rather than the correct answer of \frac{2}{5} . This is a misunderstanding of the sum of the parts of the ratio. The sum of all of the parts of the ratio gives us the denominator of the fraction.

• Incorrect value for the numerator

A common error is to incorrectly state the numerator from the ratio.

E.g. The number of mugs to glasses in a kitchen is written as the ratio 8:11 respectively. Write the fraction of mugs in the kitchen.  The solution could be incorrectly written as \frac{11}{19} taking the value for the numerator as the number of glasses, not the number of mugs. The correct answer is \frac{8}{19} .

• Not fully simplified

A common error is to not write a ratio in its simplest form by not finding the highest common factor. E.g. Simplify the ratio 12:18 Dividing both numbers by 2 will leave a ratio of 6:9 . This can be simplified further by dividing by 3 to get the ratio 2:3 , which is the correct answer.

• Not simplifying all parts of the ratio

When simplifying a ratio with more than two parts, not all of the parts are simplified. For example, “Simplify the ratio 12:6:15 ” is incorrectly written as 2:6:3 as the middle part is not cancelled down.

• Dividing the ratio by each part

A common error is to divide a value by each part of the ratio. E.g. Divide £120 into the ratio 2:3 The incorrect answer if produced by dividing £120 by 2 , and then dividing  £120 by 3 to get £60:£40 .  This does not make sense as the ratio is not equivalent to the original. The correct answers requires that the amount is divided by the sum of the parts in the ratio  120 \div (2+3)=120 \div 5=£24, then this value multiplied by each part in the ratio 24 \times 2=£48 , 24 \times 3=£72

• 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.

• Simplifying the answer

When sharing a quantity into the ratio, you are finding an equivalent ratio so you do not need to simplify the answer.

## Practice ratio questions

1. A musical requires 200 costumes. 140 costumes are allocated to the background dancers whilst the rest are for the starring roles. Write the ratio of the costumes for starring roles to backing dancers in the simplest form.

200-140=60 starring role costumes

The ratio is therefore 60:140.

The highest common factor of 60 and 140 is 20:

There are 3 shares for starring roles, and 7 shares for background dancers, hence the ratio 3:7.

2. 50 people were asked about their use of social media; everyone participated. 24 boys were asked. Write the ratio of boys to girls who participated in the study in its simplest form.

Use the bar model below to help you.

Colouring in 24 out of the 50 shares we have

This leaves us with 26 shares that are left white.

The highest common factor of 24 and 26 is 2 .

We can therefore halve the number of shares on each side of the ratio to get

Counting the shares, we now have the ratio of 12:13.

3. A soap “Duo” is made by combining lavender soap with lemon soap. Each bar of soap weighs 330g . If the ratio of lavender to lemon is 4:7 , how many grams of lemon soap are in each bar?

As there are 7+4=11 shares within the ratio

330 \div 11=30g per share

The amount of Lemon in the soap is equal to 7 \times 30=210g

4. The fraction of bananas in a bowl is \frac{13}{20} . Calculate the ratio of bananas to other pieces of fruit in the bowl.

The total number of pieces of fruit is 20 . The number of bananas is 13 . As a bar model, this looks like

The number of other pieces of fruit is therefore 7 (this is calculated by 20-13=7 or counting the number of purple bars above).

The ratio of bananas to other pieces of fruit is therefore 13:7.

5. Mel, Nicole and Orla use a bar model to show their ages.

Orla is 12 years older than Nicole. How old is Mel?

We currently have the ratio 5:6:10.

If Orla is 12 years older than Nicole, and this is 4 shares of the ratio, we have 4 shares equal to 12 years.

1 share is equal to 3 years.

As Mel has 5 shares, 5 \times 3=15 years old.

6. A model soldier is scaled down using a ratio of 5cm:1cm . Given that the height of the soldier in real life is 182cm , calculate the height of the model.

Using a bar model, we have the ratio 5:1 drawn as

If the soldier is 182cm in real life, the value of one share within the bar model is equal to 182 \div 5=36.4cm.

This means the height of the model is 36.4cm.

## Ratio GCSE questions

1. An orchestra has 100 musicians. 60\% of them play a string instrument. The ratio of violin players to the other string instruments is 4:11 .

How many musicians play the violin in the orchestra?

16 violin players

2. A florist sells 3 sizes of rose bouquets: regular, large, and extra large. The regular bouquet contains 5 roses, the large bouquet contains 8 roses, and the extra large bouquet contains 12 roses.

In one February, she sells 16 regular bouquets, 16 large bouquets and 18 extra large bouquets.

(a) How many roses are required for these orders?

(b) The ratio of roses that were used to not used in the bouquets was 8:3. What fraction of the roses were not used in the bouquets?

(c) How many roses were bought in total?

3. During one weekend, 256 planes depart from an airport to go to France and Spain in the ratio of 3:5 . On a bank holiday weekend, the number of flights increases by 68, giving the new ratio of 4:5.

How many more flights went to France on the bank holiday weekend?

## Learning checklist

You have now learned how to:

• Use ratio notation, including reduction to simplest form
• Divide a given quantity into 2 parts in a given part: part or part: whole ratio; express the division of a quantity into 2 parts as a ratio
• Understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction

## The next lessons are

• Compound measures
• Best buy maths

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## Ratio problem solving

A KS4 maths worksheet resource to practise more difficult problems involving ratio. These questions require students to recognise that the first step is to consider how the initial ratio has altered to achieve the final ratio. Solutions could be achieved by setting up an algebraic equation to solve.

Step-by-step answers are provided.

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## Ratio Practice Questions

Click here for questions, click here for answers, gcse revision cards.

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#### IMAGES

1. Solving Problems Involving Ratio

2. GCSE Maths (9-1)

3. Year 6 Problem Solving Involving Ratio and Simplifying Ratio

4. Year 6

5. Ratio_Problem Solving

6. Ratio Problem Solving

#### VIDEO

1. Solving ratio problems with tables example 1

2. Art of Problem Solving: Ratios

3. Solving Ratio Word Problems (the easy way)

4. Ratio problems, the trick to solving them easily

5. Art of Problem Solving: Introducing Ratios

6. How to Solve Ratio Word Problems

#### COMMENTS

1. Ratio problem solving for 9-1 GCSE with answers

Last updated Not quite what you were looking for? Search by keyword to find the right resource: Ratio problems that involve a bit of thinking, such as combining ratios. Perfect for practice for the new GCSE.

2. Maths Problem Solving with Ratio & Proportion Year 6

Lesson objective: To problem solve with ratio and proportion. In this lesson, students will recap what ratio and proportion is and how ratio can be calculated in given amounts. They will look at how to work out the scale factor a shape has been enlarged by as well as how to approach word problems.

3. GCSE Maths (9-1)

19 April 2021 Not quite what you were looking for? Search by keyword to find the right resource: Worksheet with 9 Problem Solving, Exam Style Questions on RATIO The idea behind the resource is to help students be able to solve problem solving questions. It could

4. Applied Ratio

This new lesson on three-way ratio problem solving looks at using given ratios to create others. Students will need to understand equivalence of ratios and sharing into a ratio. Recipes is a common exam question and the main task of this lesson is fully differentiated and focuses on the menu for the restaurant Pythagoras' Place.

5. Ratio: Problem Solving Textbook Exercise

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 ... Ratio: Problem Solving Textbook Exercise. Click here for Questions. Textbook Exercise. Previous: Ratio: Difference Between Textbook Exercise. Next: Reflections Textbook ...

6. 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.

7. AQA All About Maths

This challenging problem solving ratio activity is suitable for the most able higher tier students as an extension or challenge activity.17/06/2015. ... You will need to register for a TES account to access this resource, this is free of charge. 17/06/2015. Type(s): Activities (e-library) ... Ratio and Proportion - Lesson Plan 1. 1 ...

8. Resourceaholic: New GCSE: Ratio

The ratio of boys to girls at a school is 5:7 There are 600 children at the school. How many boys are there at the school? But GCSE questions are more challenging now. We're seeing a lot of 'ratio change' questions - this example, from Access Maths , was recently tweeted by Gayle Head ( @maths_head ): How would you solve it?

9. Ratio

This SMILE resource contains two packs of games, investigations, worksheets and practical activities supporting the teaching and learning of ratio and a booklet 'The Golden Rectangle'. Ratio pack one contains twelve work cards with a wide variety of activities covering comparing lengths, introducing simple ratio, comparing ratio, converting between units, ratio problems, and similar rectangles.

10. Secondary: TES Maths Resource of the Week

This resource provides a wonderful introduction to the basics of bar modeling for ratio, aimed at secondary teachers. The choice of questions is superb, and really helps illustrate the power of the approach. Consider the following three approaches: 1) Kallan and Adam share some money in the ratio 5:3. Between them they have £240.

11. 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.

12. Solving Problems

Lesson Objectives. To be able to: Reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation; Divide a quantity into two or more parts in a given ratio. Use the unitary method to solve simple word problems involving ratio and direct proportion. Compare two ratios.

13. Ratio Problem Solving

Students will first learn about ratio problem solving as part of ratio and proportion in 6 6 th grade and 7 7 th grade. What is 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.

14. Teaching Ratio And Proportion KS2: A Guide For Year 6 Teachers

A comprehensive guide to teaching ratio and proportion at KS2 using a maths mastery approach, with lesson ideas and example problems. Maths Tutoring for Schools. ... Pupils should consolidate their understanding of ratio when comparing quantities, sizes and scale drawings by solving a variety of problems. They might use the notation a:b to ...

15. Ratio

This would involve scaling the ratio so that one of the parts is 1. For example, Express the ratio 12:4 12: 4 is the ratio of n:1 n: 1. This would mean we have to scale the four so that it becomes 1. We can do this by dividing both parts of the ratio by 4 to become 3:1 3: 1, with n= 3 n = 3.

16. Ratio: Two Ratios Textbook Exercise

The Corbettmaths Textbook Exercise on Ratio: Two Ratios

17. Ratio problem solving practice |KS4 maths |Teachit

Ratio problem solving Last updated: 15/11/2023 Contributor: Teachit Author Main Subject Maths Key stage KS4 Category Ratio, proportion and rates of change: Ratio Inside Includes answers Resource type Worksheet A KS4 maths worksheet resource to practise more difficult problems involving ratio.

18. Solving ratio problems

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 ...

19. Ratio Practice Questions

Practice Questions. Previous: Percentages of an Amount (Non Calculator) Practice Questions. Next: Rotations Practice Questions. The Corbettmaths Practice Questions on Ratio.