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Problem solving with fractions and ratios

I can use my knowledge of fractions and ratios to solve problems.

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Lesson 17 of 17

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Year 7

Problem solving with fractions and ratios

I can use my knowledge of fractions and ratios to solve problems.

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Lesson details

Key learning points

Any fraction can be turned into a ratio.
Moving between fractions and ratios can make a problem easier.
There can be lots of information, it is important to think about what is required to solve the problem.

Keywords

Proportion - Proportionality means when variables are in proportion if they have a constant multiplicative relationship.
Ratio - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

Common misconception

Always dividing the amount by the sum of the 'parts' of the ratio to get one 'part'.

Offer opportunities to match problems to bar models ensure the same numbers are used to highlight the differences.

As a recap of ratio, ask the pupils to come up with their ratios based on their own lives and the multiplicative relationship between them. E.g. The ratio of pets to people in their house, the ratio of matches their favourite team has won to lost.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
In this list of common metric units of length which one is missing? millimetre, centimetre, metre, .

Correct Answer: kilometre, km, kilometres, kilometer, kilometers

Q2.
1 km = 1000 m, 1 m = 100 cm. What is 5 400 000 cm in kilometres?

5400 km

540 km

Correct answer: 54 km

5.4 km

0.54 km

Q3.
The scale on a map is 1:5 000 000. The distance between two places on the map is 5 cm. What is the distance in real life in kilometres?

2.5 km

25 km

Correct answer: 250 km

2500 km

25 000 km

Q4.
The scale on a map is 1:500 000. The distance between two places is 86 km. What is the distance on the map?

Correct answer: 17.2 cm

172 cm

17.2 km

172 m

Q5.
The length of a pencil is 2.5 inches. Convert this into centimetres given that 1 inch = 2.54 cm.

Correct Answer: 6.35 cm, 6.35cm, 6.35, 6.35 centimetres, 6.35centimetres

Q6.
The distance between London and Manchester is 200 miles. Convert this into kilometres given that 5 miles = 8 km.

Correct Answer: 320 km, 320, 320km, 320 kilometres

Assessment exit quiz

Download quiz pdf

6 Questions

Q1.
Fill in the missing word: Variables are in proportion if they have a multiplicative relationship.

Correct Answer: constant

Q2.
Select the bar model that is correctly labelled to solve this problem: Sam and Jacob share some stickers in the ratio of 3 : 7. Sam get 168 less than Jacob. How many stickers does Sam get?

Correct Answer: An image in a quiz

Q3.
Sam and Jacob share some stickers in the ratio of 3 : 7. Sam get 168 less than Jacob. How many stickers does Sam get?

Correct Answer: 126, 126 stickers

Q4.
The ratio of children to adults in a club is 2 : 3. If there are 26 children, how many are in the club in total?

Correct Answer: 65, 65 people, sixty-five, sixty five, sixtyfive

Q5.
A bag contains red, green and yellow sweets. $$1\over4$$ of them are red. The rest of the sweets are either green or yellow, in the ratio 4 : 5. There are 72 sweets in the bag. How many are yellow?

Correct Answer: 30, 30 yellow , 30 yellow sweets, thirty

Q6.
Andeep’s older sister Belle is 3 times his age. His brother Charlie is $$5\over6$$ of Belle's age. The total of Andeep’s and Belle’s ages is 48. How old is Charlie?

Correct Answer: 30, 30 years old, thirty, thirty years old

Lesson appears in

UnitMaths / Understanding multiplicative relationships: fractions and ratio

Maths

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Problem solving with fractions and ratios

Problem solving with fractions and ratios

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.In this list of common metric units of length which one is missing? millimetre, centimetre, metre, .

Q2.1 km = 1000 m, 1 m = 100 cm. What is 5 400 000 cm in kilometres?

Q3.The scale on a map is 1:5 000 000. The distance between two places on the map is 5 cm. What is the distance in real life in kilometres?

Q4.The scale on a map is 1:500 000. The distance between two places is 86 km. What is the distance on the map?

Q5.The length of a pencil is 2.5 inches. Convert this into centimetres given that 1 inch = 2.54 cm.

Q6.The distance between London and Manchester is 200 miles. Convert this into kilometres given that 5 miles = 8 km.

Assessment exit quiz

6 Questions

Q1.Fill in the missing word: Variables are in proportion if they have a multiplicative relationship.

Q2.Select the bar model that is correctly labelled to solve this problem: Sam and Jacob share some stickers in the ratio of 3 : 7. Sam get 168 less than Jacob. How many stickers does Sam get?

Q3.Sam and Jacob share some stickers in the ratio of 3 : 7. Sam get 168 less than Jacob. How many stickers does Sam get?

Q4.The ratio of children to adults in a club is 2 : 3. If there are 26 children, how many are in the club in total?

Q5.A bag contains red, green and yellow sweets. $$1\over4$$ of them are red. The rest of the sweets are either green or yellow, in the ratio 4 : 5. There are 72 sweets in the bag. How many are yellow?

Q6.Andeep’s older sister Belle is 3 times his age. His brother Charlie is $$5\over6$$ of Belle's age. The total of Andeep’s and Belle’s ages is 48. How old is Charlie?

Lesson appears in

UnitMaths / Understanding multiplicative relationships: fractions and ratio

Maths

Q1.
In this list of common metric units of length which one is missing? millimetre, centimetre, metre, .

Q2.
1 km = 1000 m, 1 m = 100 cm. What is 5 400 000 cm in kilometres?

Q3.
The scale on a map is 1:5 000 000. The distance between two places on the map is 5 cm. What is the distance in real life in kilometres?

Q4.
The scale on a map is 1:500 000. The distance between two places is 86 km. What is the distance on the map?

Q5.
The length of a pencil is 2.5 inches. Convert this into centimetres given that 1 inch = 2.54 cm.

Q6.
The distance between London and Manchester is 200 miles. Convert this into kilometres given that 5 miles = 8 km.

Q1.
Fill in the missing word: Variables are in proportion if they have a multiplicative relationship.

Q2.
Select the bar model that is correctly labelled to solve this problem: Sam and Jacob share some stickers in the ratio of 3 : 7. Sam get 168 less than Jacob. How many stickers does Sam get?

Q3.
Sam and Jacob share some stickers in the ratio of 3 : 7. Sam get 168 less than Jacob. How many stickers does Sam get?

Q4.
The ratio of children to adults in a club is 2 : 3. If there are 26 children, how many are in the club in total?

Q5.
A bag contains red, green and yellow sweets. $$1\over4$$ of them are red. The rest of the sweets are either green or yellow, in the ratio 4 : 5. There are 72 sweets in the bag. How many are yellow?

Q6.
Andeep’s older sister Belle is 3 times his age. His brother Charlie is $$5\over6$$ of Belle's age. The total of Andeep’s and Belle’s ages is 48. How old is Charlie?