It is important to preserve the relationship between the parts of a ratio.
Changing this relationship would change the ratio.
When the ratio changes, the quantities can be worked out by using equivalent ratios.

Common misconception

Treating the ratio as the total amount. For example sweets : chocolates in the ratio 6 : 7 and 2 chocolates are eaten, thinking the ratio must now be 6 : 5

Looking at how these problems are formed in learning cycle 1 will help and getting pupils to explore how the ratio changes when things are added or removed.

Keywords

Proportion - A part to whole (sometimes part to part) comparison. If two things are proportional then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained.
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.
LCM - LCM is an abbreviation for lowest common multiple.
Lowest common multiple - The lowest common multiple is the lowest number that is a multiple of two or more numbers.

Learning cycle 1 gives pupils a chance to consider how to solve problems where the ratio between things changes. Paying attention to equivalent ratios and what changes and what stays the same should help pupils to understand the process

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

To combine ratios they must have a component.

Correct Answer: common

Q2.

Given these bar models. What is the ratio of hearts to suns?

Correct Answer: 3 : 1, 3:1

Q3.

Given that squares : circles = 6 : 5 and circles : triangles = 1 : 3. Find the ratio of squares : triangles.

Correct Answer: 6 : 15, 6:15

Q4.

a : b = 3 : 4, b : c = 5 : 9. Find the ratio a : b : c

Correct Answer: 15 : 20 : 36, 15:20:36

Q5.

A box contains 185 sweets which are either hearts (h), stars (s) or bottles (b). The ratio of hearts to stars is 2 : 3. The ratio of stars to bottles is 5 : 4. How many bottles are in the box?

Correct Answer: 60, sixty

Q6.

b = 2a, c = 7b, find the ratio of a : c

Correct Answer: 1 : 14, 1:14

Exit quiz

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6 Questions

Q1.

Which of the following is used as a separator in a ratio?

;

Correct answer: :

Q2.

There are 30 cans of drink and bags of sweets in a vending machine. The ratio of cans : bags is 2 : 1. 5 cans and 1 packet is sold. What is the ratio of cans : bags now? (In its simplest form)

Correct Answer: 5 : 3, 5:3

Q3.

There are 24 vehicles in a car park. The ratio of cars : vans is 5 : 1. 4 more cars enter the car park. What is the ratio of cars : vans now? (Give your answer in its simplest form)

Correct Answer: 6 : 1, 6:1

Q4.

The ratio of adults to children at an athletics club is 7 : 5. 2 more children join, the ratio is now 4 : 3. How many adults are members of the club?

Correct Answer: 56, 56 adults

Q5.

3 bags contain counters in the ratio 3 : 2 : 4. Some counters are taken out of 1 bag and put into the other 2. The ratio of counters is now 1 : 1 : 2. What is the minimum number of counters removed?

Correct Answer: 3, 3 counters, three, three counters

Q6.

The ratio of the number of £1 coins to £2 in Sam’s money box is 2 : 3. Their gran gives them 4 more £1 coins, the ratio is now 5 : 6. How much money was in Sam’s money box originally?

£9

£12

£40

Correct answer: £64

£68