Ratio

April 12, 2023

Ratio

1. Using ratios

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April 12, 2023

When a quantity is divided into parts the ratio compares the amounts.

Here the parts are equal, so the ratio is 1:1

1 1:

Explanation

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April 12, 2023


Here the parts are equal, so the ratio is 1:1

1 1:

A quantity may be divided into more than two parts.

Explanation

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April 12, 2023



3 : 2 : 1

When you multiply or divide the numbers in a ratio by the same number, you get an equivalent ratio.

6 4 2

× 2

Explanation

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April 12, 2023



When you multiply or divide the numbers in a ratio by the same number, you get an equivalent ratio.

: :6 4 2

The ratio 6:4:2 can be simplified to 3:2:1

3 2 1

Explanation

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April 12, 2023

Complete this table of equivalent ratios.

2:63:94:125:15

4:66:98:12

10:15

4:146:218:28

10:35

2:72:31:3× 2× 3× 4× 5

Fill in the equivalent ratios in these sequences.

1:2 2:4 4:82:3 6:9 8:12

2:10 3:153:4 6:8

3:64:6

1:5 4:209:12 12:16

Practise

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April 12, 2023

Two families visit the cinema on a day when all adults pay the child price.There are five Pattersons and three Khans. The bill comes to £20. How much should each family pay?

Total the numbers in the ratio.

5:3Work out the ratio of Pattersons to Khans.

8

£2.50

£12.50 £7.50Multiply your answer by each number in the original ratio.

Divide the total cost by this number.

×3×5

The Pattersons pay £12.50 and the Khans £7.50.

Example

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April 12, 2023

Two brothers, Jake and Dino run an office cleaning company. They have decided to split the profits according to how many days each works in a week.Jake works Mondays and Thursdays and Dino works Tuesdays, Wednesdays and Fridays.

In one week they make £1,900. How much should each brother get?

They work 5 days in total1900

5= 380

Jake receives 2 × £380

and Dino receives 3 × £380

So

=

=

£760

£1140

Example

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April 12, 2023

1:3

The ratio of boys to girls who study ballet in the UK is

1:3 In a town, 45 girls are learning ballet.

How many boys would you expect to also be learning?

45

To make 45 from 3, you need to use the multiplier 15.

×15

To keep the ratio equivalent, you also need to multiply the 1 by 15.

×1515:

You would expect 15 boys to be studying ballet.

boys girls

Example

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April 12, 2023

A multiplier may not always be obvious. To find it you may need to use division.To make enough orange paint to cover a room, you need to mix 2 parts yellow to every 5 parts red.How much yellow paint will you need to mix with 7 litres of red paint?

2:5

To find the multiplier divide the 7 litres of red paint by the 5 in the ratio. = 1.47 ÷ 5

yellow red

×1.4

7×1.4

2.8:

You need 2.8 litres of yellow paint.

Example

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Education

Ratio