Ratio

Objectives

• Understand how to use ratios to find specific quantities

• Simplify ratios by identifying common factors

• Demonstrate a medium level of

understanding of multiplication and division

• A ratio is a comparison between two numbers or two quantities of different items.

• A ratio can be written as 3:2 and is said to be 3 to 2.

• If you have 2 biscuits and 1 cups of tea, the ratio of biscuits to cups of tea would be 2:1.

• Ratio is also a way in which quantities can be divided or shared.

Simplifying Ratios

• Like fractions, ratios can be simplified by finding common factors.

• The factors of a number are those numbers that divide into it exactly.

• E.g 1 × 12 = 12 2 × 6 = 12 3 × 4 = 12

• So the factors of 12 are 1, 2, 3, 4, 6 and 12.

Example

• There are 15 males and 12 females in a group.

What is the ratio of males to females? Give your

example in its simplest form.

• So the ratio of males to females is 15:12. However,

both sides of the ratio can be divided by 3. Dividing

15 and 12 by 3 gives 5:4.

5:4 is the ratio in its simplest form.

Simplifying Ratios QUIZ

Write 1 to ten in your margin10 seconds for each question

Simplify-4:10

Q1

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Q2

Simplify-6:12 End123456789101112131415

Q3

Simplify-9:12 End123456789101112131415

Q4

Simplify-15:25 End123456789101112131415

Q5

Simplify-6:18 End123456789101112131415

Q6

Simplify-50:70 End123456789101112131415

Q7

Simplify-27:30 End123456789101112131415

Q8

Simplify-36:48 End123456789101112131415

Q9

Simplify-4:10:12

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Q10

Simplify-6:12:21

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Answers1) 2:52) 1:23) 3:44) 3:55) 1:36) 5:77) 9:108) 3:49) 2:5:610)3:4:7

Adrian is building a barbecue and needs 300g of mortar. He needs to mix cement and sand in a ratio of 2:1.

How much of each does he need?

Ratios and finding quantities

Ask yourself 3 questions:a) How many parts are there?

a) 3 (2 of cement, 1 of sand)

b) How much is 1 share worth?a) 300g ÷ 3 = 100g

c) How much of each is needed?a) 2 parts cement = 2 x 100g = 200gb) 1 part sand = 1 x 100g = 100g

How do you split 300g in the ratio 2:1?

The next job

• Adrian runs a job renovating a house. He employs painters, carpenters and brickies.

• They earn £600 for the day. Adrian decides to pay out his painters, carpenters and brickies in the ratio 1:2:3 (painters get 1, carpenters 2 and brickies 3)

• How do they split it?

Ask yourself 3 questions:a) How many shares are there?

a) 6 (3 for Brickies, 2 for Carpenters and 1 for Painters)

b) How much is 1 share worth?a) 600 ÷ 6 = £100

c) How much do they get?a) Brickies get 3 x 100 = £300b) Carpenters get 2 x 100 = £200c) Painters get 1 x 100 = £100

How do you split £600 in the ratio 1:2:3?

Sharing in Ratios

10 multiple choice questions to be answered in pairs

20 seconds for each question

£5

£4

£3

£1A) B)

C) D)

£20 is shared in the ratio 1:3How much is 1 share worth?

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£6

£1 £5

£2

A) B)

C) D)

£30 is shared in the ratio 2:3How much is 1 share worth?

End1234567891011121314151617181920

£6£3

£18£2

A) B)

C) D)

£18 is shared in the ratio 1:2How much is 1 share worth?

End1234567891011121314151617181920

£5 £9

£4£6

A) B)

C) D)

£45 is shared in the ratio 4:5How much is 1 share worth?

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£15

£16 £12

£3

A) B)

C) D)

£20 is shared in the ratio 1:3How much is 3 shares worth?

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£18£12

£15£20

A) B)

C) D)

£30 is shared in the ratio 2:3How much is 3 shares worth?

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£12£6

£18£3

A) B)

C) D)

£18 is shared in the ratio 1:2How much is 2 share worth?

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£25

£18

£20

£15A) B)

C) D)

£45 is shared in the ratio 4:5How much is 5 shares worth?

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Tom- £5Ellie- £10

Tom- £10Ellie- £5

Tom- £1Ellie- £2

Tom- £3Ellie- £6

A) B)

C) D)

Tom and Ellie share £15 in the ratio 1:2

How much do they get each?End1234567891011121314151617181920

Libby- £18Grant- £24

Libby- £20Grant- £22

Libby- £24Grant- £18

Libby- £21Grant- £28

A) B)

C) D)

Libby and Grant share £42 in the ratio 3:4

How much do they each getEnd1234567891011121314151617181920

Questions1) £30 is shared in the ratio 1:2

a) How many shares are there?b) How much is one share worth?c) How much does each person get?

2) £40 is shared in the ratio 1:3d) How many shares are there?e) How much is one share worth?f) How much does each person get?

3) £50 is shared in the ratio 2:3g) How many shares are there?h) How much is one share worth?i) How much does each person get?

4) £42 is shared in the ratio 2:5j) How many shares are there?k) How much is one share worth?l) How much does each person get?

5) £56 is shared in the ratio 1:2:4m) How many shares are there?n) How much is one share worth?o) How much does each person get?

Questions1) Archie and Charlie share their

Thomas the tank engine toys in the ratio 1:4, how many do they each get if they have:

a) 10 toys b) 30 toys c) 45 toys

2) Tom and Jerry share sweets in the ratio 2:3, how many do they each get if they share:

a) 20 sweets b) 30 sweetsc)55 sweets

3) Sue and Linda share some money in the ratio 3:7, how many do they each get if they share:

a) £30 b)£60 c)£90

4) Mike, Dave and Henry share some little bits of blue tack in the ratio 1:2:3, how many do they each get if they share:

a) 60 pieces b) 72 pieces c) 300 pieces

Extension

1. Ben and Jerry share some money in the ratio of 3:4, Ben gets £21, how much does Jerry get?

2. Jon and Ade share some socks in the ratio 2:7 Jon gets 18 socks, how many does Ade get

3. Nora, Ben and Jon share some Easter eggs in the ratio 2:5:7, Ben gets 60, how many do Jon and Nora get?

x

y

z

Firstly, do you remember what the angles in a triangle add up to???The angles in this triangle (x, y and z) are in the ratio 5:1:3 - find the size of the angles.

Extension