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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Ratios

Fractions, ratio and percentages

Lesson 2 of 5

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before

Fractions, ratio and percentages

Lesson 2 of 5

Answer each one, then check.

1

What is the HCF of 12 and 18?

2

Last lesson: work out 3/5 of 40.

3

Simplify 15/25.

4

How many grams are in 1.2 kg?

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before - Answers

Fractions, ratio and percentages

Lesson 2 of 5

1

What is the HCF of 12 and 18?

6

2

Last lesson: work out 3/5 of 40.

24

3

Simplify 15/25.

3/5

4

How many grams are in 1.2 kg?

1200 g

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Fractions, ratio and percentages

Lesson 2 of 5

1

Simplify ratios, including ratios with different units.

2

Write a ratio in the form 1 : n or n : 1.

3

Connect ratios and fractions.

4

Share an amount in a given ratio.

5

Solve ratio problems when you know the difference or one part.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

What a Ratio Is

Fractions, ratio and percentages

Lesson 2 of 5

A ratio compares amounts: 3 red counters to 5 blue is written 3 : 5.

The order matters

3 : 5 (red to blue) is not the same as 5 : 3.

Simplify

Divide every part by the HCF: 12 : 18 = 2 : 3.

Same units first

45 cm : 1.2 m becomes 45 : 120 (both in cm), then 3 : 8.

Decimals and fractions

Multiply every part to make whole numbers: 1.5 : 2 = 3 : 4.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Simplifying with Different Units

Fractions, ratio and percentages

Lesson 2 of 5

Write 45 cm : 1.2 m in its simplest form.

1

Put both in the same units

1.2 m = 120 cm

2

Write the ratio in cm

45 : 120

3

The HCF of 45 and 120 is 15

45 ÷ 15 = 3, 120 ÷ 15 = 8

ANSWER

3 : 8

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Ratios and Fractions

Fractions, ratio and percentages

Lesson 2 of 5

A ratio tells you how many parts there are altogether.

Total parts

In the ratio 3 : 5 there are 3 + 5 = 8 parts.

As fractions

The first amount is ⅜ of the total and the second is ⅝.

Not the same thing

3 : 5 does NOT mean 3/5 of the total - it means ⅜.

Unit ratios

Divide to make one part 1: 4 : 10 = 1 : 2.5, and 10 : 4 = 2.5 : 1.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Sharing with a Bar Model

Fractions, ratio and percentages

Lesson 2 of 5

7 parts share £84, so each part is £12.

A bar model makes a ratio visible. The ratio 3 : 4 has 7 equal parts. £84 shared into 7 parts is £12 a part, so the shares are 3 × 12 = £36 and 4 × 12 = £48.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Sharing in a Ratio

Fractions, ratio and percentages

Lesson 2 of 5

Share £84 between Amy and Ben in the ratio 3 : 4.

1

Add the parts

3 + 4 = 7 parts

2

Find one part

84 ÷ 7 = 12

3

Multiply for each person

Amy 3 × 12 = 36, Ben 4 × 12 = 48

4

Check

36 + 48 = 84

ANSWER

Amy £36, Ben £48

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

When You Know the Difference

Fractions, ratio and percentages

Lesson 2 of 5

The ages of a father and son are in the ratio 5 : 2. The father is 18 years older than the son. How old is each?

1

The difference in parts

5 − 2 = 3 parts

2

3 parts are 18 years, so one part is

18 ÷ 3 = 6

3

Multiply

Father 5 × 6 = 30, son 2 × 6 = 12

4

Check the difference

30 − 12 = 18

ANSWER

Father 30, son 12

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Fractions, ratio and percentages

Lesson 2 of 5

Ratio

A comparison of the sizes of two or more quantities.

Simplest form

A ratio whose parts have no common factor other than 1.

Part

One share of a ratio; the total number of parts is the sum of the ratio.

Unit ratio

A ratio written with one part equal to 1, such as 1 : n.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Fractions, ratio and percentages

Lesson 2 of 5

YOUR TASK

Ratio Problems Relay

12 minutes

(a) Simplify 24 : 36 : 60. (b) Share 450 g of sweets in the ratio 2 : 3 : 4. (c) Paint is mixed blue to white in the ratio 2 : 7. How much white is mixed with 5 litres of blue? (d) Write 8 : 5 in the form n : 1.

1

Decide what you know: the total, one part, or a difference.

2

Find the value of one part.

3

Answer the question asked.

WHAT A GOOD ANSWER SHOWS

(a) 2 : 3 : 5 (b) 100 g, 150 g, 200 g (c) 5 ÷ 2 = 2.5 litres per part, so 7 × 2.5 = 17.5 litres (d) 1.6 : 1

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Fractions, ratio and percentages

Lesson 2 of 5

Simplify a ratio.

Simplify a ratio with different units.

Write a ratio as 1 : n or n : 1.

Write a ratio as fractions of the total.

Share an amount in a ratio.

Solve problems when I know one part or the difference.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Simplify by dividing every part by the HCF; use the same units first.

Total parts = sum of the ratio; each share is a fraction of the total.

Find the value of one part, then multiply.

A difference in amounts matches the difference in parts.

EXAM FOCUS

Red and blue beads are in the ratio 3 : 7. There are 28 more blue beads than red beads. How many beads are there altogether? (3 marks)

Decide what the number in the question stands for: the total, one person's share, or the difference. Each needs a different number of parts.

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