Ratio and proportion.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Ratio and proportion

Fractions, ratio and percentages

Lesson 3 of 5

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before

Fractions, ratio and percentages

Lesson 3 of 5

Answer each one, then check.

1

Last lesson: share 20 in the ratio 1 : 4.

2

Work out 12 × 1.5.

3

Work out 450 ÷ 6.

4

Last lesson: write 4 : 10 in the form 1 : n.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before - Answers

Fractions, ratio and percentages

Lesson 3 of 5

1

Last lesson: share 20 in the ratio 1 : 4.

4 and 16

2

Work out 12 × 1.5.

18

3

Work out 450 ÷ 6.

75

4

Last lesson: write 4 : 10 in the form 1 : n.

1 : 2.5

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Fractions, ratio and percentages

Lesson 3 of 5

1

Solve direct proportion problems with the unitary method.

2

Compare best buys.

3

Convert between currencies.

4

Solve inverse proportion problems.

5

Recognise direct and inverse proportion from a graph.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Direct Proportion

Fractions, ratio and percentages

Lesson 3 of 5

Two quantities are in direct proportion when they increase at the same rate: double one and the other doubles.

The unitary method

Find the value of ONE, then multiply: if 6 pens cost £4.20, one costs 70p, so 10 cost £7.

Scaling

Multiply both by the same number: 6 people to 9 people is × 1.5.

The graph

A straight line through the origin.

Examples

Cost and number of items, recipe amounts and servings, pounds and euros.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

A Recipe

Fractions, ratio and percentages

Lesson 3 of 5

A recipe for 6 people uses 450 g of flour. How much flour is needed for 10 people?

1

Find the amount for 1 person

450 ÷ 6 = 75 g

2

Multiply by 10

75 × 10 = 750 g

ANSWER

750 g of flour

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Best Buy

Fractions, ratio and percentages

Lesson 3 of 5

A 500 g bag of rice costs £1.85. A 750 g bag costs £2.70. Which is better value?

1

Find the cost of the same amount of each, say 100 g

185 ÷ 5 = 37p and 270 ÷ 7.5 = 36p

2

Compare

36p is less than 37p

ANSWER

The 750 g bag is better value (36p per 100 g).

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Currency Conversion

Fractions, ratio and percentages

Lesson 3 of 5

Exchange rates are direct proportion.

Multiply to convert from pounds

If £1 = €1.15, then £240 is 240 × 1.15 = 276 euros, €276.

Divide to convert back

€92 is 92 ÷ 1.15 = 80 pounds, £80.

Check the size

Each pound buys more than one euro, so the euro amount should be bigger.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Inverse Proportion

Fractions, ratio and percentages

Lesson 3 of 5

Two quantities are in inverse proportion when one goes up as the other goes down, and their product stays the same.

The idea

Double the number of workers and the job takes half the time.

The method

Find the total "work": 6 painters × 8 days = 48 painter-days. Then divide.

The graph

A curve that gets closer and closer to both axes.

Examples

Workers and time, speed and journey time, people sharing a prize.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

An Inverse Proportion Problem

Fractions, ratio and percentages

Lesson 3 of 5

6 painters take 8 days to paint a building. How long would 4 painters take, working at the same rate?

1

Find the total work

6 × 8 = 48 painter-days

2

Divide by the new number of painters

48 ÷ 4 = 12

ANSWER

12 days

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Direct and Inverse Proportion Graphs

Fractions, ratio and percentages

Lesson 3 of 5

Direct: a straight line through the origin. Inverse: a curve towards both axes.

The shape of a graph tells you which kind of proportion you have. A straight line through the origin means direct proportion. A curve falling towards both axes means inverse proportion.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Fractions, ratio and percentages

Lesson 3 of 5

Direct proportion

Two quantities that increase at the same rate; their ratio stays the same.

Inverse proportion

As one quantity increases, the other decreases; their product stays the same.

Unitary method

Finding the value of one item first, then scaling up.

Exchange rate

How much of one currency you get for one unit of another.

Best buy

The option that gives the most for your money.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Fractions, ratio and percentages

Lesson 3 of 5

YOUR TASK

Shopping Detective

12 minutes

Which is the best buy? (a) Cereal: 500 g for £2.40 or 750 g for £3.45. (b) Juice: 1 litre for £1.10 or 1.5 litres for £1.62. (c) Eggs: 6 for £1.35 or 15 for £3.30. Then: 3 friends share a prize and get £40 each. How much would each get if 5 friends shared it?

1

Compare the same amount of each.

2

Show the unit price.

3

Decide, and say why.

WHAT A GOOD ANSWER SHOWS

(a) 48p vs 46p per 100 g: 750 g box. (b) 11p vs 10.8p per 100 ml: 1.5 litres. (c) 22.5p vs 22p per egg: 15 eggs. Prize: 3 × 40 = 120; 120 ÷ 5 = £24 each.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Fractions, ratio and percentages

Lesson 3 of 5

Use the unitary method.

Scale a recipe.

Compare best buys.

Convert between currencies.

Solve inverse proportion problems.

Recognise direct and inverse proportion graphs.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Direct proportion: find one, then multiply.

Best buy: compare the price of the same amount.

Currency: multiply one way, divide the other.

Inverse proportion: the product stays the same.

EXAM FOCUS

It takes 5 machines 12 hours to make an order. How long would 3 machines take? (2 marks)

Ask first: if one quantity doubles, does the other double (direct) or halve (inverse)? Getting that right is most of the marks.

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