Fractions.pptx — OpenRevise

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Fractions

Fractions, ratio and percentages

Lesson 1 of 5

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Before We Start

Fractions, ratio and percentages

Lesson 1 of 5

Answer each one, then check.

1

Simplify 12/18.

2

What is the lowest common multiple of 4 and 6?

3

Work out ¾ of 20.

4

Write 2⅓ as an improper fraction.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Before We Start - Answers

Fractions, ratio and percentages

Lesson 1 of 5

1

Simplify 12/18.

⅔

2

What is the lowest common multiple of 4 and 6?

12

3

Work out ¾ of 20.

15

4

Write 2⅓ as an improper fraction.

7/3

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Fractions, ratio and percentages

Lesson 1 of 5

1

Add and subtract fractions and mixed numbers.

2

Multiply and divide fractions and mixed numbers.

3

Find a fraction of an amount, and write one quantity as a fraction of another.

4

Find the whole amount when you know a fraction of it.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Equivalent Fractions and Mixed Numbers

Fractions, ratio and percentages

Lesson 1 of 5

Multiplying or dividing the top and bottom by the same number gives an equivalent fraction.

Simplify

Divide the top and bottom by their HCF: 12/18 = ⅔ (dividing by 6).

Mixed to improper

2⅓ = (2 × 3 + 1)/3 = 7/3.

Improper to mixed

17/5 = 32/5, because 17 ÷ 5 = 3 remainder 2.

Always finish simply

Give answers in their simplest form, as a mixed number if the question uses them.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Adding and Subtracting

Fractions, ratio and percentages

Lesson 1 of 5

Fractions can only be added or subtracted when their denominators are the same.

Common denominator

Use the lowest common multiple of the denominators: for ¼ + 1/6, use 12.

Change each fraction

¼ = 3/12 and 1/6 = 2/12, so the answer is 5/12.

Mixed numbers

Change them to improper fractions first - it avoids borrowing mistakes.

Never add the bottoms

¼ + 1/6 is NOT 2/10.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Adding Mixed Numbers

Fractions, ratio and percentages

Lesson 1 of 5

Work out 2¾ + 15/6

1

Change to improper fractions

11/4 + 11/6

2

Common denominator: the LCM of 4 and 6 is 12

33/12 + 22/12

3

Add the numerators

55/12

4

Change back to a mixed number

55 ÷ 12 = 4 remainder 7

ANSWER

47/12

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Subtracting Mixed Numbers

Fractions, ratio and percentages

Lesson 1 of 5

Work out 3⅕ − 1⅔

1

Change to improper fractions

16/5 − 5/3

2

Common denominator 15

48/15 − 25/15

3

Subtract the numerators

23/15

4

Change back

18/15

ANSWER

18/15

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Multiplying and Dividing

Fractions, ratio and percentages

Lesson 1 of 5

No common denominator is needed - but mixed numbers must be made improper first.

Multiply

Multiply the tops and multiply the bottoms: ⅔ × ¾ = 6/12 = ½.

Cancel first

Divide a top and a bottom by a common factor before multiplying to keep numbers small.

Reciprocal

Flip a fraction to get its reciprocal: the reciprocal of 4/5 is 5/4.

Divide

Dividing by a fraction is the same as multiplying by its reciprocal: keep, flip, change.

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Why Multiplying Fractions Works

Fractions, ratio and percentages

Lesson 1 of 5

⅔ of ¾ covers 6 of the 12 small rectangles: ½.

"Of" means multiply. Take ¾ of the square, then ⅔ of that, and the overlap is 6 of the 12 small rectangles - exactly ⅔ × ¾ = 6/12 = ½.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Multiplying Mixed Numbers

Fractions, ratio and percentages

Lesson 1 of 5

Work out 2¼ × 1⅓

1

Change to improper fractions

9/4 × 4/3

2

Cancel: the 4s cancel, and 9 and 3 share a factor of 3

3/1 × 1/1

3

Multiply

3

ANSWER

3

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Dividing Mixed Numbers

Fractions, ratio and percentages

Lesson 1 of 5

Work out 3⅓ ÷ 1¼

1

Change to improper fractions

10/3 ÷ 5/4

2

Keep, flip, change

10/3 × 4/5

3

Multiply

40/15 = 8/3

4

Change back

2⅔

ANSWER

2⅔

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Fractions of Amounts

Fractions, ratio and percentages

Lesson 1 of 5

Divide by the bottom, multiply by the top.

A fraction of an amount

3/5 of 40: 40 ÷ 5 = 8, 8 × 3 = 24.

One amount as a fraction of another

15 out of 40 is 15/40 = ⅜. Make sure both are in the same units first.

Finding the whole

If 3/5 of a number is 24, then ⅕ is 8, so the whole is 5 × 8 = 40.

The rest

If 2/5 is spent, 1 − 2/5 = 3/5 is left.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Fractions, ratio and percentages

Lesson 1 of 5

Numerator

The top number of a fraction.

Denominator

The bottom number of a fraction.

Improper fraction

A fraction whose numerator is bigger than its denominator, e.g. 7/3.

Mixed number

A whole number and a fraction, e.g. 2⅓.

Reciprocal

1 divided by a number; for a fraction, the fraction flipped.

Common denominator

A denominator shared by two fractions, so they can be added or subtracted.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Fractions, ratio and percentages

Lesson 1 of 5

YOUR TASK

Fraction Target

10 minutes

Using each of the digits 1, 2, 3 and 4 once, make two fractions a/b and c/d whose sum is as close to 1 as possible. Then find the pair whose product is as small as possible.

1

Try several combinations.

2

Work out each sum exactly.

3

Explain why your best answer is best.

WHAT A GOOD ANSWER SHOWS

Closest sum to 1: ¼ + ⅔ = 11/12 (or ⅓ + 2/4 = 5/6, further away). Smallest product: ⅓ × 2/4 = 1/6 or ¼ × ⅔ = 1/6.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Fractions, ratio and percentages

Lesson 1 of 5

Simplify fractions.

Convert between mixed numbers and improper fractions.

Add and subtract fractions.

Add and subtract mixed numbers.

Multiply fractions and mixed numbers.

Divide fractions and mixed numbers.

Find a fraction of an amount.

Find the whole from a fraction of it.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Add and subtract: common denominator first; mixed numbers become improper.

Multiply: tops times tops, bottoms times bottoms; cancel first.

Divide: keep, flip, change.

Fraction of an amount: divide by the bottom, multiply by the top.

EXAM FOCUS

Work out 1¾ ÷ 2⅓. Give your answer in its simplest form. (3 marks)

Show every step - the improper fractions, the flipped fraction, the multiplication. On the non-calculator paper each step can earn a method mark.

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