Fractions decimals and percentages.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Fractions, decimals and percentages

Fractions, ratio and percentages

Lesson 5 of 5

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before

Fractions, ratio and percentages

Lesson 5 of 5

Answer each one, then check.

1

Write ¼ as a decimal.

2

Write 30% as a decimal.

3

Last lesson: what multiplier decreases by 20%?

4

Which is bigger: 0.45 or 0.405?

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before - Answers

Fractions, ratio and percentages

Lesson 5 of 5

1

Write ¼ as a decimal.

0.25

2

Write 30% as a decimal.

0.3

3

Last lesson: what multiplier decreases by 20%?

0.8

4

Which is bigger: 0.45 or 0.405?

0.45

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Fractions, ratio and percentages

Lesson 5 of 5

1

Convert between fractions, decimals and percentages.

2

Order a mixture of fractions, decimals and percentages.

3

Know which fractions give terminating decimals and which recur.

4

Convert a recurring decimal to a fraction. (Higher)

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Equivalents Worth Knowing

Fractions, ratio and percentages

Lesson 5 of 5

Fraction

Decimal

Percentage

½

0.5

50%

¼

0.25

25%

¾

0.75

75%

⅕

0.2

20%

⅛

0.125

12.5%

1/10

0.1

10%

⅓

0.dot3

33⅓%

⅔

0.dot6

66⅔%

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Converting Between the Three

Fractions, ratio and percentages

Lesson 5 of 5

Each conversion is one step.

1

Fraction to decimal

Divide the top by the bottom: ⅜ = 3 ÷ 8 = 0.375.

2

Decimal to percentage

Multiply by 100: 0.375 = 37.5%.

3

Percentage to fraction

Write over 100 and simplify: 35% = 35/100 = 7/20.

4

Decimal to fraction

Use place value: 0.36 = 36/100 = 9/25.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Terminating and Recurring Decimals

Fractions, ratio and percentages

Lesson 5 of 5

Some fractions end; others repeat for ever.

Terminating

The decimal stops: ⅜ = 0.375.

Recurring

A digit or group of digits repeats for ever: ⅓ = 0.333…= 0.dot3 and 1/7 = 0.dot14285dot7.

Dot notation

A dot over one digit repeats it; dots over the first and last digit repeat the whole group.

The rule

A fraction in its simplest form terminates only if the prime factors of its denominator are just 2s and 5s: 7/40 terminates because 40 = 2³ × 5.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Ordering a Mixture

Fractions, ratio and percentages

Lesson 5 of 5

Write in order, smallest first: ⅜, 0.38, 37%, 0.dot3

1

Change everything to decimals

⅜ = 0.375, 0.38, 37% = 0.37, 0.dot3 = 0.333…

2

Compare the decimals

0.333…< 0.37 < 0.375 < 0.38

3

Write the original forms in order

0.dot3, 37%, ⅜, 0.38

ANSWER

0.dot3, 37%, ⅜, 0.38

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

PART TWO · HIGHER

Recurring Decimals to Fractions

An exact fraction for a decimal that never ends.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

A Recurring Decimal to a Fraction

Fractions, ratio and percentages

Lesson 5 of 5

Show that 0.dot4dot5 = 5/11

1

Let x be the decimal

x = 0.454545…

2

Two digits repeat, so multiply by 100

100x = 45.454545…

3

Subtract to remove the repeating part

100x − x = 45, so 99x = 45

4

Divide and simplify

x = 45/99 = 5/11

ANSWER

0.dot4dot5 = 45/99 = 5/11

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

When the Repeat Starts Later

Fractions, ratio and percentages

Lesson 5 of 5

Write 0.2dot3 as a fraction in its simplest form.

1

Let x be the decimal

x = 0.2333…

2

Multiply by 10 and by 100, so both have the same repeating tail

10x = 2.333… and 100x = 23.333…

3

Subtract

100x − 10x = 21, so 90x = 21

4

Divide and simplify

x = 21/90 = 7/30

ANSWER

7/30

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Fractions, ratio and percentages

Lesson 5 of 5

Terminating decimal

A decimal that stops, e.g. 0.375.

Recurring decimal

A decimal in which a digit or group of digits repeats for ever.

Dot notation

Dots above digits to show which digits recur.

Equivalent

Equal in value, though written differently.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Fractions, ratio and percentages

Lesson 5 of 5

YOUR TASK

Terminate or Recur?

10 minutes

Without dividing, predict whether each fraction terminates or recurs, then check with a calculator: 3/20, 5/12, 7/16, 2/15, 9/25, 4/9. Higher: write 0.dot7 and 0.1dot6 as fractions.

1

Write each denominator in prime factors.

2

Predict, then check.

3

Higher: use the algebra method.

WHAT A GOOD ANSWER SHOWS

Terminate: 3/20 (0.15), 7/16 (0.4375), 9/25 (0.36). Recur: 5/12 (0.41dot6), 2/15 (0.1dot3), 4/9 (0.dot4). Higher: 0.dot7 = 7/9, 0.1dot6 = 15/90 = 1/6.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Fractions, ratio and percentages

Lesson 5 of 5

Convert fractions to decimals and percentages.

Convert percentages to fractions.

Order fractions, decimals and percentages.

Use dot notation for recurring decimals.

Say whether a fraction terminates or recurs.

Convert a recurring decimal to a fraction. (Higher)

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Fraction to decimal: divide. Decimal to percentage: multiply by 100.

To order a mixture, change everything to decimals.

A fraction terminates only if its denominator's prime factors are 2 and 5.

(Higher) Recurring to fraction: multiply to line up the repeats, subtract, divide.

EXAM FOCUS

Show that 0.dot4dot5 = 5/11 (3 marks)

For "show that" with recurring decimals, write out x = … and 100x = … with at least two repeats of the digits, and show the subtraction. The algebra is the method mark.

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