Maths Leve 2 - Pearson qualifications

[Pages:32]EDEXCEL FUNCTIONAL SKILLS PILOT

Maths Level 2

Chapter 2

Working with fractions, decimals and percentages

SECTION B 1 Types of fraction

15

2 Using a calculator for fractions

17

3 Fractions of quantities

18

4 One number as a fraction of another

20

5 Adding and subtracting fractions

22

6 Remember what you have learned

24

SECTION C 1 Decimal numbers

26

2 Calculating with money

28

3 Remember what you have learned

30

SECTION D 1 Percentages

32

2 Using percentages

34

3 Percentage change

36

4 Converting between forms

38

5 Using fractions, decimals and percentages in practical problemss40

6 Remember what you have learned

41

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Functional Maths Level 2 ? Chapter 2

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EDEXCEL FUNCTIONAL SKILLS: INTERIM SUPPORT MATERIAL

Maths Level 2

Su Nicholson

Chapter 2: Working with fractions, decimals and percentages

Use these free pilot resources to help build your learners' skill base We are delighted to continue to make available our free pilot learner resources and teacher notes, to help teach the skills learners need to pass Edexcel FS Mathematics, Level 2.

But use the accredited exam material and other resources to prepare them for the real assessment We developed these materials for the pilot assessment and standards and have now matched them to the final specification in the table below. They'll be a useful interim measure to get you started but the assessment guidance should no longer be used and you should make sure you use the accredited assessments to prepare your learners for the actual assessment.

New resources available for further support We're also making available new learner and teacher resources that are completely matched to the final specification and assessment ? and also providing access to banks of the actual live papers as these become available. We recommend that you switch to using these as they become available.

Coverage of accredited specification and standards The table below shows the match of the accredited specification to the unit of pilot resources. This table supersedes the pilot table within the teacher notes.

Coverage and Range Exemplification

Learner Unit

Understand and use equivalences between common fractions, decimals and percentages

t Simplifying fractions t Finding fractions of a

quantity t Improper and mixed numbers t Percentages of a quantity t Convert between fractions,

decimals and percentages t Order fractions, decimals and

percentages t Writing one number as a

fraction of another

B1 Types of fraction B2 Using a calculator for fractions B3 Fractions of quantities B4 One number as a fraction of another B5 Adding and subtracting fractions Order fractions, decimals and percentages is covered in our new publishing (see below)

B6 Remember what you have learned

D1 Percentages D2 Using percentages D3 Percentage change D4 Converting between forms D5 Using fractions, decimals and percentages in practical problems

D6 Remember what you have learned

Where to find the final specification, assessment and resource material

Visit our website fs then: t for the specification and assessments: under Subjects, click on Mathematics (Levels 1?2) t for information about resources: under Support, click on Published resources.

Published by Pearson Education, Edinburgh Gate, Harlow CM20 2JE. First published 2008. ? Pearson Education 2008. Typeset by Oxford Designers and Illustrators, Oxford

This material was developed for use with Edexcel pilot and development centres and is available for continued use with development centres. To become a development centre you need to offer Edexcel Functional Skills. The material may be used only within the Edexcel development centre that has retrieved it. It may be desk printed and/or photocopied for use by learners within that institution.

All rights are otherwise reserved and no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanic, photocopying, recording or otherwise without either the prior written permission of the Publishers or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6?10 Kirby Street, London EC1N 8TS.

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0EARSON%DUCATION

Working with fractions, decimals and percentages 2

B Working with fractions

You should already know how to:

read, write, order and compare common fractions and mixed numbers find parts of quantities or measurements.

By the end of this section you will know how to: find fractions of quantities express one number as a fraction of another use fractions to add and subtract amounts use fractions to solve practical problems use a calculator to calculate with fractions.

1 Types of fraction

Learn the skill

A fraction is a way of expressing a part of a whole.

The

fraction

3 4

means

3

parts

out

of

4.

The number on the top, 3, is called the numerator, the number on the bottom, 4, is called the denominator.

You write a fraction in its lowest terms by dividing the numerator and denominator by any common factor.

In

14 21

the

numerator

and

denominator

have

a

common

factor

of 7. You can divide `top' and `bottom' by 7:

? 7

14 21

=

2 3

? 7

14 21

and

2 3

are

equivalent

fractions.

You can find equivalent fractions by multiplying:

3 4

is

equivalent

to

6 8

? 2

3 4

=

6 8

? 2

Remember

1 2

is

bigger

than

1 3

which

is

bigger

than

1 4

.

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In an improper fraction the numerator is bigger than the denominator.

You can write an improper fraction as a mixed number:

8 5

=

5 5

+

3 5

=

1

3 5

Remember

A mixed number has a whole number part and a fraction part.

You can change mixed numbers to improper fractions.

Example:

Change

2

7 8

to

an

improper

fraction.

Because the denominator of the fraction is 8 you need to change the mixed number to eighths.

One

whole

is

8 8

,

so

two

wholes

is

8 8

+

8 8

=

16 8

.

This

means

that

2

7 8

=

8 8

+

8 8

+

7 8

=

23 8

.

Tip

A quick way of working this out is 2 ? 8 + 7 = 23.

Answer:

23 8

Try the skill

1. Write these as fractions in their lowest terms.

a

12 16

b

15 20

c

22 25

d

81 108

2. Write these improper fractions as mixed numbers.

a

16 6

b

31 7

c

21 8

d

61 9

3. Write these mixed numbers as improper fractions.

a

1

5 6

b

2

3 5

c

3

5 7

d

4

3 10

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Working with fractions, decimals and percentages 2

2 Using a calculator for fractions

Learn the skill

You can use a calculator to write fractions in their lowest terms by making use of the ab/c key.

Try keying in:

14

ab/c

21

=

You should see 2

3

on

the

screen,

which

means

2 3

.

Use the ab/c key on your calculator to check your answers to

question 1 on the previous page.

You can also use the ab/c key for improper fractions.

Try keying in:

8

ab/c

5

=

You should see 1

3

5

on

the

screen,

which

means

1

3 5

.

Use the ab/c key on your calculator to check your answers to

question 2 on the previous page.

You can use a calculator to convert mixed numbers to improper fractions.

Try keying in:

2

ab/c

7

ab/c

8

=

You should see 2

7

8

on

the

screen

which

means

2

7 8

Now press 2ndF ab/c

You should see 23

8

on

your

screen

which

means

23 8

.

Try the skill

Use the ab/c key on your calculator to check your answers to question 3 on the previous page.

Tip

Some calculators have a key to input fractions.

Tip

Some calculators will show

2

3

to

represent

2 3

.

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3 Fractions of quantities

Learn the skill

To

fi nd

1 5

of

a

quan t i t y,

divide

by

5.

To

fi nd

2 5

of

a

quan t i t y,

divide

by

5,

then

multiply

by

2.

Out

of

192

students

3 4

own

a

mobile

phone.

How many of

the students own a mobile phone?

To

fi nd

1 4

divide

by

4

To

fi nd

3 4

mul t i ply

this

answer

by

3

192 ? 4 = 48 48 ? 3 = 144

Answer: 144 students

Example

2:

3 25

of

the

money

spent

on

the

National

Lo t t ery

is

paid to the Treasury in duty.

In a year when ?5 billion is recorded in sales, how much

money will be paid to the Treasury?

Remember

To divide by 4, divide by 2 then divide by 2 again.

The

easiest

way

to

work

out

this

question

is

to

wri t e

3 25

as

an

? 4

equivalent fraction with a numerator of 100. 3 = 12

25

100

? 4

To

fi nd

1 100

divide

by

100

5 000 000 000 100

=

50 000 000

=

?50

million

To

fi nd

12 100

mul t i ply

this

answer

by

12

?50 million ? 12 = ?600 million

Answer: ?600 million

Example 3: on rent and

A

1

3

man earns of what is

?420 a left on

week.

He

spends

1 5

of

food. How much does

this he

spend on food?

You have to tackle this question in two stages.

To

fi nd

out

how

much

he

spends

on

rent,

fi nd

1 5

of

?420.

420 5

=

840 10

=

?84

spent

on

rent.

He has ?420 ? ?84 = ?336 left.

To

fi nd

out

how

much

he

spends

on

food,

fi nd

1 3

of

?336.

336 ? 3 = ?112

Answer: ?112

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Working with fractions, decimals and percentages 2

Try the skill

1.

54 000

people

a t t ended

a

football

match.

3 8

of

those

who

attended were children. How many children attended the

football match?

2.

In

a

business

employing

1080

people,

5 12

of

the

employees

are under 25. How many of the employees are under 25?

3. 1250 people went to the local cinema on a Saturday night.

Of

these

people,

2 5

paid

the

student

rate

of

?7.50

and

the

remainder paid the full adult rate of ?10. What was the

total amount of money paid to the cinema that night?

4.

When them

72 students sat the

passed.

Of

these,

4 5

driving

test

theory

exam,

5 6

went on to pass the driving

of test

practical. How many of these students passed both the

theory and the practical driving test exams?

Tip

First find the number of students who passed the exam.

5.

A man e on food

arns and

?1200 a month. a c commoda t ion

He and

spends saves

15 34 oof ft

his earn he rest.

ings How

much money does he save each month?

6.

In by

a street wi the occupi

th 420 houses,

ers,

and

1 10

of

t

5 6

he

of the houses are owned rest are rented. How many

houses in the street are rented?

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4 One number as a fraction of another

Learn the skill

One number as a fraction of another number is:

first number second number

Example 1: Express 8 as a fraction of 12.

8

as

a

fraction

of

12

is

8 12

.

? 4

8 12

=

? 4

2 3

Answer:

2 3

Tip

You should always write the fraction in its lowest terms.

To express one quantity as a fraction of another, the quantities must be in the same units.

Example 2: Express 60 g as a fraction of 1 kg.

Write the quantities in the same units.

? 10

? 2

60 1000

=

6 100

=

3 50

? 10

? 2

Answer:

3 50

Remember

1 kg = 1 000 g

Tip

Check answers on your calculator using the ab/c key.

You can work out a fraction increase or decrease. Find the actual increase or decrease first.

Example 3: On Monday 200 students used the college canteen. On Tuesday, 350 students used the canteen. By what fraction did the number of students using the canteen increase?

The actual increase in the number of students using the canteen on Tuesday is 350 ? 200 = 150.

You express this as a fraction of the number of students using the canteen on Monday.

? 10

? 5

150 200

=

15 20

=

3 4

? 10

? 5

Answer:

3 4

Tip

You always compare with the original value unless you are expressly told otherwise. This will be the denominator.

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