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
? Pearson Education 2008
Pilot material only ? see introduction before use
Functional Maths Level 2 ? Chapter 2
Draft for Pilot
Working with shape and space 5
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.
$RAFTFOR0ILOT
Pilot material only ? see introduction before use
&UNCTIONAL-ATHS,EVELo#HAPTER
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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Functional Maths Level 2 ? Chapter 2 ? page 15
Draft for Pilot
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
? Pearson Education 2008
Pilot material only ? see introduction before use
Functional Maths Level 2 ? Chapter 2 ? page 16
Draft for Pilot
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
.
? Pearson Education 2008
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Functional Maths Level 2 ? Chapter 2 ? page 17
Draft for Pilot
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
Draft for Pilot
Pilot material only ? see introduction before use
Functional Maths Level 2 ? Chapter 2 ? page 18
? Pearson Education 2008
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?
? Pearson Education 2008
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Functional Maths Level 2 ? Chapter 2 ? page 19
Draft for Pilot
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.
Draft for Pilot
Pilot material only ? see introduction before use
Functional Maths Level 2 ? Chapter 2 ? page 20
? Pearson Education 2008
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