Cambridge University Press
978-0-521-69432-2 - SMP Interact Foundation 2
The School Mathematics Project
Excerpt
More information
1
Ordering, adding and subtracting fractions
You should know
•
•
about equivalent fractions and mixed numbers
how to simplify fractions
This work will help you
•
•
A
put fractions in order of size
add and subtract fractions using a common denominator
Review: fractions
A1 Copy and complete each statement.
■
■
(a) 2 = 10
(b) 4 = 12
(c)
■
% = 20
4
(d) - = ■
A2 What fraction of the circle is coloured blue?
Write this fraction in its simplest form.
A3 Write these fractions in their simplest form.
(a) p
(b) V
(c)
F
(d) s
(e) |
A4 Write down all the fractions in the bubble
*
that are equivalent to
(a) 2
(b) 4
(c)
q
4
16
O
M
K
^
w
U
10
20
A5 Write each improper fraction as a mixed number in its simplest form.
(a) Å
9
6
(b)
(c)
14
4
(d)
12
5
(e)
24
10
A6 Write each mixed number as an improper fraction.
(a) 22
(b) 1=
(c)
43
(d) 2u
(e) 3r
A7 Write these fractions in order of size, smallest first.
10
3
22
5
15
6
5
4
8
2
A8 Work these out. Give each answer in its simplest form.
(a) 5 + q
(b) d – y
(c)
=+=
(d) P – r
1 Ordering, adding and subtracting fractions 9
© Cambridge University Press
www.cambridge.org
Cambridge University Press
978-0-521-69432-2 - SMP Interact Foundation 2
The School Mathematics Project
Excerpt
More information
B
T
Comparing (one denominator a multiple of the other)
It is easy to see from these diagrams that 3 is larger than 4.
• Which is larger, 8 or 5? Explain how you can tell.
B1 Write down the larger fraction in each pair.
(a) 3 and -
(b) 2 and 4
(c)
3 and 5
(d) - and ^
B2 Write down two fractions that are larger than 6 but smaller than 2.
We can use equivalent fractions to compare fractions.
Example
95
Which is larger, - or 11
15 ?
-
=
15 is a multiple of 3, so
change - into fifteenths.
10
15
95
So
11
15
is larger than -.
B3 For each pair of fractions, write down the smaller fraction and
the letter that goes with it.
What word do you make?
Q
2
M P
G
3
A O
7
20
4
S R
2
15
5
K T
B4 Twins Poppy and Daniel have identical birthday cakes.
Poppy and her friends eat - of her cake.
Daniel and his friends eat L of his cake.
Which group has eaten more cake?
B5 For each pair of fractions, write down the larger fraction and
the letter that goes with it.
What word do you make?
{
-
C B
%
y
R L
=
P
I A
5
16
r
W
S M
9
14
P S
B6 Write down a fraction that lies between = and 14
16 .
B7 Write each set of fractions in order of size, starting with the smallest.
(a) 2, 5, 4
(b) %, 0, 5
(c)
3, [, 6
10 1 Ordering, adding and subtracting fractions
© Cambridge University Press
www.cambridge.org
Cambridge University Press
978-0-521-69432-2 - SMP Interact Foundation 2
The School Mathematics Project
Excerpt
More information
C
Adding and subtracting (one denominator a multiple of the other)
We can only add and subtract fractions that have the same denominator,
so first write both fractions with the same denominator.
Examples
2
2+8
=–D
94
93
=
p
8 is a multiple of 2, so
change 2 into eighths.
=
94
=
|
93
p+8=E
9
12
–D=:=-
Give the answer in
its simplest form.
C1 Work these out.
(a) 2 + 4
(b) 2 – 4
(c)
4+8
(d) 2 – 8
(e) 5 + 0
(d) 2 – 6
(e) 2 – y
C2 Work these out. Simplify your answers.
(a) 2 + 0
(b) 5 + y
(c)
2+6
C3 David and Sue share a bar of chocolate.
David eats % of the bar.
Sue eats y of the bar.
(a) What fraction of the bar have they eaten altogether?
(b) What fraction of the bar is left?
C4 Work these out.
Give your answers as mixed numbers and simplify them where possible.
(a) 2 + =
(b) 2 + E
(c) 12 + 4
(d) 2= – 2
(e) 14 – 8
(f) 11
14 + &
(g) 2 + Q
(h) - + Q
(i)
3+{
(j)
1= – r
*C5 The sketch shows three villages along a country road.
Graydale =
Graydale
Blackburn 12
Whitehall 44
Blackburn
Whitehill
This signpost is at the crossroads between Graydale and Blackburn.
It shows some distances in miles.
Graydale =
What is the distance along the road
(a) from Graydale to Blackburn
(b) from Graydale to Whitehill
(c) from Blackburn to Whitehill
Blackburn 12
Whitehill 44
1 Ordering, adding and subtracting fractions 11
© Cambridge University Press
www.cambridge.org
Cambridge University Press
978-0-521-69432-2 - SMP Interact Foundation 2
The School Mathematics Project
Excerpt
More information
D
Comparing (neither denominator a multiple of the other)
Dean wants to compare - and o.
-=i=I=:=ç=
He writes out a set of
equivalent fractions
for both of them.
o=
8
14
=
12
21
=
16
28
=
12
18
20
35
=
14
21
=
16
24
=
He circles the first pair
of fractions that have
the same denominator.
=
So o is smaller than -.
12
21 is
smaller than
14
21
so o is smaller than -.
D1 Dean has written down sets of
equivalent fractions for u and = .
u=s=å=
16
20
Which fraction is smaller, u or = ?
Explain how you decided.
==U=|=
12
16
=
=
20
25
15
20
=
=
D2 For each pair of fractions, write down the larger fraction and
the letter that goes with it.
What word do you make?
3
%
=
T M
-
I A
}
=
S L
e
%
K L
D3 Work out which of the fractions q or - is larger.
Show all your working.
D4 Write these fractions in order of size, starting with the smallest.
E
-
2
D5 Write these fractions in ascending order.
-
%
3
q
D6 Which of these fractions is closest to 2?
Explain how you know.
]
!
=
*D7 Find a fraction that lies between R and q .
*D8 Find two different fractions that lie between 5 and 3 .
12 1 Ordering, adding and subtracting fractions
© Cambridge University Press
www.cambridge.org
Cambridge University Press
978-0-521-69432-2 - SMP Interact Foundation 2
The School Mathematics Project
Excerpt
More information
E
Adding and subtracting (neither denominator a multiple of the other)
Dean wants to work out % + 4 .
%=]=N=
He writes out a set of
equivalent fractions
for both of them.
8
20
4=*=G=
4
16
=
So % + 4 =
8
20
+
=
13
20
=
10
25
5
20
He circles the first pair
of fractions with the
same denominator.
=
=
6
24
=
5
20
Now he can add them.
E1 Dean has written down two sets of equivalent fractions for - and 5 .
-=i=I=:=
5=)=V=
4
20
10
15
=
=
5
25
12
18
=
14
21
=
16
24
=
=
(a) Write down two fractions, one from each set, that have the same denominator.
(b) Work out - + 5 .
E2 (a) Copy and complete this to give a set of four equivalent fractions for 2 .
2=$=?=?
(b) Copy and complete this to give a set of four equivalent fractions for 3 .
3=?=?=?
(c) Work out 2 + 3 .
E3 Work these out.
(a) 4 + 3
(b) 3 + %
(c)
4–0
(d) 2 – &
(e) = + -
E4 Maya and George share a pizza.
Maya eats 3 of the pizza.
George eats r of the pizza.
(a) What fraction of the pizza have they eaten altogether?
(b) What fraction of the pizza is left?
E5 Tina buys a 2 pint carton of milk.
She uses - pint of this to make a milkshake.
She uses another 2 pint to make some pancakes.
How much milk does she have left?
1 Ordering, adding and subtracting fractions 13
© Cambridge University Press
www.cambridge.org
Cambridge University Press
978-0-521-69432-2 - SMP Interact Foundation 2
The School Mathematics Project
Excerpt
More information
Example
Work out 1- + 2= .
We need to change - and = into equivalent fractions with the same denominator.
The denominator must be a multiple of 3 and also a multiple of 4. So 12 will do.
94
-
93
:
=
=
94
9
12
93
1: =
20
12
20
12
33
12
+
=
2| =
=
53
12
= 4J
33
12
Write the mixed numbers as improper fractions.
Give the answer as a mixed number.
E6 Work these out. Write the results as mixed numbers.
(a) 13 + 6
(b) 4 – 14
(c)
1= + %
(f) 3r + 14
(g) 2= – 13
(h) 2E + 1-
(d) 2- – =
(i)
32 – 23
(e) 35 + 13
(j)
3q – 1Q
Test yourself
T1 Write the fractions E, =, 17
24 , L in ascending order.
Edexcel
T2 (a) Here are three fractions.
=
u
E
Which of these fractions is the largest?
Show how you decide.
(b) Work out 5 + - .
OCR
T3 Work these out. Simplify your answers where possible.
(a) 5 + y
(b) = – 8
(c)
E+-
(d) 1Q – 3
(e) 27 + 1-
T4 Simon spent 3 of his pocket money on a computer game.
He spent 4 of his money on a ticket for a football match.
Work out the fraction of his pocket money that he had left.
Edexcel
T5 The sketch shows three villages and the distances between them.
Greenhaugh
Wyford
32 miles
Byfield
1= miles
Work out the total distance along the road between Wyford and Byfield.
14 1 Ordering, adding and subtracting fractions
© Cambridge University Press
www.cambridge.org