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7.5 Working with fractions mentally

7.5 Working with fractions mentally

You need to be able to work with fractions mentally. !is means that you should be able to do simple
additions, subtractions, multiplications and divisions ‘in your head’. You should also be able to solve
word problems mentally. !is section will help you practise the skills you need.

For complicated or di$cult questions, it may help if you write down some of the steps in the working.

!ese workings, or jottings, will help you remember what you have worked out so far, and what you still
need to do.

Worked example 7.5
3
3
Work these out mentally. a 3 + b 4 − 4 c 2 × 20 d 2 × 6 e 4 ÷ 8
7
5
5
9
4
3
7
8
3
3
6
a 6 + 3 = 9 = 1 1 In your head, change to so you can add it to .
8 8 8 8 4 8 8
b 4 × 4 − 3 × 5 The lowest common denominator is 5 × 4 = 20.
20
−15
1
= 16 20 = 20 In your head, work out 4 × 4 − 3 × 5 to give a numerator of 1.
c 20 ÷ 5 = 4, 4 × 2 = 8 Divide 20 by the denominator 5, then multiply the result by 2.
×
d 2 × 6 7 2 = 22 In your head divide the 3 and 6 by 3 to cancel before multiplying.
×
17
1 3
= 4 Multiply the numerators and the denominators to work out the answer.
7
1 4
×
e × 9 = 19 In your head invert and multiply the second fraction, then divide the 4 and
×
7 8 72 8 by 4.
9 2
= 14 Multiply. Use jottings to help if you need to, as there is a lot of work to do
here in your head.
In this exercise, write each answer in its simplest form and as a mixed
) Exercise 7.5 number when appropriate.
l
y
io
ddit
ntal
ns me
o
r
1 Work out these additions mentally..
W
k ou
t these a
3
1
1
+
a + 1 b 3 c 3 1 d 1 e 3 5 f 7 4
+
+
+
+
3 6 4 8 5 10 2 8 4 12 15 5
1
1
1
1
2
+
+
+
g + 1 h 1 i 2 j 3 k 5 l 1 5
+
+
3 5 4 7 9 5 4 3 8 5 4 6
2 Work out these subtractions mentally.
1
1
1
1
1
a − 1 b 1 c 1 15 d 2 e 4 10 f 11 2
−
−
−
−
−
3
20
3
6
5
5
9
5
4
8
3
1
1
1
2
−
−
g − 1 h 4 i 5 j 3 k 7 l 8 3
−
−
−
2 3 5 4 7 2 4 7 12 8 9 4
3 Work out these multiplications mentally. Use jottings to help if you need to.
1
2
8
1
2
3
×
×
×
×
×
a 1 b 2 c 3 d × e 4 f 6 4
3 5 7 3 4 5 9 7 5 9 13 5
2
8
1
1
×
×
×
×
×
g × h 3 i 4 10 j 5 k 2 9 l 4 15
3 4 5 9 5 11 6 9 3 10 5 22
72 7 Fractions