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7.1 Writing a fraction in its simplest form

7.1 Writing a fraction in its simplest form
÷2
To simplify a fraction, you divide the numerator and the denominator by a 6 3
=
common factor. 18 9
÷2
You simplify a fraction into its simplest form, or lowest terms, by dividing the numerator and the
denominator by the highest common factor (HCF).
If you do not #nd the highest common factor straight away, just cancel by one factor ÷6

at a time until you cannot cancel any further. 6 1
=
18 3
÷6
Worked example 7.1

Write the fraction 60 in its simplest form.
72
HCF of 60 and 72 is 12. The highest common factor of 60 and 72 is 12.
Divide the numerator and the denominator by 12.
÷12
5
60 = 5 60 cancels to . Notice that you could have cancelled one factor at a time like
72 6 72 6
÷12 ÷2 ÷2 ÷3
this: 60 = 30 = 15 = 5 . You still reach the same result.
72 36 18 6
÷2 ÷2 ÷3

) Exercise 7.1

1 Write each fraction in its simplest form.
4
a b 20 c 21 d 12 e 26 f 18
6 25 35 15 39 21
2 Write each fraction in its lowest terms.
a 8 b 12 c 30 d 24 e 27 f 36
24 30 45 32 45 60
w
me
s ho
o
T
k.
r
3 This is part of Razi’s homework.
f
his is par
t o
R
azi’
He has used inverse
operations to check his Write each fraction in its lowest terms.
answers but he has spilt Check your answers.
÷
×
tomato sauce over the last a a 15 = 15 5 = 3 Check : 3 = 35 = 15
÷
×
two checks! 25 25 5 5 5 55 25
÷
Check his answers to parts b b 156 = 156 12 = 13 Check :
b
216
216 12
19
÷
and c for him. 315 315 9 34
÷
If he has made a mistake, c 342 = 342 9 = 37 Check :
÷
work out the correct answer.
4 Write each fraction in its lowest terms. Check your answers.
a 81 b 78 c 121 d 104 e 105 f 54
126 108 231 120 165 90
7 Fractions 65