How_To_Be_Good_At_Math

46 NUMBERS •^ SIMPLIFYING FRACTIONS

Simplifying fractions using the highest common factor

Instead of going through several stages to simplify a fraction, we can do it by

dividing both the numerator and the denominator by their highest common

factor (HCF). Remember, we looked at common factors on page 29.

Simplifying fractions

Simplifying a fraction means reducing the size of the numerator and

denominator to make an equivalent fraction that’s easier to work with.

Can we simplify

(^4) / 12? If we divide
both the numerator and
denominator by 2
again, we get^2 / 6.
Let’s look at^8 / 24. If we
divide the numerator
and denominator by 2,
we make an equivalent
fraction:^4 / 12.
Now we can
simplify^2 / 6 by
dividing both parts by
2 again, to get^1 / 3.
= =
8
24
4
12
2
6
The highest common factor is 3
Unit
fractions
can’t be
simplified
any more
15
1 3 5 15
Let’s simplify the fraction^15 / 21. Using
the method we learned on page 29,
we first list all the factors of the
numerator, 15. They are 1, 3, 5, and 15.
Now we find the factors of the
denominator, 21. They are 1, 3, 7, and

21. The common factors of the numerator
    and the denominator are 1 and 3, with 3
    being the highest common factor.

21

1 3 7 21

So, if we divide the numerator and the

denominator by 3, we get^5 / 7. We have

worked out that^5 / 7 is the simplest fraction

we can make from^15 / 21.

=

15

21

5

7

The numerator and

denominator of^1 / 3

can’t be divided any

more, so our fraction is

now in its simplest form.

=

1

3

÷ 2

÷ 2

÷ 2

÷ 2

÷ 2

÷ 2

÷ 3

÷ 3

046_047_Finding_Fraction_of_Amount.indd 46 29/02/2016 16:39