Page 74 - Mathematics Coursebook

7.1 Simplifying fractions

7.1 Simplifying fractions

Look at these three rectangles. 1

In the #rst rectangle 1 of the shape is shaded. 4 The number at the top
4
of the fraction is the
2
In the second rectangle of the shape is shaded. 2 numerator; the number
8 8 at the bottom is the
denominator.
In the third rectangle 4 of the shape is shaded. 4
16
16

You can see that in all three rectangles the same fraction of the shape is shaded. !is shows that
1 , and 4 are equivalent fractions. You can simplify fractions into equivalent fractions by dividing
2
4 8 16

the numerator and denominator by the same number. !is number must be a common factor of the
numerator and denominator.
÷2 ÷2

4
For example 16 = 2 and 2 = 1 Simplifying fractions is also called cancelling fractions.
8
4
8

÷2 ÷2

When you have simpli#ed a fraction to give the smallest possible numerator and denominator, the
fraction is in its simplest form or lowest terms.
When you simplify a fraction, if you divide the numerator and denominator by their highest common
factor, your answer will be in its simplest form in one step.

Worked example 7.1

6
a Write the fraction 10 in its simplest form.
b Cancel the fraction 12 to its lowest terms.
18

a ÷2 2 is the highest common factor of

6 3 6 and 10, so 3 is in its simplest Don’t worry if you don’t know the highest
5
10 = 5 form. common factor. Just cancel one step at a
time. You will end up with the same answer.
÷2
÷2 ÷3
then
÷6 12 6 6 2
b 6 is the highest common factor of 12 18 = 9 9 = 3
12 2 2
18 = 3 and 18, so 3 is in its lowest terms. ÷2 ÷3

÷6

7 Fractions 73