How_To_Be_Good_At_Math

56 NUMBERS •^ DIVIDING FRACTIONS

Dividing by whole numbers

and by fractions

What happens when we divide

a whole number by a proper

fraction, compared to dividing it

by another whole number?

Remember, a proper fraction is

a fraction that’s less than 1.

Dividing fractions

Dividing a whole number by a proper fraction makes it larger. We can divide

fractions using a fraction wall, but there’s also a written way to do it.

8 ÷ 2 = 4

1

8 ÷ 2 = 16

Dividing by a proper fraction

When we divide 8 by^1 / 2 ,

we are finding how many halves

there are in 8. The answer is

16, which is larger than 8.

Dividing by a whole number

When we divide 8 by 2, the

answer is 4. This is what we’d

expect – that dividing a number

makes it smaller.

Dividing a fraction by a whole number

Why does dividing a fraction by a whole number give a

smaller fraction? We can use a fraction wall to find out.

We can think of^1 / 2 ÷ 2 as “one half shared

between two”. The fraction wall shows that if

we share a half into two equal parts, each new

part is one-quarter of the whole.

Now let’s try^1 / 4 ÷ 3. On the fraction wall,

we can see that when one-quarter is divided

into three equal parts, each new part is one-twelfth

of the whole.

1

2 ÷^2 =

1

4

1

2

1

2

1

4

1

4

1

4

1

4

1

4

1

4

1

4

1

4

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1 whole

Dividing by a fraction gives a number

that’s larger than the original one

1 whole

1

2 ÷^2 =?

1

4 ÷^3 =?

1

4 ÷^3 =

1

12

One-quarter can be divided into

three, to make three-twelfths

When a half is divided into two equal

parts, each part is a quarter of the whole

056-057_Dividing_Fractions.indd 56 29/02/2016 14:09