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