Fraction Calculations 3
Dividing Fractions

In this section we consider how to divide fractions and whole numbers by either whole numbers or fractions.

Worked Examples

1

Calculate ÷ 3.

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You can deal with this problem by thinking about the fraction being divided into 3 parts.

of the diagram has been divided into 3 parts:

Each of these parts is of the whole, so

÷ 3 =

We can also obtain the result in this way:

÷ 3 = ×
=

which uses the rule:

÷ c = ×
2

Calculate:

(a)

4 ÷ ,

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The problem is to calculate how many s there are in 4 whole units. The four whole units are shown below, and each is divided into s.

The diagram shows s, so

4 ÷ = 12

We can obtain this result from

4 ÷ = 4 × 3
= 12
(b)

4 ÷ .

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The problem is to calculate how many s there are in 4 whole units.

The diagram shows s, so

4 ÷ = 10

We can also obtain this result from

4 ÷ = 4 ×
=
= 10

using the rule:

a ÷ =
3

Calculate:

These problems can be tackled using the same approach as when a whole number is divided by a fraction.
(a)

÷

Show me
÷ = ×
=
=
(b)

÷

Show me
÷ = ×
=
=
(c)

÷

Show me

[Note: You can cancel only when the
2nd fraction has been turned upside-down.]

÷ = 12 × 53
=

We are using the rule:

÷ = ×

Exercises

Calculate:

(a)
÷ 3 =
(b)
÷ 2 =
(c)
÷ 2 =
(d)
÷ 4 =
(e)
÷ 3 =
(f)
÷ 2 = =
(g)
÷ 3 =
(h)
÷ 9 =
(i)
÷ 3 =
(j)
÷ 4 =
(k)
÷ 6 =
(l)
÷ 7 =

Calculate:

(a)
6 ÷ =
(b)
9 ÷ =
(c)
8 ÷ =
(d)
2 ÷ =
(e)
5 ÷ =
(f)
4 ÷ =
(g)
8 ÷ =
(h)
5 ÷ =
(i)
9 ÷ =
(j)
6 ÷ =
(k)
14 ÷ =
(l)
11 ÷ =

Calculate:

(a)
÷ =
(b)
÷ =
(c)
÷ = or
(d)
÷ = or
(e)
÷ =
(f)
÷ =
(g)
÷ =
(h)
÷ =
(i)
÷ =
(j)
÷ =
(k)
÷ =
(l)
÷ =

By using improper fractions, calculate:

(a)
÷ =
(b)
÷ =
(c)
÷ =
(d)
÷ =
(e)
÷ =
(f)
÷ =

Ahmed has kg of sweets. He divides these into 3 equal parts so that he can share them with his two brothers. What fraction of a kg does each boy get?

kg

Sandra has litre of orange cordial to make 10 drinks. How much orange cordial should she put in each drink?

litres

A large cake uses 3 times as much flour as a small cake. A large cake needs kg of flour. How much flour does a small cake need?

kg

A piece of leather is 20 cm wide and 45 cm long.

How many bookmarks, cm wide, can be made if the leather is:

(a)

cut as shown above, to make bookmarks 20 cm long,

(b)

cut the other way to make bookmarks 45 cm long?

A recipe for a cake requires kg of sugar. How many cakes can be made with:

(a)

kg of sugar,

cakes
(b)

kg of sugar,

cakes
(c)

kg of sugar?

cakes

A car uses litres of petrol for every 10 miles it travels. How far can the car travel on:

(a)

5 litres of petrol,

miles
(b)

litres of petrol,

miles
(c)

9 litres of petrol?

miles