3.13 More division with fractions
How about other fractions? What is 6 ÷ ? This means how many
are there in 6? Consider six squares, divided into quarters, and count how many groups of three quarters there are.
Activity 51

Answer

Three quarters is 3 × ? So dividing by
is the same as dividing by 3 and by
. Dividing by
is multiplying by 4. So dividing by
is the same as dividing by 3 and multiplying by 4, which is multiplying by
. So 6 ÷
= 6 ×
=
= 8.
The general rule for dividing by a fraction can be stated as follows.
To divide by a fraction, turn the fraction upside down and multiply.
Does this also work for dividing by ? Yes, because multiplying by n is the same as multiplying by
. It also works for division of whole numbers: dividing by 4 (=
) is the same as multiplying by
.
Example 23
Evaluate:
Answer
Using the rule above,
This is
(divide top and bottom by 3).
Alternatively divide top and bottom by 3 by cancelling by 3 to give
So
.
Turning a fraction upside down is called finding its reciprocal.
The reciprocal of is
. The reciprocal of
is
, i.e. 6.
So an alternative formulation of the rule for dividing by a number can be stated as follows.
Division by a number is the same as multiplication by its reciprocal.
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