
Procedures for multiplying fractions 
 General rule for the multiplication of fractions
Steps
for multiplication of fractions Advanced
Procedures  Quick Quiz 
Procedures for multiplying fractions
How
do we think of multiplication problems?
In
these examples we can see that x and of have the same meaning.
Thinking of multiplication as of can help us picture a model when
solving multiplication problems.

we
could say, 3 groups of 6 = 18
we
could write, 3 x 6 = 18


we
could say, a half of 6 is 3
we
could write, 1/2 of 6 = 3 or
1/2
x 6 = 3


we
could say, a quarter of a dozen
we
could write, 1/4 of 12 = 3 or
1/4
x 12 = 3

Multiplying
a whole number by a fraction
Example 2: 3 x 4/7
If
we count the green shaded areas below we can see that we have 12 sevenths
Using
the area model to multiply a fraction by a fraction
Example
1: Using the area model to illustrate 1/5 x 3/4= 3/20
The
method used in this example is sometimes referred to as the unit square
method.
Multiplying
mixed numbers & improper fractions
Example
3: 1 1/2 x 5 = 7 1/2
If
I need 5 times 1 and a 1/2 metres of ribbon to make a dress, how much
ribbon do I have to buy?
We
can use 3 methods as set out below to solve this problem.
Question

Setting
Out

Thinking

5
x 1 1/2

method
1:
=
5 x 1 + 5 x 1/2
=
7 1/2

I
think of the fractions and the whole numbers separately,
5
x 1 1/2 = 5 x (1 + 1/2)
First
I multiply the whole number and then I multiply the fractional part.
This is a use of the distributive law.


method
2:
=
5/1 x 3/2
= 15/2
=
7 1/2

I
change the 5 into a fraction, 5/1
I
change the mixed number, 1 1/2, into the improper fraction, 3/2,
1 = 2/2, 2/2 +1/2 = 3/2
I
then multiply the fractions
= (5x3)/(1x2) = 15/2


method
3:
=
5 x 3/2
=
15/2
=
7 1/2

I
change the mixed number, 1 1/2, into the improper fraction,3/2,
1 = 2/2, 2/2 + 1/2 = 3/2
I
think of the question as '5 groups of 3 halves',
(5 x 3)/2
I
then multiply the whole number by the improper fraction of 3/2

Therefore,
I need to buy seven and a half metres of ribbon.
Below
are some more examples of multiplying mixed numbers.
General rule for the multiplication of fractions
Steps
for multiplication of fractions
To
multiply fractions:

Step
1: Convert mixed numbers to improper fractions, if applicable 
Step
2: Multiply the numerators together, multiply the denominators
together

Step
3: Simplify the answer if required.

Advanced Procedures
Multiplication
with cancelling:
Cancelling
is a procedure which we can use to make multiplication of fractions easier
for us. We do not have to use cancelling  it just makes the process more
efficient. The word cancelling is not really a helpful description
of what takes place and can lead the unsuspecting into indiscriminately
crossing out numbers!
Cancelling
actually means dividing the numerator and denominator by the same number
until a fraction is renamed in its simplest form.
Example
6: 5/2 x 2/3 = 5/3
Question

Setting
Out

Thinking


using
cancelling:

I
can see that the numerator and the denominator both contain a factor
of 2. I can cancel the 2s: in effect, this step divides both
the numerator and the denominator by 2 . This does not change the
value of the fraction.


without
using cancelling:

I
multiply the fractions as usual. I can see that the answer (10/6)
is equivalent to and can be simplified to (5/3). If a factor is
not cancelled out before multiplication occurs, it will need to
be cancelled to simplify the final answer.

Example
7: multiplication with cancelling, 8/3 x 15/6 = 6 2/3
Quick
quiz
1. 
Use
the unit square method to find the answer to 2/3 x 5/8. (Think of
the question as 2/3 of 5/8 and use a unit model to solve it) 




2. 
a)

b)

c)


d)

e)

f) 


3. 
The
cancelling technique will make it easier to answer these questions.
Use this technique if you feel confident. 

a) 
b) 
c) 

d) 
e) 
f) 
To
view the quiz answers, click here.
