Lesson 8: Multiplying Fractions.
 How to Multiply Fractions
 Multiplying Simple Fractions.
 Multiplying Mixed Fractions.
 Multiplying Fractions by Whole Numbers.
 Practice Game.
HOW TO MULTIPLY FRACTIONS
The good news is you do not need a common denominator when
multiplying fractions.
To multiply two (or more) fractions you have to:
 Change all
mixed fractions
( if any)
to
improper fractions.
 Multiply
out the numerators.
 Multiply
out the denominators.
 "Tidy up" the
result  change the
improper fraction
to a
mixed fraction
and
simplify
it if possible.
MULTIPLYING SIMPLE FRACTIONS
Example
Solution:
2 
x 
2 
= 
2 x 2 



Multiply the numerators 
3 
5 
3 x 5 


Multiply the denominators 
Example
Solution:
7 
x 
1 
x 
3 
= 
7 x 1 x 3 

Multiply the numerators. 
3 
2 
2 
3 x 2 x 2 

Multiply the denominators. 
= 
21 
= 
1 
9 


Change the result to a mixed
fraction. 
12 
12 



= 
1 
3 
Simplify the result

4 
(divide both sides of the
fraction by 3). 
Sometimes you can
simplify before calculating the final result.
This can be done if any numerator and
denominator have common factors.
REMEMBER
only top numbers can cancel bottom
numbers.
In the example below you can cancel 14 and
7 (they have the common factor of 7),
but you cannot cancel 14 and 2, because they are both numerators.
Example
Solution:
14 
x 
2 
= 
14 x 2 




Multiply the numerators. 
5 
7 
5 x 7 




Multiply the denominators. 
= 
2 x 2 
= 
4 



Simplify before calculating
the final result 
5 x 1 
5 



(divide the top number 14
and the bottom number 7 by 7). 
MULTIPLYING MIXED FRACTIONS
Example
2 
1 
x 
1 
1 
= 
5 
x 
11 
Convert mixed fractions to 
2 
10 
2 
10 
improper fractions. 
= 
5 x 11 
= 
1 x 11 





Simplify before multiplying

2 x 10 
2 x 2 





(divide 5 and 10 by 5) 
= 
11 
= 
2 
3 




Change the result to a mixed
fraction. 
4 
4 





MULTIPLYING FRACTION BY WHOLE NUMBERS
We can write any whole number as a
fraction with a denominator of 1.
For example, we can write 3
as 
3 
. Why? 


1 


Example
Solution:
4 
x 
2 
= 
4 
x 
2 

Write 2 as 
2 
5 
5 
1 

1 
= 
4 x 2 
= 
8 



Multiply the numerators. 
5 x 1 
5 



Multiply the denominators. 
= 
1 
3 

Change the result to a mixed
fraction. 
5 


Example
Solution:
8 
x 
5 
= 
8 
x 
5 

Write 8 as 
8 
12 
1 
12 

1 
= 
8 x 5 
= 
2 x 5 



Simplify before multiplying

1 x 12 
1 x 3 



(divide 8 and 12 by 4) 
= 
10 
= 3 
1 



Change the result to a mixed
fraction. 
3 
3 




Do you remember that 
3 
means "3 divided by 1"? And 3 divided by 1
equals 3. 


1 


