MULTIPLYING AND DIVIDING PROPER FRACTIONS
CHECK YOUR UNDERSTANDING
1) Copy the fraction strips shown below and use shading to determine the value of one half of
three quarters. Write a corresponding multiplication statement.
2) Copy the area model shown below and use shading to determine the value of two thirds of
four fifths. Write a corresponding multiplication statement.
3) Multiply.
a)
1 2
×
3 3
b)
2 4
×
3 5
 3  2 
c)   
 7  5 
 1  1 
d)    
 5  6 
e)
 5  9 
f)    
 12   14 
3 2
×
4 5
4) Multiply.
a)
1 1 1
× ×
2 3 4
b)
2 3 1
× ×
3 5 2
c)
4 5 3
× ×
10 10 10
 3  5  7 
e)    
 4  6  10 
 2  1  3 
d)    
 7  3  5 
5) Divide.
a)
2 1
÷
5 2
b)
1 2
÷
7 3
c)
5 3
÷
11 4
d)
1 1
÷
6 4
e)
3 6
÷
10 7
f)
9 5
÷
14 6
6) Use the standard order of operations (BEDMAS) to evaluate each of the following.
a)
2 4 1
× −
3 5 6
 2  2   4  2 
b)    +   
 5  3   9  5 
c)
d)
5 1 1 5
− ÷ +
6 4 2 8
1 2 4 1 1
e)  +  −  − × 
5 3 5 3 2
 1 3  3 1 
f)  +   − 
 2 7  4 3
2 9 3
+ −
7 14 4
ANSWERS
1)
Three quarters
One half of three quarters =
3
8
1 3 3
× =
2 4 8
2)
Two thirds of four fifths =
8
15
2 4 8
× =
3 5 15
2
9
1
4) a)
24
4
5) a)
5
11
6) a)
30
3) a)
8
1
6
c)
d)
15
30
35
6  1
60 
3 
b)
c)
 or 
 or

30  5 
1000  50 
3
20
4  2
b)
d)
c)
 or 
14
33
6  3
20  4 
5
b)
c)
d)
 or 
45  9 
28
b)
e)
d)
e)
23
24
6 
3
 or

20  10 
6 
2 
 or

105  35 
21 
7 
 or

60  20 
7
e)
30
45  15 
 or

168  56 
105 
7
e)
 or

240  16 
54  27 
f)
 or

70  35 
65
f)
168
f)