Fraction
Multiplication
And Cancelation
Fraction Multiplication
•
•
Here are some fraction
multiplication problems
Can you tell how to
multiply fraction from
these examples?
2 5 10
 
3 7 21
1 1 1
 
3 3 9
4 1
4
 
5 7 35
2 5 10
 
3 1 3
3 5 15


4 12 48
6 4 24


5 10 50
Multiplication
•
•
Multiply numerator by numerator
And denominator by denominator
2 5 10
 
3 1 3
N1 N 2 N1  N 2


D1 D2 D1  D2
Try some.
• Multiply the following:
1 5
 
3 8
2 4
 
3 5
5 5
 
8 8
4 2
 
9 3
Answers
• Multiply the following:
1 5
5
 
3 8 24
2 4
8
 
3 5 15
5 5 25
 
8 8 64
4 2 8
 
9 3 27
Mixed Numbers
•
•
•
Because of the order of operations,
Mixed numbers cannot be multiplied as is
Change mixed numbers to improper fractions, then
multiply.
2 5
3 1 
5 8
17 13


5 8
17 13 221


5 8
40
221  40  5 with a remainder of 21
21
5
40
Try some
•
•
•
Change any whole or mixed numbers to
improper.
Multiply straight across.
Simplify answers
2
1 7 
5
1
8 
5
Answers
•
•
•
Change any whole or mixed numbers to
improper.
Multiply straight across.
Simplify answers
2
7 7 49
4
1 7   
9
5
5 1
5
5
1
1 8 8
3
8    1
5
5 1 5
5
Cancelling
Reduce before you multiply
Canceling
•
Reducing before mutiplying is called
canceling.
25 12 300
 
32 35 1120
•
ICK! Instead think the following in your
head.
25 12 25  12 5  5  4  3



32 35 32  35 8  4  7  5
5  5  4  3 5  3 15


8  4  7  5 8  7 56
Canceling on paper
•
Rules: One factor from
any numerator cancels
with like factor from the
denominator.
11
4444
16 9 15
 
21 20 12
3
11
3
33
1
16
9
15
16
9
15
3
16
9
15
16
9
15
16  9  15 




7
21
20
12
7
21 420
20 12
123
21
21
120
21
20
1
4444
3 3
12
3 13 3
1
1
Try one
•
•
Say “--- goes into ____ this many times.”
As you cross each number out and write what is
left after canceling above the number.
5 1

3 10
Answer
•
•
Say “--- goes into ____ this many times.”
As you cross each number out and write what is
left after canceling above the number.
1
5
1
5


3 10 2 6
Try one more
•
•
•
•
Make whole and mixed numbers improper
Cancel if you can
Multiply Numerators and denominators straight
across.
Simplify
10
1 14
4  4
21
2 15
Answer
•
•
•
•
Make whole and mixed numbers improper
Cancel if you can
Multiply Numerators and denominators straight
across.
Simplify
10
1 14
4 
4
21
2 15
10 9 14 4
 
 8
21 2 15 1