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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
Recall that multiplication by a
whole number can be
represented as repeated
addition. For example, 4 • 5 =
5 + 5 + 5 + 5. You can
multiply a whole number by a
fraction using the same
method.
1
1
__
__
3•
=
4
4
+
+
1
__
4
+
+
1
__
4
=
=
3
__
4
There is another way to multiply with fractions.
Remember that a whole number can be written as
an improper fraction with 1 in the denominator.
3.
So 3 = __
1
__
3
3•1
3
__
1 = ______
__
•
=
1
1•4
4
4
Multiply numerators
Multiply denominators
Notice that when you multiply a proper fraction and
a number greater than 1, the product is between
the factors.
1
1
One way to find __ of __ is to make a model.
4
3
1
1
Find __ of __ .
4
3
1
1
1
__
__
__
=
•
4
3
12
Multiplying Fractions
1 1

2 3
1
1
1
of

2
3
6
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 multiplying 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
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