Multiplication Model • A Fraction of a Fraction • Length X Length = Area
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Multiplication Model
• A Fraction of a Fraction• Length X Length = Area
We will think of multiplying fractions as finding a fraction of another fraction.
34
We use a fraction square to represent the fraction .3
4
Then, we shade of . We can see that it is the same as .
34
34
23
of
23
612
=34X2
3
612
But, of is the same as .
34
23
34X2
3
So,
To find the answer to , we will use the model to find of .
35
We use a fraction square to represent the fraction .3
5
12
35
12
35X
Then, we shade of . We can see that it is the same as .
35
35
12
of
12
310
310
=35X1
2So,
In this example, of has been shadedIn this example, of has been shaded
34
12
of
12
34
What is the answer to ?What is the answer to ?12
34X
In the second method, we will think of multiplying fractions as multiplying a length times a length to
get an area.
34This length is
In the second method, we will think of multiplying fractions as multiplying a length times a length to
get an area.
23This length is
34
We think of the rectangle having those sides. Its area is the product of those sides.
23
34
This area is X34
23
We can find another name for that area by seeing what part of the square is shaded.
23
34
This area is X34
23
It is also612
We have two names for the same area. They must be equal.
23
34
This area is X34
23
It is also612
34
23X =
612
Length X Length = AreaLength X Length = Area
This area is X34
123
4
12
It is also3 8
34
12X =
3 8
What is the answer to X ?What is the answer to X ?
45
14
14
45
Fraction Multiplication
And Cancelation
Fraction Multiplication• Here are some fraction
multiplication problems• Can you tell how to multiply
fraction from these examples?
4 1 45 7 35
6 4 245 10 50
21
10
7
5
3
2
3 5 154 12 48
1 1 13 3 9
2 5 103 1 3
Multiplication• Multiply numerator by numerator• And denominator by denominator
2 5 103 1 3
1 2 1 2
1 2 1 2
N N N ND D D D
Try some.
• Multiply the following:
4 29 3
1 53 8
2 43 5
5 58 8
Answers
• Multiply the following:
4 2 89 3 27
1 5 53 8 24
2 4 83 5 15
5 5 258 8 64
Mixed Numbers• Because of the order of operations,• Mixed numbers cannot be multiplied as is• GET MAD!!!!! • Change mixed numbers to improper fractions, then multiply.
8
51
5
23
17 135 8
17 13 2215 8 40
221 40 5 with a remainder of 21
215
40
Try some• Change any whole or mixed numbers to improper.• Multiply straight across.• Simplify answers
21 7
5
18
5
Answers• Change any whole or mixed numbers to improper.• Multiply straight across.• Simplify answers
2 7 7 49 41 7 9
5 5 1 5 5
1 1 8 8 38 1
5 5 1 5 5
Cancelling
Reduce before you multiply
Canceling• Reducing before mutiplying is called canceling.
• ICK! Instead think the following in your head.
1120
300
35
12
32
25
25 12 25 12 5 5 4 332 35 32 35 8 4 7 5
5 5 4 3 5 3 158 4 7 5 8 7 56
Canceling on paper• Rules: One factor from any
numerator cancels with like factor from the denominator.
12
15
20
9
21
16
4
16 921 20
15
3
1216
4
4
921 20
15
3
31216
4
4
921 20
15
3
1
312
1
164
1
4
921
120
15
31
312
1
164
1
217
9
3
4120
15
31
312
1
37
Try one• Say “--- goes into ____ this many times.”• As you cross each number out and write what is left after
canceling above the number.
10
1
3
5
Answer• Say “--- goes into ____ this many times.”• As you cross each number out and write what is left after
canceling above the number.
51
13 10
2
56
Try one more• Make whole and mixed numbers improper• Cancel if you can• Multiply Numerators and denominators straight across.• Simplify
415
14
2
14
21
10
Answer• Make whole and mixed numbers improper• Cancel if you can• Multiply Numerators and denominators straight across.• Simplify
10 1 144 4
21 2 1510 9 14 4
821 2 15 1
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