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Multiplication Model A Fraction of a Fraction Length X Length = Area

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**We use a fraction square to represent the fraction .**

We will think of multiplying fractions as finding a fraction of another fraction. 3 4 We use a fraction square to represent the fraction . 3 4

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**Then, we shade of . We can see that it is the same as .**

2 3 3 4 Then, we shade of We can see that it is the same as 6 12 But, of is the same as 2 3 3 4 3 4 2 of 2 3 3 4 X So, 6 12 = 3 4 X 2

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**To find the answer to , we will use the model to find of .**

1 2 3 5 X To find the answer to , we will use the model to find of . 1 2 3 5 3 5 We use a fraction square to represent the fraction . 3 5

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**Then, we shade of . We can see that it is the same as .**

1 2 3 5 Then, we shade of We can see that it is the same as 3 10 3 5 1 2 of 3 10 = 5 X 1 2 So,

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**In this example, of has been shaded**

12 34 In this example, of has been shaded 3 4 1 2 of 12 34 What is the answer to ? X

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In the second method, we will think of multiplying fractions as multiplying a length times a length to get an area. 3 4 This length is

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In the second method, we will think of multiplying fractions as multiplying a length times a length to get an area. 2 3 This length is 4

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**We think of the rectangle having those sides**

We think of the rectangle having those sides. Its area is the product of those sides. 2 3 4 This area is X

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**We can find another name for that area by seeing what part of the square is shaded.**

2 3 4 This area is X It is also 6 12

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**We have two names for the same area. They must be equal.**

2 3 4 This area is X 3 4 2 X = 6 12 It is also 6 12

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**Length X Length = Area 1 2 3 4 1 2 This area is X 3 4 It is also 3 8 3**

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What is the answer to X ? 45 14 1 4 4 5

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**Fraction Multiplication**

And Cancelation

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**Fraction Multiplication**

Here are some fraction multiplication problems Can you tell how to multiply fraction from these examples?

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**Multiplication Multiply numerator by numerator**

And denominator by denominator

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Try some. Multiply the following:

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Answers Multiply the following:

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**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.

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**Try some Change any whole or mixed numbers to improper.**

Multiply straight across. Simplify answers

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**Answers Change any whole or mixed numbers to improper.**

Multiply straight across. Simplify answers

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**Reduce before you multiply**

Cancelling Reduce before you multiply

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**Canceling Reducing before mutiplying is called canceling.**

ICK! Instead think the following in your head.

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Canceling on paper Rules: One factor from any numerator cancels with like factor from the denominator.

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**Try one Say “--- goes into ____ this many times.”**

As you cross each number out and write what is left after canceling above the number.

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**Answer Say “--- goes into ____ this many times.”**

As you cross each number out and write what is left after canceling above the number.

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**Try one more Make whole and mixed numbers improper Cancel if you can**

Multiply Numerators and denominators straight across. Simplify

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**Answer Make whole and mixed numbers improper Cancel if you can**

Multiply Numerators and denominators straight across. Simplify

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© 2007 M. Tallman. 1 Whole 7 1 7 1 7 1 3 3 7 24 7 1 Whole 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1.

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