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

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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 of = 3 4 X But, of is the same as X 2 3 So,

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

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

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In this example, of has been shaded of 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 3 4

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We think of the rectangle having those sides. Its area is the product of those sides 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 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 This area is X It is also X = 6

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Length X Length = Area This area is X It is also X = 3 8

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What is the answer to X ?

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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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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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