# 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 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

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

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

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,

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

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

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

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

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

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

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

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

Fraction Multiplication
And Cancelation

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

Multiplication Multiply numerator by numerator
And denominator by denominator

Try some. Multiply the following:

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.

Try some Change any whole or mixed numbers to improper.

Answers Change any whole or mixed numbers to improper.

Reduce before you multiply
Cancelling Reduce before you multiply

Canceling Reducing before mutiplying is called canceling.

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

Try one Say “--- goes into ____ this many times.”
As you cross each number out and write what is left after canceling above the number.

Answer Say “--- goes into ____ this many times.”
As you cross each number out and write what is left after canceling above the number.

Try one more Make whole and mixed numbers improper Cancel if you can
Multiply Numerators and denominators straight across. Simplify

Answer Make whole and mixed numbers improper Cancel if you can
Multiply Numerators and denominators straight across. Simplify

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