Multiplication Model A Fraction of a Fraction Length

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

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

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

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

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

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

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

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

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

We can find another name for that area by seeing what part of the square is shaded. 3 4 2 3 This area is 4 X 3 6 It is also 12

We have two names for the same area. They must be equal. 3 4 2 = 6 3 12 4 X 3 2 3 This area is 4 X 3 6 It is also 12

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

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

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:

Answers • 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. Multiply straight across. Simplify answers

• • • Answers Change any whole or mixed numbers to improper. Multiply straight across. Simplify answers

Cancelling Reduce before you multiply

Canceling • Reducing before mutiplying is called canceling. • ICK! Instead think the following in your head.

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