Fraction Multiplicatio

nAnd 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

Recall that multiplication by a whole number can be represented as repeated addition. For example, 4 • 5 = 5 + 5 + 5 + 5. You can multiply a whole number by a fraction using the same method.

++ =

3 • =14__ 1

4__ 1

4__ 1

4__ 3

4__++ =

31

__ 14

__ 3 • 11 • 4

______ 34

__•

There is another way to multiply with fractions. Remember that a whole number can be written as an improper fraction with 1 in the denominator. So 3 = .3

1__

= = Multiply numeratorsMultiply denominators

Notice that when you multiply a proper fraction and a number greater than 1, the product is between the factors.

1

3__1

4__

1

4__ 1

3__

1

4__ 1

3__

• =1

12__

One way to find of is to make a model.

Find of .

Multiplying Fractions

3

1

2

1

3

1

2

1of

6

1

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• 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 multiplying 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

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