Multiplication Model

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

We will think of multiplying fractions as finding a fraction of another fraction.

34

We use a fraction square to represent the fraction .3

4

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

34

34

23

of

23

612

=34X2

3

612

But, of is the same as .

34

23

34X2

3

So,

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

35

We use a fraction square to represent the fraction .3

5

12

35

12

35X

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

35

35

12

of

12

310

310

=35X1

2So,

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

34

12

of

12

34

What is the answer to ?What is the answer to ?12

34X

In the second method, we will think of multiplying fractions as multiplying a length times a length to

get an area.

34This length is

In the second method, we will think of multiplying fractions as multiplying a length times a length to

get an area.

23This length is

34

We think of the rectangle having those sides. Its area is the product of those sides.

23

34

This area is X34

23

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

23

34

This area is X34

23

It is also612

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

23

34

This area is X34

23

It is also612

34

23X =

612

Length X Length = AreaLength X Length = Area

This area is X34

123

4

12

It is also3 8

34

12X =

3 8

What is the answer to X ?What is the answer to X ?

45

14

14

45

Fraction Multiplication

And 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

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• GET MAD!!!!! • 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 mutiplying 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

Canceling on paper• Rules: One factor from any

numerator cancels with like factor from the denominator.

12

15

20

9

21

16

4

16 921 20

15

3

1216

4

4

921 20

15

3

31216

4

4

921 20

15

3

1

312

1

164

1

4

921

120

15

31

312

1

164

1

217

9

3

4120

15

31

312

1

37

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

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

canceling above the number.

51

13 10

2

56

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

415

14

2

14

21

10

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

10 1 144 4

21 2 1510 9 14 4

821 2 15 1