Fraction Multiplication

There are 3 approaches for There are 3 approaches for modeling fraction multiplicationmodeling fraction multiplication

A Fraction of a Fraction Length X Width = Area Cross Shading

We will now examine each of We will now examine each of these 3 approaches.these 3 approaches.

Area of a Rectangle

What is the area of this rectangle?

To find the area of a rectangle we can multiply the length by the width.

Area = Length X Width = 4 x 3 = 12 units2

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 In this example, of has been shadedshaded

34

12

of

12

34

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

34X

Modeling multiplication of fractions using the fraction of a fraction approach requires that the children understand the relationship of multiplication to the word “of.”

We can establish this understanding showing whole-number examples like: 6 threes is the same as 6 X 3.

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,

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

34This length is

In the second method, we will think of multiplying fractions as multiplying a length times a width 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 Width = AreaLength X Width = 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

Modeling multiplication of fractions using the length times width equals area approach requires that the children understand how to find the area of a rectangle.

A great advantage to this approach is that the area model is consistently used for multiplication of whole numbers and decimals. Its use for fractions, then is merely an extension of previous experience.

In the third method, we will represent both fractions on the same square.

34is

12is

The product of the two fractions is the part of the square that is shaded both

directions.

34is

12is

34

12X = 3

8

We will look at another example using cross shading. We shade one direction.

45

45

45

23

The answer to X is the part that is shaded both directions.45

23

45

23X = 8

15

Then we shade the other direction.23

The End