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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