1. Multiplication Model
A Fraction of a Fraction
Length X Length = Area

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

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

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

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

6. In this example, of has been shaded12 34
In this example, of has been shaded 3 4 1 2 of 12 34
What is the answer to ? X

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

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

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

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

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

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

13. What is the answer to X ? 45 14 1 4 4 5

14. Fraction Multiplication
And Cancelation

15. Fraction Multiplication
Here are some fraction multiplication problems
Can you tell how to multiply fraction from these examples?

16. Multiplication Multiply numerator by numerator
And denominator by denominator

17. Try some.
Multiply the following:

18. Answers
Multiply the following:

19. 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.

20. Try some Change any whole or mixed numbers to improper.
Multiply straight across.
Simplify answers

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

22. Reduce before you multiply
Cancelling
Reduce before you multiply

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

24. Canceling on paper
Rules: One factor from any numerator cancels with like factor from the denominator.

25. Try one Say “--- goes into ____ this many times.”
As you cross each number out and write what is left after canceling above the number.

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

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

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