Multiplication Model A Fraction of a Fraction Length

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

2. 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 . 3 4 3 4 2 3 of 2 3 6 12 = 3 4 X 2 3 6 12 But, of is the same as . 3 4 2 3 3 4 X 2 3 So,

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

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

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

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

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

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

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

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