1. Fraction
Multiplication
And Cancelation

2. Fraction Multiplication
• Here are some fraction
multiplication problems 4 1 4
• Can you tell how to
× =
multiply fraction from
5 7 35
these examples?
2 5 10 2 5 10
× =
× = 3 1 3
3 7 21
3 5 15
1 1 1 × =
× = 4 12 48
3 3 9
6 4 24
× =
5 10 50

3. Multiplication
• Multiply numerator by numerator
• And denominator by denominator
2 5 10
× =
3 1 3
N1 N 2 N1 × N 2
× =
D1 D 2 D1 × D 2

4. Try some.
• Multiply the following:
1 5 5 5
× = × =
3 8 8 8
2 4 4 2
× = × =
3 5 9 3

5. Answers
• Multiply the following:
1 5 5 5 5 25
× = × =
3 8 24 8 8 64
2 4 8 4 2 8
× = × =
3 5 15 9 3 27

6. Mixed Numbers
• Because of the order of operations,
• Mixed numbers cannot be multiplied as is
• Change mixed numbers to improper fractions, then
multiply.
2 5
3 ×1 =
5 8
17 13 17 13 221
× = × =
5 8 5 8 40
221 ÷ 40 = 5 with a remainder of 21
21
5
40

7. Try some
• Change any whole or mixed numbers to
improper.
• Multiply straight across.
• Simplify answers
2 1
1 ×7 = ×8 =
5 5

8. Answers
• Change any whole or mixed numbers to
improper.
• Multiply straight across.
• Simplify answers
2 7 7 49 4
1 ×7 = × = =9
5 5 1 5 5
1 1 8 8 3
×8 = × = =1
5 5 1 5 5

9. Cancelling
Reduce before you multiply

10. Canceling
• Reducing before mutiplying is called
canceling.
25 12 300
× =
32 35 1120
• ICK! Instead think the following in your
head.
25 12 25 × 12 5 × 5 × 4 × 3
× = =
32 35 32 × 35 8 × 4 × 7 × 5
5 × 5 × 4 × 3 5 × 3 15
= =
8 × 4 × 7 × 5 8 × 7 56

11. Canceling on paper
• Rules: One factor from
any numerator cancels 16 9 15
with like factor from the × ×
denominator. 21 20 12
11
4 3
1
313 1
444 3
16 × 99 × 1515 = 3
16 × 99 × 15
16
16
16 9 15
15
3 3
21 7 × 4 20 ××12
×× × 7
21
21
21
21 20 12
20 12 3
120
444 20 12 3
3
1
31
4 1 1

12. Try one
• Say “--- goes into ____ this many times.”
• As you cross each number out and write what is
left after canceling above the number.
5 1
×
3 10

13. Answer
• Say “--- goes into ____ this many times.”
• As you cross each number out and write what is
left after canceling above the number.
1
5 1 5
× =
3 10 2 6

14. Try one more
• Make whole and mixed numbers improper
• Cancel if you can
• Multiply Numerators and denominators straight
across.
• Simplify
10 1 14
×4 × ×4
21 2 15

15. Answer
• Make whole and mixed numbers improper
• Cancel if you can
• Multiply Numerators and denominators straight
across.
• Simplify
10 1 14
×4 × ×4
21 2 15
10 9 14 4
× × × =8
21 2 15 1