This document provides instructions for multiplying fractions. It explains that to multiply fractions, you multiply the numerators and multiply the denominators. It provides examples of fraction multiplication with both proper and mixed numbers. It also discusses cancelling common factors before multiplying to simplify the resulting fraction. Try examples are given to practice these skills, with step-by-step workings shown.

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