1. Multiplying Fractions
created by: Leslie Fenton

2. How does multiplication work?
The first factor (multiplier) relates to the number of groups.
The second factor (multiplicand) relates to the size of the group.
So let’s see….
3 x 2 = 6
The product
number of groups
size of the group

3. Think about this… What is one times any number?
1 x multiplier = multiplier
If multiplying by a number < 1, the product is smaller than the multiplier.
2 x ½ = 1 and 2 x 1 = 2
If multiplying by a number > 1, the product is larger than the multiplier.
2 x 1 ½ = 3 and 2 x 1 = 2

4. Multiplying Fractions
That brings us to
Multiplying Fractions

5. Try these problems (Look for the pattern)
1/6
1/3

6. Try this (Look for the pattern)
1/8
1/4
1 2
1 3
1 6 x =

7. Try this (Look for the pattern)
1/3
1/12
1/4
1 2
1 3
1 6 x =
1 4
1 2 x =
1 8

8. Try this (Look for the pattern)
1/4
2/20
1/4 0f 2/5 = ? OR 1/4 • 2/5 = ?
1 2
1 3
1 6 x =
2/5
1 4
1 2 x =
1 8
1 4
1 3 x =
1 12

9. Try this (Look for the pattern)
2/4
4/20
1 2
1 3
1 6 x =
2/5
1 4
1 2 x =
1 8
1 4
1 3 x =
1 12
2 5
1 4 x =
2 20

10. When multiplying fractions, multiply the numerators and then multiply the denominators
multiply straight across. OR
Is there a pattern?
1 2
1 3
1 6 x =
What could the algorithm be?
1 4
1 2 x =
1 8
1 4
1 3 x =
1 12
2 5
1 4 x =
2 20
2 5
2 4 x =
4 20

11. And will it work every time?
Why Does This Work?
And will it work every time?

12. Let’s Try This Four-fifths of two-thirds Estimate:
How can the area of a rectangle can be calculated?
L x w …. So if we had a 1 unit by 1 unit rectangle, the area would be…?
So if we need 4/5 groups… that is < 1
And in each group, we only need 2/3 (also < 1)

14. # of double shaded parts
1 3 x
1 5 1
1/3
# of equal size parts in the whole square = 15
1/5

15. # of double shaded parts
# of equal size parts in the whole square
1 3 x
1 5 1
2/3 = 15
2 3 x
1 5 2 = 15
1/5

16. # of double shaded parts
# of equal size parts in the whole square
1 3 x
1 5 1 = 15
2/3
2 3 x
1 5 2 = 15
2 3 x
4 5 8 = 15
4/5

17. 35 equal size parts in the whole
The Area Model
3 5
4 7
35 equal size parts in the whole x
3 5
3 5
4 7
12 double shaded parts
4 7

18. Show What You Learned Why Does This Work? 1 – 4
#1 work together as a model
2-4 work with a partner
Homework: 6-5 Skills practice – Multiplying Fractions 1-9