Multiplying Fractions created by: Leslie Fenton

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

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

Multiplying Fractions That brings us to Multiplying Fractions

Try these problems (Look for the pattern) ½ 1/6 1/3

Try this (Look for the pattern) ½ 1/8 1/4 1 2 1 3 1 6 x =

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

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

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

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

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

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)

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

# 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

# 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

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

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