Multiplying Mixed Numbers

1 2 3 4 5 6 7 8 9 1 4 9 4 2 = 8 4 1 4 9 4 + =

2 3 8 24 3 2 3 26 3 + =

5 8 3 29 8 5 8 = 3 8 2 9 − 2 4 5

5 × 2 = 5 × (2 + ) = (5 × 2) + (5 × ) = 10 + 2 = × = 12 hours = 2 Mr. White worked on his dogsled for 2 hours each day for 5 days. How much time did he spend working on the dogsled? 1 2 1 2 1 2 5 × 2 = 5 × (2 + ) = 1 2 (5 × 2) + (5 × ) = 5 1 1 2 1 2 5 2 1 2 1 2 10 + 2 = × = 12 hours = 2

1 2 5 × 2 = 5 1 5 2 25 1 2 × = = 12 hours 2

the team was able to travel 2 times One morning during a race in 1925, a dogsled team traveled 28 miles in blizzard conditions. That afternoon, the team was able to travel 2 times farther than in the morning. How many miles did the team travel in the afternoon? 1 7

2 × 28 = 28 × (2 + ) = (28 × 2) + (28 × ) = 56 + 4 = 60 miles 1 7 1 7 2 × 28 = 1 7 28 × (2 + ) = 1 7 (28 × 2) + (28 × ) = 56 + 4 = 60 miles

1 7 2 × 28 = 4 15 7 28 1 60 1 × = = 60 miles 1

Two dogsled teams ran in a race. Jack’s team finished the race in 20 minutes. Joe’s team took 1 times longer than Jack’s team. How long did Joe’s team take to finish the race? 3 4 1 3

1 3 3 4 1 × 20 = 2 3 2 7 3 8 3 1 4 3 83 4 83 3 2 3 × = = 27 minutes − 6 1 2 3 − 2 1 2

Use improper fractions. 3 × 2 = 1 5 10 8 16 5 21 10 168 25 18 25 × = = 6 5

Use the distributive property. 2 × = 3 4 2 5 3 4 2 5 (2 + ) × = 2 5 3 4 2 5 (2 × ) + ( × ) = 8 10 4 5 3 10 11 10 1 10 + = = 1

Estimating Products of Mixed Numbers

Round factors that are less than 1 to or 1. Round mixed numbers: If the fraction is less than , the whole number stays the same. If the fraction is greater than or equal to , the whole number increases by one. 1 2 1 2 1 2

3 8 10 16 6 × 5 = 1 2 4 × 3 = 1 2 × 4 = 2 7 × 5 = 35

of 5 miles an hour. About how Colin runs an average of 5 miles an hour. About how far can he run in 2 hours? 1 3 5 6 5 × 2 = 1 3 5 6 5 × 3 = 15 miles

1 6 7 9 × 11 = 1 6 × 12 = 2

Complete #1−40 (even) on Student Text pp. 154−55.