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Multiplying Mixed Numbers
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1 2 3 4 5 6 7 8 9 1 4 9 4 2 = 8 4 1 4 9 4 + =
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2 3 8 24 3 2 3 26 3 + =
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5 8 3 29 8 5 8 = 3 8 2 9 − 2 4 5
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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 = × = 12 hours = 2
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1 2 5 × 2 = 5 1 5 2 25 1 2 × = = hours 2
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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
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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 × ) = 4 = 60 miles
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1 7 2 × 28 = 4 15 7 28 1 60 1 × = = 60 miles 1
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Two dogsled teams ran in a race. Jack’s team finished the race
in 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
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1 3 3 4 1 × = 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
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Use improper fractions.
3 × 2 = 1 5 10 8 16 5 21 10 168 25 18 25 × = = 6 5
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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
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Estimating Products of Mixed Numbers
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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
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3 8 10 16 6 × 5 = 1 2 4 × = 1 2 × 4 = 2 7 × 5 = 35
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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
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1 6 7 9 × = 1 6 × 12 = 2
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Complete #1−40 (even) on Student Text pp. 154−55.
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