Main Idea and New VocabularyExample 1: Estimate by Rounding DividendsExample 2: Estimate by Rounding DivisorsExample 3: Real-World ExampleExample 4: Real-World Example

• Estimate the quotient of decimals and judge the reasonableness of the results.

• compatible numbers

Estimate by Rounding Dividends

Estimate 44.2 9.

Using multiples of 9, 44.2 is closest to 45.

Answer: The quotient is about 5.

Estimate 58.8 6.

A. 48 ÷ 6 = 8

B. 54 ÷ 6 = 9

C. 60 ÷ 6 = 10

D. 66 ÷ 6 = 11

Estimate 72 8.3.

Estimate by Rounding Divisors

Round 8.3 to 8 since 72 and 8 are compatible numbers.

Answer: So, 72 ÷ 8.3 is about 9.

A. 60 ÷ 6 = 10

B. 54 ÷ 9 = 6

C. 60 ÷ 12 = 5

D. 60 ÷ 10 = 6

MAMMALS The average weight of a Florida panther is 64.2 kilograms. The average weight of a coyote is 14.8 kilograms. About how many times heavier is the panther? Explain why your answer is reasonable.

Round 14.8 to 15 and 64.2 to 60 since 15 and 60 are compatible numbers.

Answer: The panther is about 4 times heavier than the coyote.

Check for Reasonableness Since 4 × 15 = 60 and 60 is close to 64.2, the answer is reasonable.

PUPPIES In a study, the average weight of a 6-week old male Labrador Retriever puppy was 5.63 kilograms. The average weight of the same puppies at 20 weeks old was 17.89 kilograms. By about how many times did the average weight increase from 6 to 20 weeks old?

A. about 2 times

B. about 3 times

C. about 4 times

D. about 5 times

TRAVEL The Chu family drove 163.35 miles in 4 hours. Estimate the average number of miles they drove each hour. Justify your answer.

Round 163.35 to 160.

Answer: The Chu family drove about 40 miles each hour.

Check for Reasonableness Since 40 × 4 = 160 and 160 ≈ 163.35, the answer is reasonable.

GAS MILEAGE The Mays family drove 148.5 miles using 5 gallons of gas. Estimate the number of miles they drove for each gallon of gas.

A. about 20 miles

B. about 30 miles

C. about 50 miles

D. about 450 miles