Long Division with Multi-Digit Divisors — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
To estimate 956 ÷ 32, I round 956 to 900 and 32 to 32, getting about 28 as the estimate.
Corrected: To estimate 956 ÷ 32, I round 956 to 1000 and 32 to 30, getting about 33 as the estimate.
Grade 5 estimation works best when both the dividend and divisor are rounded to friendly, compatible values.
2. Fix the sentence:
When estimating 612 ÷ 19, I should round 19 up to 100 because bigger numbers give better estimates.
Corrected: When estimating 612 ÷ 19, I should round 19 to 20 because that keeps the divisor close to its real value.
Rounding too far from the original number gives a useless Grade 5 estimate.
3. Fix the sentence:
An estimate of 5 for 4128 ÷ 41 is reasonable because the digits look small.
Corrected: An estimate of 100 for 4128 ÷ 41 is reasonable because 4000 ÷ 40 equals 100.
Grade 5 students rely on compatible-number division, not visual digit clues, to estimate quotients.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. To estimate 956 ÷ 32, you can round to 1000 ÷ 30, giving an estimate of about 33.
Rounding to compatible numbers lets Grade 5 students approximate the quotient quickly.
2. Rounding 612 ÷ 19 to compatible numbers gives 600 ÷ 20, which equals about 30.
Compatible numbers turn Grade 5 estimation into a basic-fact division.
3. When 956 ÷ 32 is exactly 29 R 28, the estimate of 33 is close, showing that estimates are approximate values.
Grade 5 estimation is meant to give a reasonable, approximate quotient for checking.
4. If you round both numbers down, your estimate of the quotient may be too high compared to the real answer.
Rounding direction affects whether a Grade 5 estimate overshoots or undershoots the true quotient.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Estimate 4128 ÷ 41 by rounding to compatible numbers and explain in Grade 5 language.
Sample answer: I rounded 4128 to 4000 and 41 to 40. Then 4000 ÷ 40 = 100, so the quotient is about 100. The exact answer is close to 100 (it is 100 R 28), so my estimate is reasonable.
Rounding both numbers to compatible values gives a quick, reasonable Grade 5 estimate.
2. Why is estimating 7235 ÷ 68 useful before doing the long division in Grade 5?
Sample answer: Estimating 7235 ÷ 68 as 7000 ÷ 70 = 100 tells me the answer should be close to 100. After I divide, I can check that my real answer (about 106) is reasonable and not off by a place-value mistake.
Grade 5 estimation is a key check on long-division reasonableness and place value.