Long Division — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
To estimate 159 ÷ 4, use 160 ÷ 4 = 42.
Corrected: To estimate 159 ÷ 4, use 160 ÷ 4 = 40.
The corrected sentence is: "To estimate 159 ÷ 4, use 160 ÷ 4 = 40." The error was wrong estimate: the original sentence "To estimate 159 ÷ 4, use 160 ÷ 4 = 42." needed to be fixed.
2. Fix the sentence:
108 ÷ 9 = 11 because 9 × 11 = 108.
Corrected: 108 ÷ 9 = 12 because 9 × 12 = 108.
The corrected sentence is: "108 ÷ 9 = 12 because 9 × 12 = 108." The error was wrong quotient: the original sentence "108 ÷ 9 = 11 because 9 × 11 = 108." needed to be fixed.
3. Fix the sentence:
372 ÷ 4 = 94 because 4 × 94 = 376.
Corrected: 372 ÷ 4 = 93 because 4 × 93 = 372.
The corrected sentence is: "372 ÷ 4 = 93 because 4 × 93 = 372." The error was wrong quotient: the original sentence "372 ÷ 4 = 94 because 4 × 94 = 376." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. To estimate 247 ÷ 5, use the compatible number 250 ÷ 5 = 50
The answer is 50. Rounding 247 up to 250 makes the division easier because 250 divides evenly by 5, giving an estimate of 50.
2. 312 ÷ 4 = 78
The answer is 78. Dividing step by step: 4 goes into 31 seven times (28) with 3 left over, bring down 2 to get 32, and 4 goes into 32 eight times.
3. To estimate 355 ÷ 6, use 360 ÷ 6 = 60
The answer is 60. Rounding 355 up to the nearby compatible number 360 makes the division simple, since 360 ÷ 6 = 60.
4. 455 ÷ 5 = 91
The answer is 91. Since 5 x 91 = 455, dividing 455 by 5 gives exactly 91 with nothing left over.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why is estimating a quotient before dividing a helpful strategy?
Sample answer: Estimating gives you a rough idea of the answer so you can check whether your exact quotient is reasonable.
A good answer includes: Estimating gives you a rough idea of the answer so you can check whether your exact quotient is reasonable.
2. Estimate 427 ÷ 6 using a compatible number. Then find the exact answer.
Sample answer: Use 420 ÷ 6 = 70 as the estimate. The exact answer is 427 ÷ 6 = 71 R1.
A good answer includes: Use 420 ÷ 6 = 70 as the estimate. The exact answer is 427 ÷ 6 = 71 R1.