Long Division — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
57 ÷ 4 = 13 R5 because 4 × 13 = 52 and 57 − 52 = 5.
Corrected: 57 ÷ 4 = 14 R1 because 4 × 14 = 56 and 57 − 56 = 1.
The corrected sentence is: "57 ÷ 4 = 14 R1 because 4 × 14 = 56 and 57 − 56 = 1.". The original sentence "57 ÷ 4 = 13 R5 because 4 × 13 = 52 and 57 − 52 = 5." contained an error that needed to be fixed.
2. Fix the sentence:
150 ÷ 7 = 22 R1 because 7 × 22 = 154 and 154 − 150 = 1.
Corrected: 150 ÷ 7 = 21 R3 because 7 × 21 = 147 and 150 − 147 = 3.
The corrected sentence is: "150 ÷ 7 = 21 R3 because 7 × 21 = 147 and 150 − 147 = 3.". The original sentence "150 ÷ 7 = 22 R1 because 7 × 22 = 154 and 154 − 150 = 1." contained an error that needed to be fixed.
3. Fix the sentence:
239 ÷ 6 = 40 R1 because 6 × 40 = 240 and 240 − 239 = 1.
Corrected: 239 ÷ 6 = 39 R5 because 6 × 39 = 234 and 239 − 234 = 5.
The corrected sentence is: "239 ÷ 6 = 39 R5 because 6 × 39 = 234 and 239 − 234 = 5.". The original sentence "239 ÷ 6 = 40 R1 because 6 × 40 = 240 and 240 − 239 = 1." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 85 ÷ 6 = 14 R 1
6 × 14 = 84. 85 − 84 = 1. Remainder = 1.
2. 193 ÷ 8 = 24 R1
8 × 24 = 192. 193 − 192 = 1. Quotient = 24.
3. 100 ÷ 7 = 14 R 2
7 × 14 = 98. 100 − 98 = 2. Remainder = 2.
4. 347 ÷ 9 = 38 R 5
9 × 38 = 342. 347 − 342 = 5. Remainder = 5.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why must a remainder always be less than the divisor?
Sample answer: If the remainder equals or exceeds the divisor, you can divide one more time, so the quotient should be larger.
By definition, the division process continues as long as the leftover amount (remainder) is ≥ divisor. Once the remainder < divisor, the division is complete.
2. A teacher has 53 stickers to share equally among 8 students. How many does each student get, and how many are left over?
Sample answer: Each student gets 6 stickers with 5 left over because 8 × 6 = 48 and 53 − 48 = 5.
53 ÷ 8 = 6 R5. Each of the 8 students gets 6 stickers, and 5 stickers remain.