Find the error: long division (zeros in the quotient, remainders)

A find-the-error worksheet for dividing 3- and 4-digit numbers by one digit, like 1,236 ÷ 6. Each problem shows a student's worked solution with one planted mistake; students find the wrong step, name the misconception and solve it correctly. The answer key is computed, so it is always right.

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Mistakes this sheet plants

Left out the zero in the quotient. When a brought-down number is smaller than 4, write 0 in the quotient before bringing down the next digit.Example: 412 ÷ 4 worked to 13 instead of 103.
Wrote the remainder as a decimal. A remainder of 1 means 1/4 more, not 1 tenths. Write it as R1.Example: 89 ÷ 4 worked to 22.1 instead of 22 R1.

Grade 5 · 4.NBT.B.6, 5.NBT.B.6

Find the error: long division (zeros in the quotient, remainders)

Name Date

Each problem was solved by a student, and each has exactly one mistake. Find the step with the mistake, say what went wrong, and solve the problem correctly.

1 89 ÷ 4

Tess's work
1. 8 ÷ 4 = 2. Write 2 in the tens place. 2 × 4 = 8, 8 − 8 = 0.
2. Bring down 9: 9 ÷ 4 = 2. Write 2 in the ones place. 2 × 4 = 8, 9 − 8 = 1.
3. The remainder is 1, so the answer is 22.1.
Tess's answer: 22.1

Wrong step: What went wrong: Correct answer:
2 412 ÷ 4

Noah's work
1. 4 ÷ 4 = 1. Write 1 in the hundreds place. 1 × 4 = 4, 4 − 4 = 0.
2. Bring down 1: 1 is less than 4, so bring down 2 too. 12 ÷ 4 = 3. Write 3. 3 × 4 = 12, 12 − 12 = 0.
Noah's answer: 13

Wrong step: What went wrong: Correct answer:
3 3,642 ÷ 6

Sam's work
1. 36 ÷ 6 = 6. Write 6 in the hundreds place. 6 × 6 = 36, 36 − 36 = 0.
2. Bring down 4: 4 is less than 6, so bring down 2 too. 42 ÷ 6 = 7. Write 7. 7 × 6 = 42, 42 − 42 = 0.
Sam's answer: 67

Wrong step: What went wrong: Correct answer:
4 222 ÷ 5

Rosa's work
1. 22 ÷ 5 = 4. Write 4 in the tens place. 4 × 5 = 20, 22 − 20 = 2.
2. Bring down 2: 22 ÷ 5 = 4. Write 4 in the ones place. 4 × 5 = 20, 22 − 20 = 2.
3. The remainder is 2, so the answer is 44.2.
Rosa's answer: 44.2

Wrong step: What went wrong: Correct answer:

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Answer key · Grade 5 · 4.NBT.B.6, 5.NBT.B.6

Find the error: long division (zeros in the quotient, remainders)

#	Wrong step	The mistake	Correct answer
1	Step 3	Wrote the remainder as a decimal. A remainder of 1 means 1/4 more, not 1 tenths. Write it as R1.Correct step 3: The remainder is 1, so the answer is 22 R1.	22 R1not 22.1
2	Step 2	Left out the zero in the quotient. When a brought-down number is smaller than 4, write 0 in the quotient before bringing down the next digit.Correct step 2: Bring down 1: 1 ÷ 4 = 0. Write 0 in the tens place. 0 × 4 = 0, 1 − 0 = 1.	103not 13
3	Step 2	Left out the zero in the quotient. When a brought-down number is smaller than 6, write 0 in the quotient before bringing down the next digit.Correct step 2: Bring down 4: 4 ÷ 6 = 0. Write 0 in the tens place. 0 × 6 = 0, 4 − 0 = 4.	607not 67
4	Step 3	Wrote the remainder as a decimal. A remainder of 2 means 2/5 more, not 2 tenths. Write it as R2.Correct step 3: The remainder is 2, so the answer is 44 R2.	44 R2not 44.2

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