Find the error: multiplying and dividing integers

A find-the-error worksheet for sign rules for products and quotients, like (−6)(−4) and (−2)(−3)(−4). 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

Said negative times negative is negative. Two negative factors (or a negative divided by a negative) give a positive result.Example: (−30) ÷ (−6) worked to −5 instead of 5.
Made the answer positive because there were negatives to cancel. Count the negative factors: an odd number of them makes the product negative.Example: (−2)(−3)(−3) worked to 18 instead of −18.

Grade 7 · 7.NS.A.2

Find the error: multiplying and dividing integers

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 (−30) ÷ (−6)

Rosa's work
1. Divide the sizes: 30 ÷ 6 = 5.
2. A negative divided by a negative is negative. Answer: −5.
Rosa's answer: −5

Wrong step: What went wrong: Correct answer:
2 (−2)(−3)(−3)

Ravi's work
1. Multiply the sizes: 2 × 3 × 3 = 18.
2. The negatives cancel, so the answer is positive. Answer: 18.
Ravi's answer: 18

Wrong step: What went wrong: Correct answer:
3 (−60) ÷ (−5)

Sam's work
1. Divide the sizes: 60 ÷ 5 = 12.
2. A negative divided by a negative is negative. Answer: −12.
Sam's answer: −12

Wrong step: What went wrong: Correct answer:
4 (−2)(−4)(−6)

Tess's work
1. Multiply the sizes: 2 × 4 × 6 = 48.
2. The negatives cancel, so the answer is positive. Answer: 48.
Tess's answer: 48

Wrong step: What went wrong: Correct answer:

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Answer key · Grade 7 · 7.NS.A.2

Find the error: multiplying and dividing integers

#	Wrong step	The mistake	Correct answer
1	Step 2	Said negative times negative is negative. Two negative factors (or a negative divided by a negative) give a positive result.Correct step 2: A negative divided by a negative is positive. Answer: 5.	5not −5
2	Step 2	Made the answer positive because there were negatives to cancel. Count the negative factors: an odd number of them makes the product negative.Correct step 2: There are 3 negative factors, an odd number, so the answer is negative. Answer: −18.	−18not 18
3	Step 2	Said negative times negative is negative. Two negative factors (or a negative divided by a negative) give a positive result.Correct step 2: A negative divided by a negative is positive. Answer: 12.	12not −12
4	Step 2	Made the answer positive because there were negatives to cancel. Count the negative factors: an odd number of them makes the product negative.Correct step 2: There are 3 negative factors, an odd number, so the answer is negative. Answer: −48.	−48not 48

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