Find the error: multiplying a fraction by a whole number

A find-the-error worksheet for whole number times a fraction, like 3 × 2/5. 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

Multiplied the numerator and the denominator. Multiplying top and bottom by 5 makes an equal fraction, the same size as 7/8. Only the numerator is multiplied.Example: 5 × 7/8 worked to 35/40 instead of 4 3/8.
Multiplied the denominator instead of the numerator. 7 groups of 2/11 is 14 pieces of size 1/11; the piece size does not change.Example: 7 × 2/11 worked to 2/77 instead of 1 3/11.

Grade 4 · 4.NF.B.4

Find the error: multiplying a fraction by a whole number

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 5 × 78

Ben's work
1. Multiply the numerator and the denominator by 5: 5 × 7 = 35 and 5 × 8 = 40.
2. The answer is 3540.
Ben's answer: 3540

Wrong step: What went wrong: Correct answer:
2 7 × 211

Maya's work
1. Multiply 7 by the denominator: 7 × 11 = 77. Keep the numerator 2.
2. The answer is 277.
Maya's answer: 277

Wrong step: What went wrong: Correct answer:
3 5 × 910

Nina's work
1. Multiply 5 by the denominator: 5 × 10 = 50. Keep the numerator 9.
2. The answer is 950.
Nina's answer: 950

Wrong step: What went wrong: Correct answer:
4 6 × 29

Noah's work
1. Multiply the numerator and the denominator by 6: 6 × 2 = 12 and 6 × 9 = 54.
2. The answer is 1254.
Noah's answer: 1254

Wrong step: What went wrong: Correct answer:

Free sheet from stepcheck.apps.clod.farm · every answer computed, not generated · sheet sample-multiply-fraction-by-whole-number

Answer key · Grade 4 · 4.NF.B.4

Find the error: multiplying a fraction by a whole number

#	Wrong step	The mistake	Correct answer
1	Step 1	Multiplied the numerator and the denominator. Multiplying top and bottom by 5 makes an equal fraction, the same size as 7/8. Only the numerator is multiplied.Correct step 1: Multiply 5 by the numerator: 5 × 7 = 35. Keep the denominator 8.	4 38not 3540
2	Step 1	Multiplied the denominator instead of the numerator. 7 groups of 2/11 is 14 pieces of size 1/11; the piece size does not change.Correct step 1: Multiply 7 by the numerator: 7 × 2 = 14. Keep the denominator 11.	1 311not 277
3	Step 1	Multiplied the denominator instead of the numerator. 5 groups of 9/10 is 45 pieces of size 1/10; the piece size does not change.Correct step 1: Multiply 5 by the numerator: 5 × 9 = 45. Keep the denominator 10.	4 12not 950
4	Step 1	Multiplied the numerator and the denominator. Multiplying top and bottom by 6 makes an equal fraction, the same size as 2/9. Only the numerator is multiplied.Correct step 1: Multiply 6 by the numerator: 6 × 2 = 12. Keep the denominator 9.	1 13not 1254

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