Find the error: adding fractions with unlike denominators

A find-the-error worksheet for common denominators first, like 3/4 + 1/6. 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

Added the numerators and the denominators. Denominators name the size of the pieces; they are not added. Rename both fractions with a common denominator (10) first.Example: 4/5 + 1/10 worked to 1/3 instead of 9/10.
Changed the denominator but not the numerator. When the denominator is changed to 10, the numerator must be multiplied by the same number.Example: 4/5 + 1/2 worked to 1/2 instead of 1 3/10.

Grade 5 · 5.NF.A.1

Find the error: adding fractions with unlike denominators

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 45 + 12

Leo's work
1. Find a common denominator: the least common multiple of 5 and 2 is 10.
2. Rename: 45 = 410 and 12 = 110.
3. Add the numerators: 410 + 110 = 510.
4. Simplify: 510 = 12.
Leo's answer: 12

Wrong step: What went wrong: Correct answer:
2 45 + 110

Jade's work
1. Add the numerators and the denominators: 4 + 1 = 5 and 5 + 10 = 15, so 515.
2. Simplify: 515 = 13.
Jade's answer: 13

Wrong step: What went wrong: Correct answer:
3 25 + 67

Max's work
1. Add the numerators and the denominators: 2 + 6 = 8 and 5 + 7 = 12, so 812.
2. Simplify: 812 = 23.
Max's answer: 23

Wrong step: What went wrong: Correct answer:
4 23 + 45

Nina's work
1. Find a common denominator: the least common multiple of 3 and 5 is 15.
2. Rename: 23 = 215 and 45 = 415.
3. Add the numerators: 215 + 415 = 615.
4. Simplify: 615 = 25.
Nina's answer: 25

Wrong step: What went wrong: Correct answer:

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Answer key · Grade 5 · 5.NF.A.1

Find the error: adding fractions with unlike denominators

#	Wrong step	The mistake	Correct answer
1	Step 2	Changed the denominator but not the numerator. When the denominator is changed to 10, the numerator must be multiplied by the same number.Correct step 2: Rename: 45 = 810 and 12 = 510.	1 310not 12
2	Step 1	Added the numerators and the denominators. Denominators name the size of the pieces; they are not added. Rename both fractions with a common denominator (10) first.Correct step 1: Find a common denominator: the least common multiple of 5 and 10 is 10.	910not 13
3	Step 1	Added the numerators and the denominators. Denominators name the size of the pieces; they are not added. Rename both fractions with a common denominator (35) first.Correct step 1: Find a common denominator: the least common multiple of 5 and 7 is 35.	1 935not 23
4	Step 2	Changed the denominator but not the numerator. When the denominator is changed to 15, the numerator must be multiplied by the same number.Correct step 2: Rename: 23 = 1015 and 45 = 1215.	1 715not 25

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