Students fix three unit fraction division errors — dividing 1/4 by 3 incorrectly, computing 6 ÷ 1/2 as 3, and flipping a unit fraction. Part B has four division problems. Part C has two questions about dividing by a fraction and writing a word problem.
Correcting unit fraction division errors — distinguishing a unit fraction divided by a whole from a whole divided by a unit fraction — builds the conceptual foundation for the reciprocal rule.
Style:
Multiplying and Dividing Fractions
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
14 ÷ 3 = 34 because you multiply the numerator by 3.
Rewrite: 14 ÷ 3 = 112 because you multiply the denominator by 3.
2. Fix the sentence:
6 ÷ 12 = 3 because 6 divided by 2 is 3.
Rewrite: 6 ÷ 12 = 12 because you multiply 6 by the reciprocal 21.
3. Fix the sentence:
15 ÷ 2 = 25 because dividing flips the fraction.
Rewrite: 15 ÷ 2 = 110 because you multiply the denominator by 2.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 13 ÷ 4 = 112
2. 8 ÷ 14 = 32
3. 16 ÷ 3 = 118
4. 5 ÷ 15 = 25
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why does 4 ÷ 13 give a number larger than 4?
Each whole contains 3 thirds, so 4 wholes contain 4 × 3 = 12 thirds.
2. Write a word problem where the answer uses 16 ÷ 2 = 112.
If you split 16 of a pizza equally between 2 friends, each gets 112 of the pizza.
Multiplying and Dividing Fractions
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
1/4 ÷ 3 = 3/4 because you multiply the numerator by 3.
Rewrite: 1/4 ÷ 3 = 1/12 because you multiply the denominator by 3.
2) Fix the sentence:
6 ÷ 1/2 = 3 because 6 divided by 2 is 3.
Rewrite: 6 ÷ 1/2 = 12 because you multiply 6 by the reciprocal 2/1.
3) Fix the sentence:
1/5 ÷ 2 = 2/5 because dividing flips the fraction.
Rewrite: 1/5 ÷ 2 = 1/10 because you multiply the denominator by 2.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) 1/3 ÷ 4 = 1/12
2) 8 ÷ 1/4 = 32
3) 1/6 ÷ 3 = 1/18
4) 5 ÷ 1/5 = 25
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) Why does 4 ÷ 1/3 give a number larger than 4?
Each whole contains 3 thirds, so 4 wholes contain 4 × 3 = 12 thirds.
2) Write a word problem where the answer uses 1/6 ÷ 2 = 1/12.
If you split 1/6 of a pizza equally between 2 friends, each gets 1/12 of the pizza.
Ready to Practice?
Complete each section carefully.
9 Questions
15-20 minutes
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