This set tackles dividing whole numbers by unit fractions. Students rewrite three sentences fixing wrong answers like 9 / 1/3 = 3 and the false claim that 2/7 is its own reciprocal, replacing them with reciprocal-multiplication reasoning. Fill-in problems ask for 7 / 1/2, the reciprocal of 4/9, and 1/8 / 5.
A shelf word problem (how many 1/4-foot books fit in 6 feet?) and an explain-the-reciprocal prompt close things out. Fifth graders walk away knowing why dividing by a small fraction produces a bigger answer.
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:
9 ÷ 13 = 3 because you divide 9 by 3.
Rewrite: 9 ÷ 13 = 27 because you multiply 9 by the reciprocal 31.
2. Fix the sentence:
The reciprocal of 27 is 27 because flipping it gives the same fraction.
Rewrite: The reciprocal of 27 is 72 because you swap the numerator and denominator.
3. Fix the sentence:
10 ÷ 15 = 2 because 10 divided by 5 is 2.
Rewrite: 10 ÷ 15 = 50 because you multiply 10 by the reciprocal 51.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 7 ÷ 12 = 14
2. The reciprocal of 49 is 94.
3. 12 ÷ 13 = 36
4. 18 ÷ 5 = 140
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A shelf is 6 feet long. Each book takes up 14 foot. How many books fit on the shelf? Explain.
6 ÷ 14 = 24 books, because each foot holds 4 books and 6 × 4 = 24.
2. Explain in your own words what a reciprocal is and give one example.
A reciprocal is the fraction you get by flipping the numerator and denominator. The reciprocal of 35 is 53.
Multiplying and Dividing Fractions
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
9 ÷ 1/3 = 3 because you divide 9 by 3.
Rewrite: 9 ÷ 1/3 = 27 because you multiply 9 by the reciprocal 3/1.
2) Fix the sentence:
The reciprocal of 2/7 is 2/7 because flipping it gives the same fraction.
Rewrite: The reciprocal of 2/7 is 7/2 because you swap the numerator and denominator.
3) Fix the sentence:
10 ÷ 1/5 = 2 because 10 divided by 5 is 2.
Rewrite: 10 ÷ 1/5 = 50 because you multiply 10 by the reciprocal 5/1.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) 7 ÷ 1/2 = 14
2) The reciprocal of 4/9 is 9/4.
3) 12 ÷ 1/3 = 36
4) 1/8 ÷ 5 = 1/40
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) A shelf is 6 feet long. Each book takes up 1/4 foot. How many books fit on the shelf? Explain.
6 ÷ 1/4 = 24 books, because each foot holds 4 books and 6 × 4 = 24.
2) Explain in your own words what a reciprocal is and give one example.
A reciprocal is the fraction you get by flipping the numerator and denominator. The reciprocal of 3/5 is 5/3.
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