Multiplying and Dividing Fractions — Answer Key
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.
Corrected: 9 ÷ 13 = 27 because you multiply 9 by the reciprocal 31.
Dividing by 13 means multiplying by its reciprocal, 3. So 9 × 3 = 27, not 9 ÷ 3 = 3.
2. Fix the sentence:
The reciprocal of 27 is 27 because flipping it gives the same fraction.
Corrected: The reciprocal of 27 is 72 because you swap the numerator and denominator.
Flipping 27 swaps the 2 and the 7, giving 72. A fraction is never its own reciprocal unless it equals 1.
3. Fix the sentence:
10 ÷ 15 = 2 because 10 divided by 5 is 2.
Corrected: 10 ÷ 15 = 50 because you multiply 10 by the reciprocal 51.
Dividing by 15 means multiplying by 5 (the reciprocal), so 10 × 5 = 50. The mistake was dividing 10 by 5 instead.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 7 ÷ 12 = 14
Dividing by 12 means multiplying by its reciprocal, 2, so 7 × 2 = 14.
2. The reciprocal of 49 is 94.
To find a reciprocal, swap the numerator and denominator, so 49 flipped becomes 94.
3. 12 ÷ 13 = 36
Dividing by 13 means multiplying by 3, so 12 × 3 = 36.
4. 18 ÷ 5 = 140
Dividing a fraction by a whole number means multiplying the denominator by that number: 8 × 5 = 40, so 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.
Sample answer: 6 ÷ 14 = 24 books, because each foot holds 4 books and 6 × 4 = 24.
A good answer includes: 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.
Sample answer: A reciprocal is the fraction you get by flipping the numerator and denominator. The reciprocal of 35 is 53.
A good answer includes: A reciprocal is the fraction you get by flipping the numerator and denominator. The reciprocal of 35 is 53.