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:
14 ÷ 3 = 34 because you multiply the numerator by 3.
Corrected: 14 ÷ 3 = 112 because you multiply the denominator by 3.
The corrected sentence is: "14 ÷ 3 = 112 because you multiply the denominator by 3.". The original sentence "14 ÷ 3 = 34 because you multiply the numerator by 3." contained an error that needed to be fixed.
2. Fix the sentence:
6 ÷ 12 = 3 because 6 divided by 2 is 3.
Corrected: 6 ÷ 12 = 12 because you multiply 6 by the reciprocal 21.
The corrected sentence is: "6 ÷ 12 = 12 because you multiply 6 by the reciprocal 21.". The original sentence "6 ÷ 12 = 3 because 6 divided by 2 is 3." contained an error that needed to be fixed.
3. Fix the sentence:
15 ÷ 2 = 25 because dividing flips the fraction.
Corrected: 15 ÷ 2 = 110 because you multiply the denominator by 2.
The corrected sentence is: "15 ÷ 2 = 110 because you multiply the denominator by 2.". The original sentence "15 ÷ 2 = 25 because dividing flips the fraction." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 13 ÷ 4 = 112
Dividing a fraction by a whole number: multiply the denominator by the whole number. 13 ÷ 4 = 1/(3×4) = 112.
2. 8 ÷ 14 = 32
Dividing a whole number by a unit fraction: 8 ÷ 14 = 8 × 4 = 32. (Each whole has 4 fourths, so 8 wholes have 8×4=32 fourths.)
3. 16 ÷ 3 = 118
16 ÷ 3 = 1/(6×3) = 118.
4. 5 ÷ 15 = 25
5 ÷ 15 = 5 × 5 = 25. Each whole has 5 fifths, so 5 wholes have 25 fifths.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why does 4 ÷ 13 give a number larger than 4?
Sample answer: Each whole contains 3 thirds, so 4 wholes contain 4 × 3 = 12 thirds.
Dividing by a fraction less than 1 always gives a result larger than the original number, because you are asking how many small pieces fit into the larger quantity.
2. Write a word problem where the answer uses 16 ÷ 2 = 112.
Sample answer: If you split 16 of a pizza equally between 2 friends, each gets 112 of the pizza.
16 ÷ 2 means dividing 16 into 2 equal parts. The result is 112 — each part is half of one-sixth.