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:
3 × 25 = 615 because you multiply both the numerator and denominator by 3.
Corrected: 3 × 25 = 65 = 115 because you multiply only the numerator by 3.
The corrected sentence is: "3 × 25 = 65 = 115 because you multiply only the numerator by 3.". The original sentence "3 × 25 = 615 because you multiply both the numerator and denominator by 3." contained an error that needed to be fixed.
2. Fix the sentence:
4 × 38 = 128 = 32 = 212.
Corrected: 4 × 38 = 128 = 32 = 112.
The corrected sentence is: "4 × 38 = 128 = 32 = 112.". The original sentence "4 × 38 = 128 = 32 = 212." contained an error that needed to be fixed.
3. Fix the sentence:
5 × 16 = 530 because you multiply 5 by both 1 and 6.
Corrected: 5 × 16 = 56 because you multiply only the numerator 1 by 5.
The corrected sentence is: "5 × 16 = 56 because you multiply only the numerator 1 by 5.". The original sentence "5 × 16 = 530 because you multiply 5 by both 1 and 6." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 2 × 37 = 67
Multiply the whole number by the numerator: 2 × 3 = 6. Keep the denominator: 67.
2. 6 × 14 simplified is 112.
6 × 1 = 6, over denominator 4. 64 = 32 = 112.
3. 3 × 49 simplified is 113.
3 × 4 = 12, over 9. 129 = 43 = 113.
4. 5 × 23 as a mixed number is 313.
5 × 2 = 10, over 3. 103 = 313.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain why 4 × 25 equals 85 and not 820.
Sample answer: You only multiply the numerator by the whole number, so 4 × 2 = 8 over the same denominator 5.
Multiplying a whole number by a fraction multiplies the numerator only. The denominator stays unchanged because it still names the type of fractional part.
2. A recipe uses 13 cup of oil. If you triple the recipe, how much oil do you need?
Sample answer: You need 3 × 13 = 1 cup of oil.
Triple means multiply by 3. 3 × 13 = 33 = 1 cup.