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:
23 × 34 = 612 and that is already in simplest form.
Corrected: 23 × 34 = 612 = 12 after simplifying by dividing both by 6.
While 612 is correct before simplifying, both 6 and 12 share a factor of 6, so 612 reduces to 12 and is not already in simplest form.
2. Fix the sentence:
12 × 13 = 25 because you add the numerators and denominators.
Corrected: 12 × 13 = 16 because you multiply the numerators and multiply the denominators.
When multiplying fractions you multiply across, not add. 1 × 1 = 1 and 2 × 3 = 6, so the product is 16, not 25.
3. Fix the sentence:
7 × 14 = 728 because you multiply 7 by the denominator too.
Corrected: 7 × 14 = 74 = 134 because you multiply only the numerator by 7.
When multiplying a whole number by a fraction, only the numerator is multiplied: 7 × 1 = 7 over 4, giving 74 = 134. The denominator stays the same.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 35 × 56 simplified is 12.
Multiply the numerators: 3 × 5 = 15, and the denominators: 5 × 6 = 30, giving 1530, which simplifies to 12 when you divide both by 15.
2. 4 × 27 as a mixed number is 117.
Multiply 4 by the numerator: 4 × 2 = 8, keeping the denominator 7, so you get 87, which equals 117 as a mixed number.
3. 14 × 23 = 16.
Multiply the numerators: 1 × 2 = 2, and the denominators: 4 × 3 = 12, giving 212, which simplifies to 16 by dividing both by 2.
4. 6 × 38 simplified is 214.
Multiply 6 by the numerator: 6 × 3 = 18, keeping the denominator 8, so you get 188, which simplifies to 94 or 214.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why is the product of two proper fractions always less than either fraction?
Sample answer: Each fraction is less than 1, so multiplying by it takes only a part of the other fraction, making the product smaller.
A good answer includes: Each fraction is less than 1, so multiplying by it takes only a part of the other fraction, making the product smaller.
2. A runner covers 34 of a mile in one lap. After 2 laps, how far has the runner gone? Show your work.
Sample answer: 2 × 34 = 64 = 112 miles.
A good answer includes: 2 × 34 = 64 = 112 miles.