Students correct three fraction-times-whole-number errors — multiplying both numerator and denominator, a wrong simplification, and a denominator incorrectly multiplied. Part B has four multiplication and simplification problems. Part C has two questions about why only the numerator is multiplied and a recipe tripling problem.
Correcting the multiply-both-parts error — where students apply the whole number to the denominator as well — establishes the fundamental rule for all fraction-by-whole-number multiplication at Grade 5.
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:
3 × 25 = 615 because you multiply both the numerator and denominator by 3.
Rewrite: 3 × 25 = 65 = 115 because you multiply only the numerator by 3.
2. Fix the sentence:
4 × 38 = 128 = 32 = 212.
Rewrite: 4 × 38 = 128 = 32 = 112.
3. Fix the sentence:
5 × 16 = 530 because you multiply 5 by both 1 and 6.
Rewrite: 5 × 16 = 56 because you multiply only the numerator 1 by 5.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 2 × 37 = 67
2. 6 × 14 simplified is 112.
3. 3 × 49 simplified is 113.
4. 5 × 23 as a mixed number is 313.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain why 4 × 25 equals 85 and not 820.
You only multiply the numerator by the whole number, so 4 × 2 = 8 over the same denominator 5.
2. A recipe uses 13 cup of oil. If you triple the recipe, how much oil do you need?
You need 3 × 13 = 1 cup of oil.
Multiplying and Dividing Fractions
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
3 × 2/5 = 6/15 because you multiply both the numerator and denominator by 3.
Rewrite: 3 × 2/5 = 6/5 = 1 1/5 because you multiply only the numerator by 3.
2) Fix the sentence:
4 × 3/8 = 12/8 = 3/2 = 2 1/2.
Rewrite: 4 × 3/8 = 12/8 = 3/2 = 1 1/2.
3) Fix the sentence:
5 × 1/6 = 5/30 because you multiply 5 by both 1 and 6.
Rewrite: 5 × 1/6 = 5/6 because you multiply only the numerator 1 by 5.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) 2 × 3/7 = 6/7
2) 6 × 1/4 simplified is 1 1/2.
3) 3 × 4/9 simplified is 1 1/3.
4) 5 × 2/3 as a mixed number is 3 1/3.
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) Explain why 4 × 2/5 equals 8/5 and not 8/20.
You only multiply the numerator by the whole number, so 4 × 2 = 8 over the same denominator 5.
2) A recipe uses 1/3 cup of oil. If you triple the recipe, how much oil do you need?
You need 3 × 1/3 = 1 cup of oil.
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9 Questions
15-20 minutes
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