Multiplying Fractions by Whole Numbers — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
To find 5 x 1/2, we multiply 5 by 2 and write the answer as 10/2.
Corrected: To find 5 x 1/2, we multiply 5 by the numerator 1 and keep the denominator, getting 5/2.
Grade 4 rule says a x (b/c) keeps the denominator c, so 5 x 1/2 = 5/2.
2. Fix the sentence:
The product 3 x 2/5 is 5/2 because we swap the numerator and the whole number.
Corrected: The product 3 x 2/5 is 6/5 because we multiply 3 x 2 and keep the denominator 5.
Grade 4 students apply 3 x (2/5) = (3 x 2)/5 = 6/5.
3. Fix the sentence:
When 6 x 1/8 is computed, the answer 6/8 cannot be simplified at all.
Corrected: When 6 x 1/8 is computed, the answer 6/8 simplifies to 3/4 by dividing top and bottom by 2.
Grade 4 learners write fractions in simplest form when possible.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The product 5 x 1/2 is 5/2 when written as a single fraction.
Grade 4 rule: a x 1/b = a/b.
2. Computing 3 x 2/5 by multiplying numerators gives 6/5.
Grade 4 rule a x (b/c) = (a x b)/c.
3. The product 6 x 1/8 equals 6/8 before simplifying.
Grade 4 students see 6 x 1/8 as repeated addition of 1/8.
4. Two groups of 3/4 can be written as 2 x 3/4 = 6/4.
Grade 4 product rule keeps the denominator unchanged.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A Grade 4 student says 3 x 2/5 = 6/10. Explain the mistake and give the correct product.
Sample answer: The student multiplied both the numerator and the denominator by 3, but only the numerator should be multiplied. The denominator names the size of each part, and that size does not change when we add copies of 2/5. The correct work is 3 x 2/5 = (3 x 2)/5 = 6/5. As a check, 2/5 + 2/5 + 2/5 = 6/5, which matches.
Grade 4 rule: a x (b/c) = (a x b)/c keeps c unchanged.
2. Find 6 x 1/8 and write the answer in simplest form. Show each step a Grade 4 learner uses.
Sample answer: First multiply: 6 x 1/8 = 6/8. Then look for a common factor of 6 and 8. Both share a factor of 2. Divide top and bottom by 2: 6 / 2 = 3 and 8 / 2 = 4. So 6/8 simplifies to 3/4. Check: 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 6/8 = 3/4.
Grade 4 learners simplify fractions after multiplying.