Grade 4 introduction to multiplying fractions by whole numbers using repeated addition of unit fractions. Students see expressions like 4 x 1/3 as 1/3 + 1/3 + 1/3 + 1/3 = 4/3, learning that the denominator names part size while the numerator counts parts. Short questions guide reasoning toward the rule a x 1/b = a/b for CCSS 4.NF.4. This Grade 4 worksheet supports classroom practice or homework review and works for math centers.
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Multiplying Fractions by Whole Numbers
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
4 x 1/3 equals 4/12 because we multiply both numerator and denominator by 4.
Rewrite: 4 x 1/3 equals 4/3 because we add 1/3 four times: 1/3 + 1/3 + 1/3 + 1/3 = 4/3.
2. Fix the sentence:
Three times one fifth is one fifteenth, written as 1/15 in simplest form.
Rewrite: Three times one fifth is three fifths, written as 3/5 in simplest form.
3. Fix the sentence:
When we write 5 x 1/2, the answer cannot be a fraction greater than one whole.
Rewrite: When we write 5 x 1/2, the answer is 5/2, which is a fraction greater than one whole.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Using repeated addition, 4 x 1/3 = 1/3 + 1/3 + 1/3 + 1/3 = 4/3.
2. The product 5 x 1/2 written as a fraction is 5/2.
3. Six copies of the unit fraction 1/8 give the product 6/8.
4. Three groups of 2/5 can be written as 3 x 2/5 = 6/5.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Show how 4 x 1/3 equals 4/3 using repeated addition. Write each step a Grade 4 student would write.
Start with 1/3 + 1/3 + 1/3 + 1/3. Each piece is 1/3, and there are four pieces, so the total is 4/3. The denominator 3 stays the same because the size of the parts does not change. The numerator becomes 4 because we have four parts. Therefore 4 x 1/3 = 4/3.
2. Explain in your own words why 6 x 1/8 is written as 6/8 and not as 1/48.
When we multiply 6 x 1/8, we are adding 1/8 six times. The denominator 8 names the size of each piece, and that size does not change. Only the count of pieces changes, so the numerator becomes 6. The product is 6/8. Multiplying both numbers by 6 would give 6/48, which is wrong because it shrinks each piece.
Multiplying Fractions by Whole Numbers
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
4 x 1/3 equals 4/12 because we multiply both numerator and denominator by 4.
Rewrite: 4 x 1/3 equals 4/3 because we add 1/3 four times: 1/3 + 1/3 + 1/3 + 1/3 = 4/3.
2) Fix the sentence:
Three times one fifth is one fifteenth, written as 1/15 in simplest form.
Rewrite: Three times one fifth is three fifths, written as 3/5 in simplest form.
3) Fix the sentence:
When we write 5 x 1/2, the answer cannot be a fraction greater than one whole.
Rewrite: When we write 5 x 1/2, the answer is 5/2, which is a fraction greater than one whole.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) Using repeated addition, 4 x 1/3 = 1/3 + 1/3 + 1/3 + 1/3 = 4/3.
2) The product 5 x 1/2 written as a fraction is 5/2.
3) Six copies of the unit fraction 1/8 give the product 6/8.
4) Three groups of 2/5 can be written as 3 x 2/5 = 6/5.
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) Show how 4 x 1/3 equals 4/3 using repeated addition. Write each step a Grade 4 student would write.
Start with 1/3 + 1/3 + 1/3 + 1/3. Each piece is 1/3, and there are four pieces, so the total is 4/3. The denominator 3 stays the same because the size of the parts does not change. The numerator becomes 4 because we have four parts. Therefore 4 x 1/3 = 4/3.
2) Explain in your own words why 6 x 1/8 is written as 6/8 and not as 1/48.
When we multiply 6 x 1/8, we are adding 1/8 six times. The denominator 8 names the size of each piece, and that size does not change. Only the count of pieces changes, so the numerator becomes 6. The product is 6/8. Multiplying both numbers by 6 would give 6/48, which is wrong because it shrinks each piece.
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