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:
Four jumps of 1/3 on a number line lands on 4/12.
Corrected: Four jumps of 1/3 on a number line lands on 4/3.
Each jump adds one third; four jumps give 4/3, which is the same as 1 1/3.
2. Fix the sentence:
If we make 5 jumps of 1/4, we ends on the point 5/4.
Corrected: If we make 5 jumps of 1/4, we end on the point 5/4.
Subject-verb agreement requires 'we end', and 5 x 1/4 = 5/4 confirms the position.
3. Fix the sentence:
Two jump of 2/5 each lands on 4/5 of the number line.
Corrected: Two jumps of 2/5 each land on 4/5 of the number line.
Plural subjects need plural verbs, and 2 x 2/5 = 4/5 gives the landing point.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Starting at 0, four jumps of 1/3 land at 4/3.
4 x 1/3 = 4/3, which equals 1 1/3 on the number line.
2. Three jumps of 1/2 from zero finish at the point 3/2.
3 x 1/2 = 3/2 = 1 1/2, so the third jump passes the whole.
3. Six jumps of 1/8 along the number line end at 6/8.
6 x 1/8 = 6/8, which simplifies to 3/4 on the number line.
4. Five jumps of 2/5 starting at 0 land on the number 2.
Ten fifths equal 2 wholes, so the fifth jump lands exactly on 2.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Describe the number-line picture for 4 x 1/3 and the final point.
Sample answer: I begin at 0 and make four equal jumps of 1/3. After the fourth jump I land on 4/3, which is 1 1/3.
Each jump represents one unit fraction, and four jumps total 4/3 on the number line.
2. How does a number line show that 3 x 2/4 equals 6/4?
Sample answer: From 0, I jump 2/4 three times. Each jump skips two fourths, so I land on 6/4, which equals 1 2/4.
3 x 2/4 = 6/4 because the whole-number factor multiplies the numerator only.