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:
3 x 1/4 equals 3/12 because we multiply both numbers by 3.
Corrected: 3 x 1/4 equals 3/4 because we add three quarter bars: 1/4 + 1/4 + 1/4.
Multiplying a whole number by a unit fraction means repeated addition; only the numerator changes.
2. Fix the sentence:
Five bars of 1/6 each shows 5 x 1/6 = 1/30 in the model.
Corrected: Five bars of 1/6 each shows 5 x 1/6 = 5/6 in the model.
Each bar contributes one sixth, so five bars together cover five sixths of the whole.
3. Fix the sentence:
If we draw 2 bars of 3/5, the model show 6/10 shaded total.
Corrected: If we draw 2 bars of 3/5, the model shows 6/5 shaded total.
When multiplying a whole number by a fraction, multiply only the numerator; the denominator stays the same.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Three stacked bars of 1/4 each combine to show 3/4 shaded.
3 x 1/4 = 3/4 because the numerator becomes 3 and the denominator stays 4.
2. A bar model of 4 x 1/5 has 4 fifths shaded in total.
Four bars of 1/5 give 4/5, so 4 fifths are shaded.
3. Six bars of 1/8 stacked together cover 6/8 of one whole.
6 x 1/8 = 6/8, which simplifies to 3/4 of the whole.
4. Two bars of 2/3 each, drawn end to end, shade 4 thirds total.
2 x 2/3 = 4/3, so four thirds are shaded across the bars.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Draw a bar model that shows 5 x 1/6 and explain the result.
Sample answer: I draw five bars, each shaded 1/6. Together they cover 5/6 of the whole because 5 x 1/6 = 5/6.
Multiplying a whole number by a unit fraction repeats the unit, so the numerator equals the whole number.
2. Use a bar model to show why 4 x 1/3 is greater than one whole.
Sample answer: Four bars of 1/3 give 4/3. Since 3/3 makes one whole, the extra 1/3 makes the total greater than 1.
When the numerator is larger than the denominator, the fraction is improper and greater than one whole.