To convert a fraction multiplication problem into an addition problem, you need to express the multiplication as repeated addition of the fractional part. In general, multiplying a whole number by a fraction \( a \cdot \frac{b}{c} \) can be rewritten as adding \( \frac{b}{c} \) a number of times equal to the whole number \( a \).
Let's look at each choice:
A. \( 6 \cdot \frac{1}{3} = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} \)
- Incorrect, as it should be \( \frac{1}{3} \) added six times.
B. \( 3 \cdot \frac{3}{5} = \frac{3}{5} + \frac{3}{5} + \frac{3}{5} \)
- Correct, since it represents adding \( \frac{3}{5} \) three times.
C. \( 2 \cdot \frac{2}{5} = \frac{5}{2} + \frac{5}{2} \)
- Incorrect, since it should be \( \frac{2}{5} \) added twice.
D. \( 1 \cdot \frac{4}{7} = \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} \)
- Incorrect, it should just be \( \frac{4}{7} \) added once.
The correct answer is:
B. \( 3 \cdot \frac{3}{5} = \frac{3}{5} + \frac{3}{5} + \frac{3}{5} \)
1 answer