Which choice shows the correct way to write a fraction multiplication problem as an addition. A. 6•1/3=1/6+1/6+1/6+1/6 b. 3•3/5=3/5+3/5+3/5+3/5 c. 2•2/5=5/2+5/2 d. 1•4/7=1/7+1/7+1/7+1/7

Answer 1

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. $3\cdot \frac{3}{5}=\frac{3}{5}+\frac{3}{5}+\frac{3}{5}$