Question

Find the unknown number in the proportion. Write your answer as a whole number or a mixed number if possible.
StartFraction four fifths Over two fifths EndFraction
​= StartFraction x Over two thirds EndFraction
.
.
.
Question content area right
Part 1
A.2 and one half
2 and one half
B.StartFraction 16 Over 75 EndFraction
StartFraction 16 Over 75 EndFraction
C.1 and one third
1 and one third
D.eight fifteenths
eight fifteenths

Answer 1

To solve the proportion

\[
\frac{\frac{4}{5}}{\frac{2}{5}} = \frac{x}{\frac{2}{3}},
\]

we can first simplify the left side of the equation.

1. Divide \(\frac{4}{5}\) by \(\frac{2}{5}\):

\[
\frac{4}{5} \div \frac{2}{5} = \frac{4}{5} \times \frac{5}{2} = \frac{4 \times 5}{5 \times 2} = \frac{4}{2} = 2.
\]

So the left side simplifies to \(2\). The proportion is now:

\[
2 = \frac{x}{\frac{2}{3}}.
\]

2. To solve for \(x\), we can multiply both sides by \(\frac{2}{3}\):

\[
x = 2 \times \frac{2}{3} = \frac{4}{3}.
\]

3. Now, \(\frac{4}{3}\) can be expressed as a mixed number:

\[
\frac{4}{3} = 1 \frac{1}{3}.
\]

Thus, the value of \(x\) is \(1 \frac{1}{3}\).

The correct answer is:

**C. \(1 \frac{1}{3}\)**