Question

Find the unknown number in the proportion. Write your answer as a whole number or a mixed number if possible.
StartFraction 7 Over one fourth EndFraction
​= StartFraction 8 Over x EndFraction

Answer 1

To solve the proportion \( \frac{7}{\frac{1}{4}} = \frac{8}{x} \), we can first simplify the left side.

To divide by a fraction, we multiply by its reciprocal. Thus, we have:

\[
\frac{7}{\frac{1}{4}} = 7 \times 4 = 28.
\]

Now, the proportion can be rewritten as:

\[
28 = \frac{8}{x}.
\]

Next, we can cross-multiply to solve for \( x \):

\[
28x = 8.
\]

Now, divide both sides by 28 to isolate \( x \):

\[
x = \frac{8}{28}.
\]

This fraction can be simplified:

\[
x = \frac{2}{7} \quad \text{(by dividing the numerator and the denominator by 4)}.
\]

Therefore, the unknown number \( x \) in the proportion is:

\[
\boxed{\frac{2}{7}}.
\]