Question

Find the unknown number in the proportion.   
StartFraction 5 Over 1 and two thirds EndFraction equals StartFraction 21 Over x EndFraction

Answer 1

To solve the proportion

\[
\frac{5}{1 \frac{2}{3}} = \frac{21}{x}
\]

we first need to convert the mixed number \(1 \frac{2}{3}\) into an improper fraction.

1. Convert \(1 \frac{2}{3}\):
\[
1 \frac{2}{3} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}
\]

Now the proportion can be expressed as:

\[
\frac{5}{\frac{5}{3}} = \frac{21}{x}
\]

2. To simplify \(\frac{5}{\frac{5}{3}}\), multiply by the reciprocal:

\[
\frac{5}{\frac{5}{3}} = 5 \times \frac{3}{5} = 3
\]

So now we have:

\[
3 = \frac{21}{x}
\]

3. To find \(x\), we can cross-multiply:

\[
3x = 21
\]

4. Now, divide both sides by 3:

\[
x = \frac{21}{3} = 7
\]

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

\[
\boxed{7}
\]