# To solve: The proportion \frac{24}{n}=\frac{\frac{8}{15}}{\frac{5}{9}} for the given variable n.

To solve: The proportion $\frac{24}{n}=\frac{\frac{8}{15}}{\frac{5}{9}}$ for the given variable n.
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pierretteA
Approach:
If two ratios are equal then it is a proportion. If $\frac{p}{q}$ and $\frac{r}{s}$ are two ratios, then $\frac{p}{q}=\frac{r}{s}$ is a proportion.
Ex: $\frac{3}{4}=\frac{15}{20}$
For finding unknown numbers in proportions, we use cross product to find the unknown number.
Ex: $\frac{2}{7}=\frac{x}{14}$
Here in the example x is the unknown number. To calculate the value of x, we use the cross product.
Calculation:
Given $\frac{24}{n}=\frac{\frac{8}{15}}{\frac{5}{9}}$
Apply the cross product in order to find the unknown number.
$24×\frac{5}{9}=n×\frac{8}{15}$
Cancel out the common factors.
$\frac{40}{3}=\frac{8n}{15}$
Multiply both the sides by $\frac{15}{8}$
$\frac{40}{3}×\frac{15}{8}=\frac{8n}{15}×\frac{15}{8}$
Cancel out common factors
$25=n$
Final statement: The solution for the proportion $\frac{24}{n}=\frac{\frac{8}{15}}{\frac{5}{9}}$ for the indicated variable is $n=25$
Jeffrey Jordon