To solve proportion \frac{21}{x}=\frac{\frac{7}{2}}{3}.

Approach:
The quotient of two numbers is called a ratio.
Ex. ${\displaystyle \frac{2}{3}}$.
The ratio is no different from a fraction, except that a ratio is sometimes written using notation other than fractional notation.
Ex. The ratio of 5 to 7 can be written as fractional notation ${\displaystyle \frac{5}{7}}$ or colon notation ${\displaystyle 5:7}$.
If a ratio contains decimal numbers or mixed numbers, then the ratio can be written only by the ratio of whole numbers.
Ex. ${\displaystyle 5.7:3}$ can be written as ${\displaystyle \frac{57}{30}}$
A proportion is a statement that two ratios or rates are equal.
Ex. If ${\displaystyle \frac{a}{b}}$ and ${\displaystyle \frac{c}{d}}$ are two ratios, then ${\displaystyle \frac{a}{b}=\frac{c}{d}}$ is a proportion.
If the cross products are not equal, the proportion is true.
Ex, If ${\displaystyle a\cdot d=b\cdot c}$, then it is true.
If the cross products are not equal, the proportion is false.
Ex. If ${\displaystyle a\cdot d\ne b\cdot c}$, then it is false.
When one number of proportion is unknown, then use cross products to find the unknown number.
Ex. Find the unknown number x in the proportion ${\displaystyle \frac{4}{2}=\frac{20}{x}}$. It can be found by cross product. That is, ${\displaystyle x=10}$.
Calculation:
Determine the value of x in the proportion ${\displaystyle \frac{21}{x}=\frac{\frac{7}{2}}{3}}$ by using the cross product.
${\displaystyle \frac{21}{x}=\frac{\frac{7}{2}}{3}}$
${\displaystyle 21\cdot 3=\frac{7}{2}\cdot x}$
${\displaystyle 63=\frac{7}{2}\cdot x}$
On further simplification,
${\displaystyle x=63\cdot \frac{2}{7}}$
${\displaystyle x=\frac{126}{7}}$
${\displaystyle x=18}$
Therefore, the value is ${\displaystyle x=18}$.
The final Statement:
The value of x in the proportion ${\displaystyle \frac{21}{x}=\frac{\frac{7}{2}}{3}}$ is ${\displaystyle x=18}$.

Answer is given below (on video)