### Theory:

In our day-to-day life, we use the ratio in various ways.

Now, we will study how the ratio helps us to solve our real-life situations.

When two numbers are in the ratio of $$a$$:$$b$$, they can be represented as $$ax$$ and $$bx$$.

Because whatever the value we substitute as $$x$$ in the expression which will be equal to the original form.

That is,

$\begin{array}{l}\mathit{ax}:\mathit{bx}=a:b\\ \\ \frac{\mathit{ax}}{\mathit{bx}}=\frac{a}{b}\\ \\ \mathit{Where}\phantom{\rule{0.147em}{0ex}}x\ne 0\end{array}$

Consider a ratio of two number 4$$:$$14. Which can also be written as 4$$x$$$$:$$14$$x$$.

$\begin{array}{l}4x:14x=4:14\\ \\ \frac{4x}{14x}=\frac{4}{14}\\ \\ \mathit{If}\phantom{\rule{0.147em}{0ex}}x=1,\phantom{\rule{0.147em}{0ex}}\mathit{then}\phantom{\rule{0.147em}{0ex}}\frac{4}{14}=\frac{4}{14}\end{array}$

We will see some application-oriented problems on ratios to understand this concept clearly.