Theoretical explanation about finding a percentage — lesson. Mathematics State Board, Class 8.

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1. Finding a percentage of a given number:

To find the percentage of a given number, multiply the number by the require percent.

Let the number

$= x$

Required percent

$= p$

$\%$

Percentage of given number

$= p$

$\%$ of

$x$

$=$

$\frac{p}{100} \times x$

2. Finding the original number from its percent:

Let original number

$= x$

Required percent

$= p$

$\%$

Obtained percentage

$= y$

Now

$p$

$\%$ of

$x = y$

$\frac{p}{100} \times x$

$= y$

$x =$

$\frac{y}{p} \times 100$

Original Number

$=$

$\frac{\text{Obtained Number}}{\text{percent}}$

$\times100$

3. Finding how much percent one quantity is of another quantity:

To find what percent of one quantity is of the other quantity if two quantities are given, we proceed as follows:

Let

$a$ and

$b$ are two quantities and we want to know 'what percent of '

$a$ ' is '

$b$ '?

Let

$x$

$\%$ of

$a$ is equal to

$b$ then:

$\begin{array}{l} \frac{x}{100} \times a = b \\ x = \frac{b}{a} \times 100 \end{array}$

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2. Theoretical explanation about finding a percentage

Theory: