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}

Did you find an error?

2. Theoretical explanation about finding a percentage