Flexi Says:
Apercent is a ratio that describes a quantity out of 100. A percent is also a part of a whole. Finding the percent of a number is the part of a number that is equivalent to the percent.
Steps to find the percentage of a number - Method 1
Let's, find 25% of 100 using proportion.
First, write the percent as a fraction. 25% is also 25 out of 100.
@$$\begin{align*}25\%=\frac{25}{100}\end{align*}@$$
Next, write a proportion to find the equivalent fraction of 25% of 100. The second fraction is the unknown quantity, represented by@$\begin{align*}x\end{align*}@$, over the whole, 100.
@$$\begin{align*}\frac{25}{100}=\frac{x}{100}\end{align*}@$$
Now, cross-multiply to find the cross-product. To cross-multiply, multiply thenumerator of one fraction with the denominator of the other fraction. The products should be equal.
@$$\begin{align*}25(100)=100x\end{align*}@$$
Finally, simplify the equation to solve for @$\begin{align*}x\end{align*}@$. Multiply 25 by 100 and divide both sides by 100.
@$$\begin{align*}25(100)&=100x\\[6pt]\frac{2500}{100}&=\frac{100x}{100}\\[6pt]25&=x\end{align*}@$$
Hence, 25% of 100 is 25.
Steps to find the percentage of a number - Method 2
Another method is to use keywords and multiplication. Let's look again at the problem.
What is 25% of 100?
First, look for keywords that suggest an operation. The word "of" tells you to multiply 100 by 25%.
Next, convert 25% to a decimal.
@$$\begin{align*}25\%=0.25\end{align*}@$$
Then, write an equation to find the unknown number, @$\begin{align*}x\end{align*}@$.
@$$\begin{align*}x=100\times 0.25\end{align*}@$$
Finally, solve for @$\begin{align*}x\end{align*}@$ by multiplying 100 by 0.25.
@$$\begin{align*}x=100\times 0.25=25\end{align*}@$$ The answer is the same. 25% of 100 is 25.
Steps to find the percentage of a number - Method 3
The relationship@$\begin{align*}\text{percent} = \frac{\text{part}}{\text{whole}}\end{align*}@$ can be used to solve for a percent using the part and the whole. By multiplying the whole by the other side you get the following equation:@$$\begin{align*}\text{percent} \cdot \text{whole}= \text{part}\end{align*}@$$
Step 1: Divide the percentage by 100.
Step 2: Multiply the result by the number you want to find the percentage of.
For example, find 25% of 100.
Part = ?
Whole = 100.
Percent = @$\begin{align*}25\% \rightarrow \frac{25}{100}.\end{align*}@$
@$$\begin{align*}\text{Percent} \cdot \text{Whole}& = \text{Part} \\\frac{25}{100} \cdot 100 & = \text{Part} \\25 & = \text{Part}\end{align*}@$$
∴ 25% of 100 is 25.
To learn more about percentages, click here!
