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 15% of 30 using proportion.
First, write the percent as a fraction. 15% is also 15 out of 100.
@$$\begin{align*}15\%=\frac{15}{100}\end{align*}@$$
Next, write a proportion to find the equivalent fraction of 15% of 30. The second fraction is the unknown quantity, represented by@$\begin{align*}x\end{align*}@$, over the whole, 30.
@$$\begin{align*}\frac{15}{100}=\frac{x}{30}\end{align*}@$$
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.
@$$\begin{align*}15(30)=100x\end{align*}@$$
Finally, simplify the equation to solve for @$\begin{align*}x\end{align*}@$. Multiply 15 by 30 and divide both sides by 100.
@$$\begin{align*}15(30)&=100x\\[6pt]\frac{450}{100}&=\frac{100x}{100}\\[6pt]4.5&=x\end{align*}@$$
Hence, 15% of 30 is 4.5.
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 15% of 30?
First, look for keywords that suggest an operation. The word "of" tells you to multiply 30 by 15%.
Next, convert 15% to a decimal.
@$$\begin{align*}15\%=0.15\end{align*}@$$
Then, write an equation to find the unknown number, @$\begin{align*}x\end{align*}@$.
@$$\begin{align*}x=30\times 0.15\end{align*}@$$
Finally, solve for @$\begin{align*}x\end{align*}@$ by multiplying 30 by 0.15.
@$$\begin{align*}x=30\times 0.15=4.5\end{align*}@$$ The answer is the same. 15% of 30 is 4.5.
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 15% of 30.
Part = ?
Whole = 30.
Percent = @$\begin{align*}15\% \rightarrow \frac{15}{100}.\end{align*}@$
@$$\begin{align*}\text{Percent} \cdot \text{Whole}& = \text{Part} \\\frac{15}{100} \cdot 30 & = \text{Part} \\4.5 & = \text{Part}\end{align*}@$$
∴ 15% of 30 is 4.5.
To learn more about percentages, click here!
