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 20% of 400 using proportion.
First, write the percent as a fraction. 20% is also 20 out of 100.
@$$\begin{align*}20\%=\frac{20}{100}\end{align*}@$$
Next, write a proportion to find the equivalent fraction of 20% of 400. The second fraction is the unknown quantity, represented by@$\begin{align*}x\end{align*}@$, over the whole, 400.
@$$\begin{align*}\frac{20}{100}=\frac{x}{400}\end{align*}@$$
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.
@$$\begin{align*}20(400)=100x\end{align*}@$$
Finally, simplify the equation to solve for @$\begin{align*}x\end{align*}@$. Multiply 20 by 400 and divide both sides by 100.
@$$\begin{align*}20(400)&=100x\\[6pt]\frac{8000}{100}&=\frac{100x}{100}\\[6pt]80&=x\end{align*}@$$
Hence, 20% of 400 is 80.
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 20% of 400?
First, look for keywords that suggest an operation. The word "of" tells you to multiply 400 by 20%.
Next, convert 20% to a decimal.
@$$\begin{align*}20\%=0.2\end{align*}@$$
Then, write an equation to find the unknown number, @$\begin{align*}x\end{align*}@$.
@$$\begin{align*}x=400\times 0.2\end{align*}@$$
Finally, solve for @$\begin{align*}x\end{align*}@$ by multiplying 400 by 0.2.
@$$\begin{align*}x=400\times 0.2=80\end{align*}@$$ The answer is the same. 20% of 400 is 80.
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 20% of 400.
Part = ?
Whole = 400.
Percent = @$\begin{align*}20\% \rightarrow \frac{20}{100}.\end{align*}@$
@$$\begin{align*}\text{Percent} \cdot \text{Whole}& = \text{Part} \\\frac{20}{100} \cdot 400 & = \text{Part} \\80 & = \text{Part}\end{align*}@$$
∴ 20% of 400 is 80.
To learn more about percentages, click here!
