This page of our online ParaPro Study Guide covers percentages. You will learn how to convert a fraction to a percentage, find a percentage of a value, and change a value by a certain percentage. Four examples are included to help you master these skills. Once you are comfortable with this material, you can try the percentages review test at the bottom of the page.
What are Percentages?
Percentages are a way of expressing a portion of a whole in terms of a fraction of 100. The term “percent” means “per hundred,” so when you express a value as a percentage, you’re essentially describing how many parts out of 100 something represents. You can remember this by thinking of your pocket change; one penny is one cent, and it takes 100 pennies to equal a whole dollar.
For example, if you have 30 out of 100 marbles, you can express this as 30%. This means you have 30 parts out of the total 100 parts.
Percentages are commonly used to compare relative values, express proportions, or describe changes over time. They’re extensively used in finance, statistics, everyday calculations, and many other fields.
Working with Percentages
To convert a fraction to a percentage, divide the numerator by the denominator to get the equivalent decimal value. Multiply the decimal value by $100$ to get the percentage (represented by the symbol $\%$).
Example 1
What is the decimal $.2$ represented as a percentage?
Multiply $.2$ by $100$ to get the percentage.
$.2 \cdot 100 = 20 \%$
Example 2
What is the fraction $\frac{6}{8}$ represented as a percentage?
To convert $\frac{6}{8}$ to a decimal, divide the numerator by the denominator.
$6 ÷ 8 = .75$
You can see that $.75$ is equal to $75\%$ since the decimal goes to the hundredths place, but you can also multiply $.75$ by $100$ to get the percentage value, $75\%$.
Remember, since decimals work in functions of ten, multiplying by $100$ is the same as moving the decimal point two places to the right.
To find a certain percentage of a number, multiply the percentage’s decimal equivalent by the number. If you are unsure how to multiply by a decimal value, see our decimal study guide.
Example 3
What is $30 \%$ of $80$?
To find $30 \%$ of $80$, you multiply the percentage’s decimal equivalent by the number.
$\dfrac{30}{100} = .3$
$.3 \cdot 80 = 24$
To increase or decrease a value by a percentage, add or subtract the percentage to or from $100 \%$, respectively. We do this because the number is already a whole; it is $100 \%$ of itself. Thus, if we are increasing it by a percentage, we want more than $100 \%$ of it, and if we are decreasing, we want less than $100 \%$ of it.
An increase of $10 \%$ will be worth $110 \%$ of the original number, just as a decrease of $10 \%$ will be worth $90 \%$ of the original number.
Example 4
What do you get if you increase $25$ by $20 \%$?
To increase the value of $25$ by $20 \%$, you add $20 \%$ to $100 \%$.
To find $120 \%$ of $25$, you multiply the percentage’s decimal equivalent by the number.
$\dfrac{120}{100} = 1.2$
$1.2 \cdot 25 = 30$
Now that you have learned about percentages and reviewed the four example questions, you should know what to expect for the ParaPro test. Before moving on, try the percentages review test below to ensure that you are fully prepared.