Percent of a
Number
Master how to find any percent of any number using fractions, decimals, and proportions: a critical skill for the SSAT.
What Is a Percent?
The word percent comes from the Latin per centum, meaning "per hundred." A percent tells you how many parts out of \(100\) you are talking about.
Three Forms, One Value
Every percent can be written as a fraction or a decimal. Converting between them is the foundation for finding a percent of a number.
Why Percents Matter on the SSAT
Finding a percent of a number appears in word problems, data interpretation, and mental math sections. Mastering the concept lets you solve problems quickly and accurately.
The Core Rule
This single formula answers every "find a percent of a number" question. You can also write it as:
\(\text{Part} = \text{decimal} \times \text{Whole}\)
\(\text{Part} = \frac{p}{100} \times \text{Whole}\)
Visualizing \(30\%\) of \(200\)
"Of" vs "Is" in Percent Problems
SSAT word problems use specific language. Knowing what each word translates to is essential:
| English Word | Math Symbol | Role |
|---|---|---|
| "of" | \(\times\) (multiply) | Connects percent to the whole |
| "is" | \(=\) (equals) | Shows the result (the part) |
| "what" | \(x\) (unknown) | The value to find |
| "percent" | \(\div 100\) | Divide by 100 |
How to Apply the Rule
Example 1: \(15\%\) of \(80\)
Example 2: \(25\%\) of \(360\)
Using the fraction method can be faster when the percent simplifies nicely.
Example 3: Word Problem
A store sells a backpack for \(\$60\). During a sale, the price is reduced by \(35\%\). What is the sale price?
Mental Math Shortcuts
On the SSAT, speed matters. Memorize these benchmark percents to save time:
| Percent | Fraction | Quick Method |
|---|---|---|
| \(1\%\) | \(\frac{1}{100}\) | Divide by \(100\) |
| \(10\%\) | \(\frac{1}{10}\) | Divide by \(10\) |
| \(20\%\) | \(\frac{1}{5}\) | Divide by \(5\) |
| \(25\%\) | \(\frac{1}{4}\) | Divide by \(4\) |
| \(50\%\) | \(\frac{1}{2}\) | Divide by \(2\) |
| \(75\%\) | \(\frac{3}{4}\) | Multiply by \(3\), divide by \(4\) |
Building Any Percent from Benchmarks
You can combine benchmarks to calculate any percent mentally. Example: find \(35\%\) of \(240\).
The Proportion Method
Some students prefer setting up a proportion. This works especially well on harder SSAT problems:
Example: What is \(40\%\) of \(150\)?
Common Mistakes
Method Comparison
| Feature | Decimal Method | Fraction Method | Proportion |
|---|---|---|---|
| Setup | \(0.\text{xx} \times \text{Whole}\) | \(\frac{p}{100} \times \text{Whole}\) | \(\frac{x}{\text{W}} = \frac{p}{100}\) |
| Best For | Calculator or simple percents | Percents that simplify nicely | Complex word problems |
| Speed | Fast | Fast | Medium |
| Error Risk | Decimal placement | Low | Cross-multiply errors |
Question 1 of 5
What is \(20\%\) of \(150\)?
Question 2 of 5
A shirt costs \(\$45\). It is on sale for \(20\%\) off. What is the sale price?
Question 3 of 5
If \(75\%\) of a number is \(60\), what is the number?
Question 4 of 5
There are \(300\) students in a school. If \(12\%\) are in the chess club, how many students are in the chess club?
Question 5 of 5
Which expression gives \(8\%\) of \(250\)?