Finding a Percent of a Number
How much is 25% of 80? What is 15% of a $40 bill? In this lesson you'll see what "percent of" really means, learn three ways to find it, check that your answers make sense, and then practice with three activities.
New to percents? Start with Understanding Percents and Fractions, Decimals & Percents.
What Does "Percent Of" Mean?
A percent always describes a part of some whole. When we ask for "25% of 80," the whole is 80, and we want the part that is 25 out of every 100.
Picture the whole as a bar. Cut the bar into 10 equal sections and each section is 10% of the whole. Choose a whole, then slide the percent to see how big the part is.
Next come three methods, one section each: Use a decimal (it always works), Use a fraction (for friendly percents), and Build with 10% (for multiples of 5%).
Method 1: Use a Decimal
There are three good ways to find a percent of a number, and this one comes first because it is the only one that never lets you down. Percents like 37%, 6.5%, or 125% do not turn into simple fractions, but every percent turns into a decimal.
Any percent can be changed this way. Add zeros as placeholders when you need them:
| Percent | Decimal | What happened |
|---|---|---|
| 7% | 0.07 | A zero is added as a placeholder |
| 37% | 0.37 | Move the point two places left |
| 6.5% | 0.065 | Works even when the percent has a decimal |
| 100% | 1 | The whole thing |
| 125% | 1.25 | More than 1 whole |
| 0.5% | 0.005 | Less than 1% is a tiny decimal |
When the decimal method is the best choice
=0.37*240 to get 88.8Method 2: Use a Fraction
Some percents are simple fractions in disguise. 50% is one half and 25% is one quarter. When you spot one, you can skip the decimal and just divide the number into equal pieces.
These benchmark percents are worth memorizing. Each one turns into a quick calculation:
| Percent | Fraction | Quick way | Of 80 |
|---|---|---|---|
| 50% | Divide by 2 | 40 | |
| 25% | Divide by 4 | 20 | |
| 75% | Divide by 4, then multiply by 3 | 60 | |
| 20% | Divide by 5 | 16 | |
| 10% | Move the decimal point 1 place left | 8 | |
| 5% | Divide by 20 (or take half of 10%) | 4 | |
| 1% | Move the decimal point 2 places left | 0.8 |
When the fraction method is the best choice
Method 3: Build with 10%
Finding 10% is easy: just move the decimal point one place to the left. Every multiple of 5% can then be built from 10% pieces and 5% pieces (half of a 10% piece). Here is how to build different percents of $40:
| Percent | Build it | Of $40 |
|---|---|---|
| 10% | Move the point one place left | $4 |
| 20% | 2 × 10%, so 2 × $4 | $8 |
| 30% | 3 × 10%, so 3 × $4 | $12 |
| 5% | Half of 10%, so $4 ÷ 2 | $2 |
| 15% | 10% + 5%, so $4 + $2 | $6 |
| 25% | 20% + 5%, so $8 + $2 | $10 |
| 35% | 30% + 5%, so $12 + $2 | $14 |
When building with 10% is the best choice
Which Method Should I Use?
All three methods give the same answer. The skill is picking the quickest one for the situation. Ask yourself two questions:
- Do I have a calculator, phone, or computer? Then use the decimal method. It works every time and gives the exact answer.
- Doing it in my head? If the percent is a friendly fraction like 50%, 25%, 20%, or 1%, use a fraction. If it is a multiple of 5% like 15% or 35%, build with 10%.
| Method | Works for | Best when |
|---|---|---|
| Decimal | Every percent | You have a calculator or computer, the percent is messy, or the number is large |
| Fraction | Percents that match a simple fraction | You are doing mental math with 50%, 25%, 75%, 20%, 10%, or 1% |
| Build with 10% | Multiples of 5% | You are figuring tips and discounts in your head |
Does Your Answer Make Sense?
Before you trust an answer, check it against the whole:
- A percent less than 100% gives a part that is smaller than the whole.
- 100% of a number is the number itself.
- A percent greater than 100% gives something bigger than the whole.
You can also estimate by rounding the percent to a nearby benchmark and the number to a friendly number. Pick a problem and watch:
Using It in Real Life
Finding a percent of a number is one of the most useful math skills. Here are three everyday examples.
Let's Practice
Three activities: quick benchmark picks, typing in answers for any percent, and real-life word problems.
Quick Pick
Use the benchmark percents to find the answer, then choose it. Try it in your head first!
Type It In
Find the percent of the number and type your answer. Use any method you like. Decimal answers are fine.
Word Problems
Read each problem, decide what the whole is, and type your answer.