Lesson S.1 · Start Here: Money Math Refresher
Percentages without the headache
4-minute read · No dated figures
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The short answer
A percent is a share out of 100, so 15% means 15 out of every 100. To find a percent of a number, turn the percent into a decimal and multiply: 15% of $1,200 is 0.15 × $1,200 = $180. To find what percent one number is of another, divide the part by the whole. To find a percent change, divide the change by the number you started with.
Percent of a number: move the decimal, then multiply
Percent means "per 100." To turn a percent into a decimal, move the decimal point two places left: 15% is 0.15, 25% is 0.25 and 7% is 0.07. Then multiply.
15% of $1,200 = 0.15 × $1,200 = $180.
You can check that in your head. For 10% of any number, move its decimal point one place left: 10% of $1,200 is $120. Half of that is 5%, or $60. Add them and 15% comes to $180.
Tax set-asides, deposits and interest all use this math. At 4% a year, $1,000 in savings earns about $40 in a year (example).
Example. Marcus gets $900 cash for a weekend driveway job. The day he's paid, he sets aside 25% for taxes: 0.25 × $900 = $225. (25% is a quarter, so $900 ÷ 4 gives the same $225.) Cash pay is income and gets reported even when no tax form shows up. The 25% is only an example. The lesson W-2, 1099 or cash (P101.2) helps you find the right share for you.
What percent is one number of another?
Divide the part by the whole, then multiply by 100.
$300 out of $2,000: $300 ÷ $2,000 = 0.15, and 0.15 × 100 = 15%.
The whole is whatever you're measuring against, so always ask: percent of what? Example: if $300 of a $2,000 month goes to groceries, groceries take 15% of that month's money. Measured against a $3,000 month, the same $300 is 10%.
This is how you see what share of your pay goes to rent, or how much of a job's money went to materials. The Move below uses the same math: your take-home pay as a percent of your gross pay.
Percent change: divide by where you started
Percent change is the change divided by the number you started with.
Example (made-up numbers, not a pay guide): Dana's pay goes from $20 to $22 an hour. The change is $2, and $2 ÷ $20 = 0.10, so that's a 10% increase. Dividing by the new number instead ($2 ÷ $22) gives about 9%, a common slip.
Each change is figured on a different starting number, so a 10% cut and a 10% increase don't cancel out:
| Step | Math | Result |
|---|---|---|
| Cut $1,000 by 10% | $1,000 − $100 | $900 |
| Add 10% to $900 | $900 + $90 | $990 |
The increase is figured on $900, so it adds back only $90. Getting from $900 back to $1,000 takes $100 ÷ $900, about an 11% increase.
Your Move
Do this week
Figure what share of your gross pay you took home.
- Find your last pay stub, on paper or in your payroll app.
- Write down two numbers: gross pay (before anything came out) and net pay (what reached your account).
- Divide net by gross and multiply by 100. Example: $780 ÷ $1,000 = 0.78, so you took home 78%.
- Subtract that from 100% to see the share that went to taxes and deductions: 100% − 78% = 22%.
If you're paid by 1099 or cash, use your last job instead: divide what you set aside for taxes by what you were paid.
Log it: Take-home percent.
Common questions
How do I figure a percent on a phone calculator?
Turn the percent into a decimal and multiply. For 15% of $1,200, type 0.15 × 1200. The % key works differently from one calculator to the next, so the decimal way is the safer habit.
How do I add or take off a percent in one step?
To add 10%, multiply by 1.10: $900 × 1.10 = $990. To take off 15%, multiply by 0.85, because 100% minus 15% leaves 85%: $1,200 × 0.85 = $1,020.
Why don't a 10% cut and a 10% increase cancel out?
Each one is figured on a different starting number. Cut $1,000 by 10% and you have $900; add 10% to $900 and you're at $990, not $1,000.
Free help
- IRS Tax Withholding Estimator: see whether the share taken out of your paycheck fits your year.
- IRS free tax return preparation: Volunteer Income Tax Assistance (VITA) sites prepare returns free for people with moderate incomes.
Free practice
Lesson check
5 questions on this lesson, one at a time, with the answer and the reason after each. Pass with 4 right, including every must-know question.
This is general education, not tax, legal, investment or insurance advice. Rules change and every situation is different. Check the sources below, and talk to a qualified professional before you act on it.