Why the percentage formula works
Percent means “out of 100.” So 30% is 30 out of every 100. As a decimal, that’s 0.30.
In a percent question, “of” means times. So 30% of 40 is 0.30 × 40, which is 12.
That’s the percentage formula: part = percent × whole. The whole is the full amount, the 100%. The part is the piece you care about.
Here’s why one formula is enough. Every percent question gives you two of those numbers. You find the third.
| What’s missing | How to find it |
|---|---|
| The part | Multiply the percent by the whole. |
| The percent | Divide the part by the whole. Then change the decimal to a percent. |
| The whole | Divide the part by the percent. |
Bottom line: name the whole before you do any math. It’s usually the number right after “of” or “out of.”
Example 1: find the part (a tip)
Your takeout order comes to $38. You want to leave a 15% tip. How much is the tip?
The working
- Name what you have. The whole is $38 and the percent is 15%. The part is missing.
- Change the percent to a decimal. Move the point two places left: 15% = 0.15
- Multiply: part = 0.15 × 38 = 5.70
- Check it backward: 5.70 ÷ 38 = 0.15, which is 15%.
Answer: $5.70
On the test, the calculator’s % key can do step 2 for you. The calculator guide shows how it works.
Example 2: find the percent (a test score)
You got 34 out of 40 questions right on a practice quiz. What percent did you get right?
The working
- Name the whole. It’s all 40 questions. The part is the 34 you got right.
- Divide the part by the whole: 34 ÷ 40 = 0.85
- Change the decimal to a percent. Move the point two places right: 0.85 = 85%
- Check it: 0.85 × 40 = 34. That matches.
Answer: 85%
Example 3: find the whole (work backward)
Some questions give you the part and the percent, then ask for the whole. It’s the same formula, run backward.
A jacket is on sale for $42. The tag says 30% off. What was the price before the sale?
The working
- The price before the sale is the whole, the 100%. That’s what’s missing.
- Taking 30% off leaves 70%. So $42 is 70% of the whole.
- Write the formula: 42 = 0.70 × whole
- Divide both sides by 0.70: whole = 42 ÷ 0.70 = 60
- Check it: 30% of $60 is $18, and 60 − 18 = 42.
Answer: $60
4 mistakes that cost points
Mistake 1: dividing the wrong way
To find a percent, the whole goes on the bottom. 12 out of 48 is 12 ÷ 48 = 0.25, or 25%. Flip it and you get 48 ÷ 12 = 4, or 400%.
Quick check: if the part is smaller than the whole, the answer is under 100%.
Mistake 2: using 3 instead of 0.03
A 3% raise on $15 an hour is 0.03 × 15 = 0.45, so 45 cents more an hour. Multiply by 3 instead and you’d get a $45 raise. Change the percent to a decimal first, every time.
Mistake 3: adding the percent back to a sale price
A coat costs $80 after 20% off. Adding 20% of $80 back on gives $96. That’s wrong, because the 20% came off the original price.
The sale price is 80% of the original, so divide: 80 ÷ 0.80 = 100. The coat was $100.
Mistake 4: rounding too early
Keep every digit until the last step. Say you’ve made 7 of the 9 payments on a phone. That’s 7 ÷ 9 = 0.777…, or about 77.8%. Round to 0.8 first and you’d say 80%.
Practice: 5 new questions
Every set is new. Check each answer as you go, and read the working on any you miss before the next one.
How to calculate percentages: 5 questions
- Questions
- 5
- Timer
- None
- No calculator
- None
New questions every time you start. Do this set as many times as you like.
- Check each answer as you go and read the working before the next question.
- The formula sheet and calculator sit in the toolbar, as they do on the real test.
No account or email needed.
Want more? Practice all of fractions, decimals and percents (25 questions, every skill in the topic), or take the full GED math practice test.
Frequently asked questions
How much is 20% of 70?
It's 14. Write 20% as the decimal 0.20, then multiply: 0.20 × 70 = 14. To check it, divide the part by the whole: 14 ÷ 70 = 0.20, which is 20%. If the question says 20% out of 70, the steps are the same, because 70 is still the whole.
How can I calculate a percentage of a number in my head?
Start with 10%: move the decimal point one place to the left. So 10% of $60 is $6. Halve that for 5% ($3), or double it for 20% ($12). Build other percents from those pieces: 15% is $6 + $3 = $9. It's also a fast way to check a calculator answer.
Keep going
Simple interest formula
I = Prt runs on percents. Work out a car loan and a savings account, then try the calculator.
GED math word problems
15 solved step by step, including a double discount, sales tax and a rent increase.
GED math formula sheet
What the official sheet gives you, and the 7 formulas it leaves out, percent change among them.
The GED calculator, explained
How the % key works on the TI-30XS, and the first questions you answer without it.
Written by
Coach Crissy
Math instructor
Coach Crissy teaches the video lessons behind the BooknBoost GED math course, working through GED-style problems on camera: ratios and proportions, percent and interest, mean, median and mode, slope, and the geometry students meet on test day.