What is 25% of 80?
- 1.Stage 1 — Understand: 25% means 25 out of 100, i.e. 0.25
- 2.Stage 2 — Set up: part = 0.25 × 80
- 3.Stage 3 — Solve: part = 20
25% of 80 is 20
Verified backwards: 20 ÷ 80 × 100 = 25% — the stated percent ✓.
Percent problems — the part, the percent, or the whole
Three questions wear the percent sign, and students mix them up because the setups look alike. Here they don’t: understand → set up → solve → verify by working backwards. Pick the question type, enter the numbers, and watch the setup happen.
What is a percent of a number? The classic "what is 25% of 80?" — plus the discount and tax versions below.
- ✓100% free — no paywall, ever
- ✓No sign-up, no app
- ✓Every answer verified before you see it
In short
Every percent word problem asks one of three questions: find the part, find the percent, or find the whole. All three run on one relationship — part = percent × whole — and discounts and tax are the same idea with money. VerifySolve sets each one up in stages, solves it exactly, and checks the answer by working backwards.
One relationship, three questions
Everything here is part = percent × whole. What changes is which piece is missing — and the solver’s Stage 2 is exactly that rearrangement, written out.
Find the part
Find the percent
Find the whole
Discount and tax
Worked examples — checked by working backwards
Each note re-tests the answer the other way round: the percent recomputed from the answer, or the money adding back to the original price. Run them live in the solver above.
18 is what percent of 60?
- 1.Stage 1 — Understand: the part is 18, the whole is 60
- 2.Stage 2 — Set up: percent = 18 ÷ 60 × 100
- 3.Stage 3 — Solve: 0.3 × 100
18 is 30% of 60
Verified: 30% of 60 = 18 — the stated part ✓.
45 is 15% of what number?
- 1.Stage 1 — Understand: the whole is unknown; call it W
- 2.Stage 2 — Set up: 0.15 × W = 45
- 3.Stage 3 — Solve: W = 45 ÷ 0.15
45 is 15% of 300
Verified: 15% of 300 = 45 — the stated part ✓.
A jacket costs $80 and is 25% off. What do you pay?
- 1.Stage 1 — Understand: the discount is 25% of the $80 price
- 2.Stage 2 — Set up: saved = 0.25 × $80; sale = $80 − saved
- 3.Stage 3 — Solve: saved = $20.00; sale = $60.00
You save $20.00 and pay $60.00
Verified both ways: $20.00 + $60.00 = $80.00 ✓, and $20.00 is 25% of $80 ✓.
Common mistakes — and how to dodge them
Forgetting to divide by 100
25% is 0.25, not 25. Multiplying by 25 instead of 0.25 gives an answer exactly 100 times too big. Convert the percent to a decimal (or a fraction over 100) before it touches any other number.
Using the sale price as the base
A percent off is always a percent of the ORIGINAL price. Taking 25% of the reduced price answers a different question — and it is the most common discount error in homework. The base is the price before the change.
Adding percents with different wholes
20% off and then 10% off is not 30% off: the second discount applies to the already-reduced price, so the total saving is 28%. Percents only add when they share the same whole.
Percent Problems — questions
What is the percent formula?
part = percent × whole, with the percent written as a decimal (25% = 0.25). That one relationship rearranges into all three question types: find the part by multiplying, find the percent by dividing part by whole and multiplying by 100, and find the whole by dividing the part by the decimal percent.
How do you find what percent one number is of another?
Divide the part by the whole, then multiply by 100. For example, 18 out of 60 is 18 ÷ 60 = 0.3, which is 30%. The solver shows that division in Stage 2 and then checks it by taking 30% of 60 and getting 18 back.
What is the difference between a discount problem and a tax problem?
Only the direction. A discount subtracts the percent-part from the price (you pay less); tax adds it (you pay more). The percent calculation is identical — the solver keeps the two stories on separate tabs so the direction is never ambiguous.
Can a percent be more than 100%?
Yes — whenever the part is bigger than the whole. If a value grows from 20 to 30, the new value is 150% of the old one. Percents above 100% are normal in growth and comparison problems, and the solver handles them the same way.
How are the answers verified?
By working backwards from the story’s own numbers: for a part problem, the answer is re-expressed as a percent of the whole and must return the stated percent; for discount and tax, the saved/tax amount and the final price must add (or subtract) back to the original price exactly.
Is this solver free?
Yes — free, no sign-up, no app, with the full staged solution and backwards verification included.
Keep solving
Mixture Problems →
Percent mixtures: two solutions, one target strength, two equations.
Word Problems Hub →
The staged method explained, plus every word-problem family we cover.
Fraction Calculator →
Percents are fractions with denominator 100 — the fraction family handles the arithmetic underneath.
Equation Solver →
Already have the equation? Solve it directly, with plug-back proof.
A note on honest use: VerifySolve is built for learning. Use the steps to understand the method, then close the tab and try one on your own — that is where the grade actually comes from. If your teacher or school has a policy on calculators, follow it.