Percent of a quantity is one of 2 percent formulas in the arithmetic section of this library, and it is used at middle school level.
Why percent of a quantity works
Percent means out of a hundred, so 15 percent is the fraction 15/100. Turning it into the decimal 0.15 and multiplying takes that share of whatever you point it at. The whole quantity acts as the 100 percent, and the multiplication scales it down to the slice you asked for.
What each symbol means
$p$ is the percent, part is the selected amount, and whole is the reference amount.
Percent of a quantity: when it holds
The whole must represent the same unit and reference group as the part.
When it stops applying
Two percents in a row do not simply add, because the second one is taken from a new whole. Half off followed by 20 percent off leaves 40 dollars from 100, which is 60 percent off in total, not the 70 percent you would get by adding.
Percent of a quantity: a worked example
$15\%$ of $80$ is $0.15(80)=12$.
The mistake to avoid
What people do: Students multiply by the percent number itself and calculate 15 times 80.
Why it goes wrong: That gives 1200, which is fifteen times the whole amount rather than a small part of it. A percent under 100 must always shrink the number.
Do this instead: Move the decimal point two places left before multiplying: 15 percent becomes 0.15, and 0.15 times 80 is 12. Since 10 percent of 80 is 8, an answer near 12 makes sense while 1200 clearly does not.
Percent of a quantity: step by step
- Name the unknown, and the unit the answer has to come out in.
- Match the symbols to your values. $p$ is the percent, part is the selected amount, and whole is the reference amount.
- Check the conditions before substituting. The whole must represent the same unit and reference group as the part.
- Substitute, keep exact values to the last line, then test the sign, size, and unit against a rough estimate — the check that catches most arithmetic slips.
Where this formula fits
- Subject
- Arithmetic formulas — 13 entries in this library
- Topic
- Percent
- Level
- Middle school
Formulas are easiest to keep when they sit inside a method rather than on a list. Use the links below to see where percent of a quantity comes from, to check a calculation against a tool, and to practise it until you can recall it without looking.
- Understanding Percentages — the lesson behind this formula: translate among percentages, decimals, and proportions.
- Arithmetic Calculator — check your substitution and the value it produces.
- Study arithmetic — the subject guide that explains the ideas these formulas compress.
- Arithmetic Practice — questions that make you retrieve the formula instead of recognising it.
- All 13 arithmetic formulas — the full grouped reference, or the complete formula library.
Questions about percent of a quantity
How do I turn a percent into a decimal?
Divide by 100, which just moves the decimal point two places to the left. So 7 percent is 0.07, 42 percent is 0.42, and 250 percent is 2.5.
What if the percent is more than 100?
Then the answer is bigger than the whole, which is fine. 150 percent of 80 is 1.5 times 80, or 120, and that is exactly how a price rise of more than double gets described.
How do I find the whole when I know the part and the percent?
Divide instead of multiplying. If 12 is 15 percent of something, then that something is 12 divided by 0.15, which is 80.
Does the word of always mean multiply?
In percent questions it does. Reading 15 percent of 80 as 0.15 times 80 turns the sentence straight into a calculation, and the same trick works for a fraction of an amount too.