How can I find what percentage one amount is of another?
Quick answer
Identify which amount is the part and which is the whole, or base. Divide the part by the whole, then multiply the quotient by 100 and add the percent sign. For example, 18 out of 60 is 18 ÷ 60 = 0.3, so it is 30%. Check that you used the total you actually mean by “the whole.” [S1]
The question, the details, the next step.
How do I work out what percentage one amount is of another? I know I should divide, but I get mixed up about which amount goes on top.
First identify the roles: the part is the amount you are asking about; the whole is the total it belongs to. Divide the part by the whole, then multiply by 100 to express the answer as a percentage. In symbols: part ÷ whole × 100 = percentage. A percent expresses a number per 100, and the total is the base for finding the part’s percentage. [S1]
For example, suppose a group has 60 people and 18 are attending a workshop. The part is 18 attendees; the whole is 60 people. Calculate 18 ÷ 60 = 0.3, then 0.3 × 100 = 30. So 18 is 30% of 60.
What if the question says, “What percentage is 18 of 60?” How can I be sure 60 is the whole?
Ask, “18 is what fraction of which total?” In “18 of 60,” 60 is the reference total, so it is the whole; 18 is the part being compared with it. You can write the relationship before calculating: 18 ÷ 60 = 0.3. Since a percentage is per 100, convert 0.3 to 30 per 100: 30%. [S1]
If the wording gives several possible totals, use the one the question asks you to compare against. For instance, if 18 people out of 60 attendees chose an option, the percentage of attendees is 18 ÷ 60. Don’t silently substitute a different group total.
Could I instead do 60 divided by 18 and turn that into a percentage?
That reverses the comparison. Here, 18 is the part and 60 is the whole, so use 18 ÷ 60. Reversing it gives 60 ÷ 18, which answers a different question: how many times 18 fits into 60. It does not tell you what percentage 18 is of 60.
A useful check is to estimate first: 18 is less than half of 60, so its percentage should be below 50%. The calculated answer, 30%, fits that check. If the part equals the whole, the answer is 100%; if the part is greater than the whole, a result above 100% can make sense. The calculation alone does not decide which total a word problem intends—you must identify that from its wording.
Can you give me a short format I can use for a new problem, including what to do if I’m unsure about the total?
Use this copyable setup, filling in the labels before doing the arithmetic:
Part: [amount being compared] Whole/base: [total it is being compared with] Calculation: [part] ÷ [whole] × 100 = [percentage]%
Worked example: Part: 18 attendees. Whole/base: 60 people in the group. Calculation: 18 ÷ 60 × 100 = 30%.
If you cannot confidently name the whole, pause and reread the question: “Percentage of what?” The answer should be the total that the part is being compared with. A different whole can give a different percentage, so write the chosen total beside the calculation rather than leaving it implicit.
A practical checklist
Name the amount being asked about as the part.
State the comparison total as the whole or base.
Write part ÷ whole before calculating.
Multiply the quotient by 100 and attach the % sign.
Check that the chosen whole matches the question and that the result is plausible.
A few more useful answers
How do I convert the division result to a percentage?
Divide the part by the whole, then multiply the quotient by 100 and express the result with a percent sign. For example, 18 ÷ 60 = 0.3, and 0.3 × 100 = 30%, so 18 is 30% of 60. [S1]
Can the percentage be more than 100%?
Yes. If the part is greater than the chosen whole, dividing the part by the whole gives a quotient greater than 1, so the percentage is greater than 100%. First make sure that the comparison total is really the whole intended by the question.
Why do I get a different answer when I swap the amounts?
The order matters: part ÷ whole answers what percentage the part is of the whole. Swapping them changes the comparison and answers a different question. [S1]
Sources
References used for this guide.
- [S1] 6.1 Understanding Percent — Contemporary Mathematics openstax.org · Checked