These questions give a whole amount and ask for a percentage share of it. Your first job is to keep the whole as the base and turn the percentage into a multiplier.
Multiply the base by the rate
Translate the wording directly: p% of N means (p / 100) x N. The word of signals multiplication, and N is the whole amount being split. For example, 18% of 350 is 0.18 x 350 = 63. This route works for whole-number, decimal and greater-than-100 percentages.
Mental anchors can make the same calculation quicker. Ten per cent is one tenth of the base, 5% is half of 10%, 1% is one hundredth, and 2.5% is half of 5%. Split a rate into useful anchors and add the resulting parts. For example, 12.5% of 480 is 10% + 2.5%, giving 48 + 12 = 60.
| Signal | Form to use | Check |
|---|---|---|
| p% of a stated whole | Whole x p / 100 | If p is between 0 and 100, the result lies between zero and the whole. |
| A composite rate | Find convenient percentage parts of the same whole, then add them. | The split rates must add back to the stated rate. |
| A rate above 100% | Use the full decimal multiplier greater than 1. | The result must be greater than the whole; do not calculate only the extra part. |
Estimate before calculating. A rate near 50% should give about half the base, a rate near 1% should give about one hundredth, and a rate above 100% should give more than the base. The estimate catches an incorrect multiplier even when the arithmetic itself is neat.
Avoid these percent-of-amount traps
| Tempting route | How to reject it |
|---|---|
| Divide the whole by the percentage number or its decimal form. | The task asks for a proportional part, so multiply the whole by p/100. Division answers a different reverse problem and can even produce more than the whole for a small rate. |
| Add or subtract the printed percentage number as though it were an amount. | A percentage has no amount unit until it is applied to the base. Convert it to a multiplier before combining anything with the whole. |
| Use a decimal that is ten or one hundred times too large or too small. | Write p/100 explicitly. Then compare with a 10%, 1% or 50% estimate to catch a misplaced decimal point. |
| Treat 30% as one third, or treat 5% as though it were 10%. | Friendly fractions are useful only when they are equal to the rate. Thirty per cent is three tenths, while 5% is one twentieth of the base. |
Try it
A concert hall sets aside 17.5% of its 320 seats for a community group. Enter the number of seats set aside.
A bus depot inspects 6% of its 450 tires today. Enter the number of tires inspected.
A machine produces 125% of its usual 64 parts during an extended shift. Enter the number of parts produced.