These questions compare one quantity with another and ask for the comparison as a percentage. The calculation is short, but its direction depends on identifying which quantity is being described and which quantity is the base.
Put the described quantity over the base
Translate the phrase a as a percentage of b into a / b x 100. The first quantity, a, is being described. The quantity after of, b, is the comparison base and belongs in the denominator. For example, 33 as a percentage of 60 is 33 / 60 x 100 = 55%.
Use the same order for part-to-whole language such as successes out of attempts: put the successes over the attempts, then multiply by 100. For a target or reference comparison, put the actual amount over the target or reference. If the described quantity is larger than the base, the ratio is above 1 and the percentage must be above 100%. For example, 42 compared with a reference of 35 gives 42 / 35 x 100 = 120%.
| Wording pattern | Ratio before multiplying by 100 |
|---|---|
| a as a percentage of b | a / b |
| part out of whole | part / whole |
| actual as a percentage of target | actual / target |
Make a size prediction before dividing. A part smaller than its whole gives less than 100%. Equal quantities give 100%. A described amount larger than its base gives more than 100%. This check will often reveal a reversed ratio immediately.
Avoid these comparison traps
| Tempting route | How to reject it |
|---|---|
| Reverse the ratio and divide the base by the described quantity. | Say the comparison aloud: a as a percentage of b. Write a first and b after the division sign. The reverse ratio answers b as a percentage of a instead. |
| Report only the percentage above or below the base. | This topic asks for the described quantity's full percentage of the base. The amount of increase or decrease is a separate calculation. |
| Subtract the two quantities and use that raw difference as the percentage. | A difference still has the original unit. To form a percentage comparison, divide the described quantity by the stated base and multiply by 100. |
| Choose the denominator by whichever number looks like a convenient whole. | Grammar, not convenience, identifies the base. Find the quantity after of, or the total, target or reference named by the comparison. |
Try it
A greenhouse has 18 flowering plants among 45 plants. What percentage are flowering? Enter the number of percent.
A solar panel supplies 15 kilowatt-hours against a 12 kilowatt-hour target. What percentage of the target is supplied? Enter the number of percent.
A football team scores on 14 of 20 penalty attempts. What is its scoring percentage? Enter the number of percent.