The whole from a known percentage

Learning outcome

When a part and its percentage are known, you can recover the whole.

Concepts and why

The whole is the part multiplied by 100, then divided by the percentage. This is the reverse of finding a percentage of a whole. There, you multiply by the percentage and divide by 100. Here, you multiply by 100 and divide by the percentage. If 36 is 20 percent of a number, the number is 36 times 100, divided by 20.

Worked examples

36 is 20 percent of 180, because 36 x 100 / 20 = 180. 24 is 40 percent of 60, because 24 x 100 / 40 = 60. The wrong turn, 36 x 20 / 100, gives 7.2. That finds a percentage of 36. It does not recover the whole.

Common mistakes

Multiplying the part by the percentage and dividing by 100. That shrinks the part again. Dividing the part by the percentage with no 100. 36 divided by 20 is 1.8, not the whole.

Practice questions

1. 15 is 25 percent of which number?
2. 48 is 60 percent of which number?
3. 18 is 30 percent of which number?
4. 24 is 40 percent of which number?

Answers and explanations

1. 60. 15 x 100 / 25 = 60.
2. 80. 48 x 100 / 60 = 80.
3. 60. 18 x 100 / 30 = 60.
4. 60. 24 x 100 / 40 = 60.

Analogy

If 20 mangoes are one fifth of a basket, the basket is five times 20, which is 100. You scale up from the part to the whole. You do not take one fifth of the 20 mangoes again.

Quick reference

Whole = part x 100 / percentage. 36 is 20 percent of 180. Do not multiply the part by the percentage and divide by 100.