Lesson 4 of 5 | Reasoning and Mental Ability / Percentage of a whole
A percentage of a whole
Learning outcome
When the whole and the percentage are known, you can find the part.
Concepts and why
The part is the whole multiplied by the percentage, then divided by 100. Percent means per hundred. 18 percent of 250 is 250 times 18, divided by 100. Dividing the whole by the percentage is a different operation. 20 percent of 80 is not 80 divided by 20.
Worked examples
18 percent of 250 = 250 x 18 / 100 = 45. 6 percent of 450 = 450 x 6 / 100 = 27. 20 percent of 80 = 16. It is not 80 / 20, which is 4.
Common mistakes
Dividing the whole by the percentage. Moving the decimal the wrong way: 15 percent of 80 is 12, not 120. Treating the percentage as the part. If the question asks for 25 percent of 64, the answer is 16, not 25.
Practice questions
- What is 15 percent of 80?
- What is 12 percent of 150?
- What is 25 percent of 64?
- What is 5 percent of 80?
Answers and explanations
- 12. 80 x 15 / 100 = 12.
- 18. 150 x 12 / 100 = 18.
- 16. 64 x 25 / 100 = 16.
- 4. 80 x 5 / 100 = 4.
Analogy
A basket of 100 mangoes gives 18 mangoes when the rate is 18 percent. A basket of 250 mangoes is two and a half such baskets, so the part is 45.
Quick reference
Part = whole x percentage / 100. 18 percent of 250 is 45. Do not divide the whole by the percentage.