Understanding Percent Problems
- the base ( B ) or whole or total amount, a standard used for comparison
- the portion ( P ) or part being compared with the base
- the rate ( R ) or percent, a percent number
Example: What is 20% of 280?
- is indicates the portion (or percent) P to be found.
- % indicate the percent rate R, here R = 30%
- of indicates the base B which is equal to 280.
This third type of percent problem requires that you find the whole (or base) when the portion (or part) and the rate (in percent) are given. Problems of this kind can be worded as:
- 18 is 15% of what number?
- Find a number such that 15% of it is 18.
- 15% of what number is 18?
Finding the base
Finding the base when percent and portion are given is done in 2 steps:
- Change the percent to a decimal
- Divide the portion by this decimal.
15% of what number is 18?
In this problem the percent is the number with the percent symbol (15%). The other number is the portion (18).
- Change the percent into decimal: 15% = 0.15
- Divide the portion by the decimal: 18 ÷ 0.15 = 120
The answer is: 15% of 120 is 18.
Check out the ADVANCED section. The exercises will further your understanding and help with building a bigger mental picture. It builds links between numbers and algebra. It is important to try alternative calculations or approaches, tracking changes to units of measure, visualizing to cross-link the concepts of percentage and numbers. If you spend 20 – 40 min working with the different ideas in the ADVANCED page, you`ll remember key formulas easier and you`ll learn new skills faster.