**Understanding Percent Problems**

All calculations involving percent can fall into one of the three basic types of problems. These three are related to all percent problems that arise in business, technology, or the trades. By learning these three types of problems you will be able to solve any percent problem, and we examine each of the three types of problems. All percent problems involve three quantities:

- 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

**Identify the Parameters:**

To solve any percent problem, you need to identify which of the quantities given in the problem is P, which is B, and which is R. The percent number R is easy to identify because it always has the % symbol attached to it. If you have trouble distinguishing the part P from the base B, notice that B usually follows the word “of” and P usually follows the word “is”.

*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.

**Finding the percent of a number**

Calculating the percent of a number is done in 2 steps:

- Change the rate (percent form) to a decimal and
- Multiply the base amount by this decimal

EXAMPLE

The next three questions are all forms of the same problem. They are all asking you to find the portion P. In fact the percent is given (R = 40%), and the base is known (B = 70). The only unknown information is the portion P.

- What is 40% of 70?
- Find 40% of 70.
- 40% of 70 is what number?

SOLUTION

- Change 40% into decimal:

40% = 0.40 - Multiply the number by the decimal:

70 x 0.40 = 28

State your answer:

**28 represents 40% of 70**