**Three Types of Percent Problems**

There are three basic types of percent problems, and there are several different methods that can be used to solve these problems. The circle method will be used in this chapter. The equation method will be used in the next chapter, and finally, the proportion method will be used in Chapter 8 . A percent problem has three values: the base (B) or whole, the rate (R) or percent, and the part (P). For example, if a class consisted of 20 students, 5 of whom were absent today, the base or whole would be 20, the part would be 5, and the rate or percent of students who were absent would be = 25%.

Draw a circle and place a horizontal line through the center and a vertical line halfway down in the center also. In the top section, write the word "is." In the lower left section write the % sign, and in the lower right section write the word "of." In the top section place the part (P). In the lower left section place the rate (R) or percent number, and in the lower right section place the base (B). One of these three quantities will be unknown (see Fig. 6-2).

*If you are given the two bottom numbers, multiply them to get the top number: i.e., P = R × B. If you are given the top number and one of the bottom numbers, divide to find the other number: i.e.,* *or* (see Fig-6-3)

**Type 1: Finding the Part**

Type 1 problems can be stated as follows:

- "Find 20% of 60."
- "What is 20% of 60?"
- "20% of 60 is what number?"

In Type 1 problems, you are given the base and the rate and are asked to find the part. From the circle: P = R × B. Here, then, you change the percent to a decimal or fraction and multiply.

**Examples**

**Example 1**

Find 40% of 80.

**Solution 1**

Draw the circle and put 40% in the % section and 80 in the "of " section (see Fig. 6-4 ).

Change the percent to a decimal and multiply: 0.40 × 80 = 32.

**Example 2**

Find 25% of 60.

**Solution 2**

Draw the circle and put 25 in the % section and 60 in the "of" section (see Fig. 6-5 ).

Change 25% to a decimal and multiply: 0.25 × 60 = 15.

**Math Note:** Always change the percent to a decimal or fraction before multiplying or dividing.

Find practice problems and solutions at Percent Practice Problems - Set 1.

**Type 2: Finding the Rate**

Type 2 problems can be stated as follows:

- "What percent of 16 is 10?"
- "10 is what percent of 16?"

In type 2 problems, you are given the base and the part and are asked to find the rate or percent. The formula is In this case, divide the part by the base and then change the answer to a percent (see Fig. 6-6).

**Examples**

**Example 1**

What percent of 5 is 2?

**Solution 1**

Draw the circle and place 5 in the "of" section and 2 in the "is" section (see Fig. 6-7 ).

Then divide Change the decimal to a percent: 0.40 = 40%.

**Example 2**

45 is what percent of 60?

**Solution 2**

Draw the circle and put 45 in the "is" section and 60 in the "of" section (see Fig. 6-8 ).

Then divide Change the decimal to a percent: 0.75 = 75%.

Find practice problems and solutions at Percent Practice Problems - Set 2.

**Type 3: Finding the Base**

Type 3 problems can be stated as follows:

- "16 is 20% of what number?"
- "20% of what number is 16?"

In type 3 problems, you are given the rate and the part, and you are asked to find the base. From the circle: B = (see Fig. 6-9).

**Examples**

**Example 1**

42% of what number is 294?

**Solution 1**

Draw the circle and place 42 in the percent section and 294 in the "is" section (see Fig. 6-10 ).

Change 42% to 0.42 and divide: 294 ÷ 0.42 = 700.

**Example 2**

36 is 80% of what number?

**Solution 2**

Draw the circle and place 36 in the "is" section and 80 in the percent section (see Fig. 6-11 ).

Change 80% to 0.80 and divide: 36 ÷ 0.80 = 45.

Find practice problems and solutions at Percent Practice Problems - Set 3.

More practice problems for these concepts can be found at: Percent Practice Test.

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