Title Rate, Base, Percentage 265.5 KB 6
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Identifying Rate, Base,
and Amount

6.3

489

6.3 OBJECTIVES

1. Identify the rate in an application problem
2. Identify the base in an application problem
3. Identify the amount in an application problem

There are many practical applications of our work with percents. All these problems have
three basic parts that need to be identified. Let’s look at some definitions that will help with
that process.

Let’s look at some examples of determining the parts of a percent problem.

The base (B) is the whole, or 100%, in the problem. The base will often follow the word
“of.” Look at our next example.

Example 1

Identifying Rates

Identify each rate.

(a) What is of 200?

R%

(b) of what number is 50?

R%

(c) 20 is of 40?

R% Here the rate is unknown.

what percent

25% is the rate.

25%

Here 15% is the rate because it
has the percent symbol attached.

15%

C H E C K Y O U R S E L F 1

Identify the rate.

(a) 15% of what number is 75? (b) What is 8.5% of 200?

(c) 200 is what percent of 500?

The base is the whole in a problem. It is the standard used for comparison.

The amount is the part of the whole being compared to the base.

The rate is the ratio of the amount to the base. It is written as a percent.

Definitions: Base, Amount, and Rate

NOTE The rate (which we will
label R%) is the easiest of the
terms to identify. The rate is
written with the percent
symbol (%) or the word
“percent.”

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Exercises

Identify the rate, base, and amount in each statement or question. Do not solve the
exercise at this point.

1. of is . 2. is of .

3. of is . 4. is of .

5. is of ? 6. is of ?

7. of is ? 8. of is ?

9. is of ? 10. is of ?

11. of is ? 12. is of ?

Identify the rate, base, and amount in the following applications. Do not solve the
applications at this point.

13. Commission. Jan has a commission rate on all her sales. If she sells
worth of merchandise in 1 month, will she earn?

14. Salary. of Shirley’s monthly salary is deducted for withholding. If those
deductions total , what is ?

15. Chemistry. In a chemistry class of students, received a grade of A.
of the students received A’s?What percent

5 30

her salary\$209
22%

what commission\$40,000
5%

what number75%15040120What percent

25060%Whatwhat number60%480

30150What percent56what number16%

400what percent803257%What

50040%20024060040%

75020%1509240023%

6.3

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