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Concepts 1 BasicFunctions Copyright © Cengage Learning. All rights reserved. Unit 1C Review of Operations with Decimal Fractions and Percent Copyright © Cengage Learning. All rights reserved. 1.14 Rate, Base, and Part Copyright © Cengage Learning. All rights reserved. Rate, Base, and Part Any percent problem calls for finding one of three things: 1. the rate (percent), 2. the base, or 3. the part. Such problems are solved using one of three percent formulas. In these formulas, we let R = the rate (percent) B = the base P = the part or amount (sometimes called the percentage) 4 Rate, Base, and Part The following may help you identify which letter stands for each given number and the unknown in a problem: 1. The rate, R, usually has either a percent sign (%) or the word percent with it. 2. The base, B, is usually the whole (or entire) amount. The base is often the number that follows the word of. 5 Rate, Base, and Part 3. The part, P, is usually some fractional part of the base, B. If you identify R and B first, then P will be the number that is not R or B. Note: The base and the part should have the same unit(s) of measure. 6 Example 1 Given: 25% of $80 is $20. Identify R, B, and P. R is 25%. 25 is the number with a percent sign. Remember to change 25% to the decimal 0.25 for use in a formula. B is $80. $80 is the whole amount. It also follows the word of. P is $20. $20 is the part. It is also the number that is not R or B. 7 Percent Problems: Finding the Part 8 Percent Problems: Finding the Part After you have determined which two numbers are known, you find the third or unknown number by using one of three formulas. Formulas for Finding Part, Base, and Rate 1. P = BR Use to find the part. 2. B = Use to find the base. 3. R = Use to find the rate or percent. 9 Example 3 Find 75% of 180. R = 75% = 0.75 75 is the number with a percent sign. B = 180 180 is the whole amount and follows the word of. P = the unknown Use Formula 1. P = BR P = (180)(0.75) = 135 10 Percent Problems: Finding the Part The process of finding the percent increase or percent decrease may be summarized by the following formula: 11 Example 12 Normal ac line voltage is 115 volts (V). Find the percent decrease if the line voltage drops to 109 V. (rounded to the nearest tenth of a percent) 12 Percent Problems: Finding the Part The triangle in Figure 1.36 can be used to help you remember the three percent formulas, as follows: 1. P = BR To find the part, cover P; B and R are next to each other on the same line, as in multiplication. 2. B = To find the base, cover B; P is over R, as in division. 3. R = To find the rate, cover R; P is over B, as in division. Figure 1.36 13