Concepts
1 BasicFunctions
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Unit 1C
Review of Operations with
Decimal Fractions and Percent
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1.14
Rate, Base, and Part
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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)
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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.
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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.
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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.
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Percent Problems: Finding the Part
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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.
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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
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Percent Problems: Finding the Part
The process of finding the percent increase or percent
decrease may be summarized by the following formula:
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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)
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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
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