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The word The word percentpercent comes from the Latin comes from the Latin phrase phrase per centumper centum, which means , which means “per“per 100.”100.”
PercentPercent means means per one hundredper one hundred. The “%” . The “%” symbol is used to denote percent.symbol is used to denote percent.
Understanding PercentUnderstanding Percent
1% 0.011
100
3Martin-Gay, Prealgebra, 5ed
Writing a Percent as a DecimalWriting a Percent as a Decimal
43% 43(0.01) 0.43
100% 100(0.01) 1.00 or 1
Replace the percent symbol with its Replace the percent symbol with its decimal equivalent, decimal equivalent, 0.01; then multiply.; then multiply.
4Martin-Gay, Prealgebra, 5ed
0.65 0.65(100%) 65.% or 65%
Writing a Decimal as a PercentWriting a Decimal as a Percent
Multiply by 1 in the form of 100%.Multiply by 1 in the form of 100%.
5Martin-Gay, Prealgebra, 5ed
43% 43 43
100
Writing a Percent as a FractionWriting a Percent as a Fraction
1
100
Replace the percent symbol with its Replace the percent symbol with its fraction equivalent, ; thenfraction equivalent, ; then
multiply. Don’t forget to simplify the multiply. Don’t forget to simplify the fraction, if possible.fraction, if possible.
1
100
6Martin-Gay, Prealgebra, 5ed
Writing a Fraction as a PercentWriting a Fraction as a Percent
•3 3
5 5 100% •
3 100%
5 1
300%
560%
Multiply by 1 in the form of 100%.Multiply by 1 in the form of 100%.
7Martin-Gay, Prealgebra, 5ed
Helpful HintHelpful Hint
We know that We know that
100% = 1
Recall that when we multiply a number by 1, we are not changing the value of that number.
Therefore, when we multiply a number by 100%, we are not changing its value but rather writing the number as an equivalent percent.
8Martin-Gay, Prealgebra, 5ed
To write a percent as a fractionTo write a percent as a fraction, replace the , replace the % symbol with its fraction equivalent, ; % symbol with its fraction equivalent, ; then multiply.then multiply.
1
100
Summary of Converting Percents, Summary of Converting Percents, Decimals, and FractionsDecimals, and Fractions
To write a percent as a decimalTo write a percent as a decimal, replace the , replace the % symbol with its decimal equivalent, % symbol with its decimal equivalent, 0.01; ; then multiply.then multiply.
To write a decimal or fraction as a percentTo write a decimal or fraction as a percent, , multiply by multiply by 100%..
9Martin-Gay, Prealgebra, 5ed
Learning objectives
Understand percents Write percents as decimals or
fractions Write decimals or fractions as
percents
Key WordsKey Words
ofof means means multiplicationmultiplication ( ())
isis means means equalsequals ( ())
whatwhat (or some equivalent) means the (or some equivalent) means the unknown numberunknown number
Let Let xx stand for the unknown number. stand for the unknown number.
12Martin-Gay, Prealgebra, 5ed
Helpful HintHelpful Hint
Remember that an equation is simply a Remember that an equation is simply a mathematical statement that contains an mathematical statement that contains an equal sign (equal sign ().).
6 18x
equal sign
13Martin-Gay, Prealgebra, 5ed
20% of 50 10
20% • 50 10percent base amount
Percent EquationPercent Equation
percent • base amount
Solving Percent ProblemsSolving Percent Problems
14Martin-Gay, Prealgebra, 5ed
Helpful HintHelpful Hint
When solving a percent equation, write the When solving a percent equation, write the percent as a decimal or fraction.percent as a decimal or fraction.
If your unknown in the percent equation is If your unknown in the percent equation is percent, don’t forget to convert your percent, don’t forget to convert your answer to a percent.answer to a percent.
15Martin-Gay, Prealgebra, 5ed
Helpful HintHelpful Hint
Use the following to see if your answers Use the following to see if your answers are reasonable.are reasonable.
a percent greater than 100%
a percent less than 100%
a number larger than the original number
a number less than the original number
100% of a number the number
16
To understand the proportion To understand the proportion method, recall that 30% means themethod, recall that 30% means the
ratio of 30 to 100, or .ratio of 30 to 100, or .
30%
Writing Percent Problems as Writing Percent Problems as ProportionsProportions
30
100
30
100
3
10
18Martin-Gay, Prealgebra, 5ed
Since the ratio is equal to theSince the ratio is equal to the
ratio , we have the proportionratio , we have the proportion
called the called the percent proportionpercent proportion..
Writing Percent Problems as Writing Percent Problems as Proportions . . .Proportions . . .
,,
30
1003
1030 3
100 10
19Martin-Gay, Prealgebra, 5ed
always 100
or
percent
base
amount
Percent ProportionPercent Proportion
amount percent
base 100
100
a p
b
20Martin-Gay, Prealgebra, 5ed
When we translate percent problems to When we translate percent problems to proportions, the proportions, the percentpercent can be can be identified by looking for the symbol % identified by looking for the symbol % or the word or the word percentpercent. The . The basebase usually usually follows the word follows the word ofof. The . The amountamount is the is the part compared to the whole.part compared to the whole.
21Martin-Gay, Prealgebra, 5ed
Helpful HintHelpful Hint
Part of Part of ProportionProportion
How It’s How It’s IdentifiedIdentified
Percent Percent % or percent% or percent
Base Base
Amount Amount
Appears after Appears after of of
Part compared to Part compared to whole whole
22Martin-Gay, Prealgebra, 5ed
What number is 20% of 8?
amount percent base
amountbase
percent
Solving Percent Proportions for Solving Percent Proportions for the Amountthe Amount
20
8 100
a
23Martin-Gay, Prealgebra, 5ed
20 is 40% of what number?
amount percent base
amountbase
percent
Solving Percent Proportions for Solving Percent Proportions for the Basethe Base
20 40
100b
24Martin-Gay, Prealgebra, 5ed
What percent of 40 is 8?
amountpercent base
amountbase
percent
Solving Percent Proportions for Solving Percent Proportions for the Percentthe Percent
8
40 100
p
Helpful HintHelpful HintRecall from our percent proportion that this number, p already is a percent. Just keep the number the same and attach a % symbol. 25