Percent Chapter Seven. Percents, Decimals, and Fractions Section 7.1.

PercentPercent

Chapter SevenChapter Seven

Percents, Decimals, and Percents, Decimals, and FractionsFractions

Section 7.1

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.


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%.


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


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%.


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.


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%..


Learning objectives

Understand percents Write percents as decimals or

fractions Write decimals or fractions as

percents

Solving Percent Problems Solving Percent Problems with Equationswith Equations

Section 7.2

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.



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


20% of 50 10

20% • 50 10percent base amount

Percent EquationPercent Equation

percent • base amount

Solving Percent ProblemsSolving Percent Problems



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.



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

Solving Percent Problems Solving Percent Problems with Proportionswith Proportions

Section 7.3

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


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


always 100

or

percent

base

amount

Percent ProportionPercent Proportion

amount percent

base 100

100

a p

b


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.



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


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


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


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


A ratio in a proportion may be simplified A ratio in a proportion may be simplified before solving the proportion. The before solving the proportion. The unknown number in bothunknown number in both

andand

is 20.

6 30

4 b

3 30

2 b


Percent Chapter Seven. Percents, Decimals, and Fractions Section 7.1.

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