Chapter Seven Percent Section 7 1 Percents Decimals

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Chapter Seven Percent

Chapter Seven Percent

Section 7. 1 Percents, Decimals, and Fractions

Section 7. 1 Percents, Decimals, and Fractions

Understanding Percent The word percent comes from the Latin phrase per centum, which means

Understanding Percent The word percent comes from the Latin phrase per centum, which means “per 100. ” Percent means per one hundred. The “%” symbol is used to denote percent. Martin-Gay, Prealgebra, 5 ed 3

Writing a Percent as a Decimal Replace the percent symbol with its decimal equivalent,

Writing a Percent as a Decimal Replace the percent symbol with its decimal equivalent, 0. 01; then multiply. 43% 43(0. 01) 0. 43 100% 100(0. 01) 1. 00 or 1 Martin-Gay, Prealgebra, 5 ed 4

Writing a Decimal as a Percent Multiply by 1 in the form of 100%.

Writing a Decimal as a Percent Multiply by 1 in the form of 100%. 0. 65(100%) 65. % or 65% Martin-Gay, Prealgebra, 5 ed 5

Writing a Percent as a Fraction Replace the percent symbol with its fraction equivalent,

Writing a Percent as a Fraction Replace the percent symbol with its fraction equivalent, ; then multiply. Don’t forget to simplify the fraction, if possible. 43% 43 Martin-Gay, Prealgebra, 5 ed 6

Writing a Fraction as a Percent Multiply by 1 in the form of 100%.

Writing a Fraction as a Percent Multiply by 1 in the form of 100%. Martin-Gay, Prealgebra, 5 ed 7

Helpful Hint We know that 100% = 1 Recall that when we multiply a

Helpful Hint 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. Martin-Gay, Prealgebra, 5 ed 8

Summary of Converting Percents, Decimals, and Fractions To write a percent as a decimal,

Summary of Converting Percents, Decimals, and Fractions To write a percent as a decimal, replace the % symbol with its decimal equivalent, 0. 01; then multiply. To write a decimal or fraction as a percent, multiply by 100%. Martin-Gay, Prealgebra, 5 ed 9

Learning objectives Understand percents Write percents as decimals or fractions Write decimals or fractions

Learning objectives Understand percents Write percents as decimals or fractions Write decimals or fractions as percents

Section 7. 2 Solving Percent Problems with Equations

Section 7. 2 Solving Percent Problems with Equations

Key Words of means multiplication ( ) is means equals ( ( ) what

Key Words of means multiplication ( ) is means equals ( ( ) what (or some equivalent) means the unknown number Let x stand for the unknown number. Martin-Gay, Prealgebra, 5 ed 12

Helpful Hint Remember that an equation is simply a mathematical statement that contains an

Helpful Hint Remember that an equation is simply a mathematical statement that contains an equal sign ( ( ). 6 18 x equal sign Martin-Gay, Prealgebra, 5 ed 13

Solving Percent Problems 20% of 50 10 20% percent • 50 10 base amount

Solving Percent Problems 20% of 50 10 20% percent • 50 10 base amount Percent Equation percent • base amount Martin-Gay, Prealgebra, 5 ed 14

Helpful Hint When solving a percent equation, write the percent as a decimal or

Helpful Hint When solving a percent equation, write the percent as a decimal or fraction. If your unknown in the percent equation is percent, don’t forget to convert your answer to a percent. Martin-Gay, Prealgebra, 5 ed 15

Helpful Hint Use the following to see if your answers are reasonable. 100% of

Helpful Hint Use the following to see if your answers are reasonable. 100% of a number the number a number larger than the original number a number less than the original number 16

Section 7. 3 Solving Percent Problems with Proportions

Section 7. 3 Solving Percent Problems with Proportions

Writing Percent Problems as Proportions To understand the proportion method, recall that 30% means

Writing Percent Problems as Proportions To understand the proportion method, recall that 30% means the ratio of 30 to 100, or 30% . Martin-Gay, Prealgebra, 5 ed 18

Writing Percent Problems as Proportions. . . Since the ratio is equal to the

Writing Percent Problems as Proportions. . . Since the ratio is equal to the , we have the proportion , called the percent proportion. Martin-Gay, Prealgebra, 5 ed 19

Percent Proportion always 100 or amount base percent Martin-Gay, Prealgebra, 5 ed 20

Percent Proportion always 100 or amount base percent Martin-Gay, Prealgebra, 5 ed 20

When we translate percent problems to proportions, the percent can be identified by looking

When we translate percent problems to proportions, the percent can be identified by looking for the symbol % or the word percent. The base usually follows the word of. The amount is the part compared to the whole. Martin-Gay, Prealgebra, 5 ed 21

Helpful Hint Part of Proportion How It’s Identified Percent % or percent Base Appears

Helpful Hint Part of Proportion How It’s Identified Percent % or percent Base Appears after of Amount Part compared to whole Martin-Gay, Prealgebra, 5 ed 22

Solving Percent Proportions for the Amount What number is 20% of 8? amount percent

Solving Percent Proportions for the Amount What number is 20% of 8? amount percent base amount base percent Martin-Gay, Prealgebra, 5 ed 23

Solving Percent Proportions for the Base 20 is 40% of what number? amount percent

Solving Percent Proportions for the Base 20 is 40% of what number? amount percent base amount base percent Martin-Gay, Prealgebra, 5 ed 24

Solving Percent Proportions for the Percent What percent of 40 is 8? percent amount

Solving Percent Proportions for the Percent What percent of 40 is 8? percent amount base amount percent 25

Helpful Hint A ratio in a proportion may be simplified before solving the proportion.

Helpful Hint A ratio in a proportion may be simplified before solving the proportion. The unknown number in both and is 20. Martin-Gay, Prealgebra, 5 ed 26