# Chapter Seven Percent Section 7 1 Percents Decimals

- Slides: 26

Chapter Seven Percent

Section 7. 1 Percents, Decimals, and Fractions

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, 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%. 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, ; 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%. Martin-Gay, Prealgebra, 5 ed 7

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, 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 as percents

Section 7. 2 Solving Percent Problems with Equations

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 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 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 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 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

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 , 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

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 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 base amount base percent Martin-Gay, Prealgebra, 5 ed 23

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 base amount percent 25

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

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- Round off 56