1. Percent Chapter Seven

2. Percents, Decimals, and Fractions Section 7.1

3. 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. Understanding Percent 1%   0.01 3 Martin-Gay, Prealgebra, 5ed

4. Writing 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 decimal equivalent, ; then multiply. Replace the percent symbol with its decimal equivalent, 0.01; then multiply. 4 Martin-Gay, Prealgebra, 5ed

5. 0.65  0.65(100%)  65.% or 65% Writing a Decimal as a Percent Multiply by 1 in the form of 100%. 5 Martin-Gay, Prealgebra, 5ed

6. 43%  43  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. 6 Martin-Gay, Prealgebra, 5ed

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

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

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

10. Learning objectives  Understand percents  Write percents as decimals or fractions  Write decimals or fractions as percents

11. Solving Percent Problems with Equations Section 7.2

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

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

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

15. 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. 15 Martin-Gay, Prealgebra, 5ed

16. Helpful Hint Use the following to see if your answers 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

17. Solving Percent Problems with Proportions Section 7.3

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

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

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

21. 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. 21 Martin-Gay, Prealgebra, 5ed

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

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

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

25. What percent of 40 is 8? amountpercentbase amount base percent Solving Percent Proportions for the Percent Helpful Hint Recall from our percent proportion that this number, p already is a percent. Just keep the number the same and attach a % symbol. 25

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