Percents

1. Percents Pages 96 – 122

2. Page 98 Understanding Percents • A percent shows a part of a whole. • Remember • Fractions: the denominator tells how many parts a whole is divided into. Any whole number except for zero can be a denominator. • Decimals: a whole is divided into tenths, hundredths, thousandths, & so on. • Percent: the whole is always divided into 100 parts. The word percent means “by the hundred or per one hundred.” Percent is shown with the sign %.

3. Page 98 Example • Fill in the blank • Percent means that a whole has been divided into ___________ equal parts. • 49¢ is 49/100 of a dollar or __________% of a dollar. • 75% of something means 75 of the _________ equal parts of something.

4. Page 98 Group Work • Fill in the blank • If every registered student attends a night class, you can say that ______% of the students are there. • If Gloria gets every problem right on a math quiz, you can say she got ______% of the problems right • If Bernard gets only half of the problems right on the math quiz, you can say that he got ______% of the problems right.

5. Page 99 Changing Decimals to Percents • Percent is similar to a two-place decimal. • To change a decimal to a percent, move the decimal point two places to the right & write the percent sign (%). • If the decimal point moves to the end of the number, it is not necessary to write it. • You may have to add zeros.

6. Page 99 Example • Write each decimal as a percent • 0.32 • 0.005 • 0.125

7. Page 99 Group Work • Write each decimal as a percent • 0.09 • 0.0375 • 0.2

8. Page 100 Changing Percents to Decimals • To change a percent to a decimal, drop the percent sign (%) & move the decimal point two places to the left. • You may have to add zeros.

9. Page 100 Example • Write each percent as a decimal. • 62 ½% • 7% • 200%

10. Page 100 Group Work • Write each percent as a decimal. • 6 2/3% • 1.5% • 8%

11. Page 101 Changing Fractions to Percents • There are two ways to change a fraction to a percent: • Method 1: Multiply fraction by 100% • Method 2: Divide the denominator of the fraction into the numerator & move the point two places to the right.

12. Page 101 Example 1 4 25 • Write each fraction as a percent. 2 1 6 3 3 7

13. Page 101 Group Work 1 3 10 • Write each fraction as a percent. 2 4 5 3 1 8

14. Page 102 Changing Percents to Fractions • To change a percent to a fraction, write the percent as a fraction with 100 as the denominator & reduce.

15. Page 102 Example • Write each percent as a common fraction. • 8 1/3% • 4% • 80%

16. Page 102 Group Work • Write each percent as a common fraction. • 66 2/3% • 12% • 90%

17. Pages 104 – 105 Finding a Percent of a Number • To find a percent of a number, change the percent • Method 1: to a decimal or • Method 2:to a fraction • & multiply. • If you want to multiply by a complex percent like 16 ⅔%, it is easiest to change the percent to the fraction that it is equal to & then multiply. • If you don’t know the fraction value of a complex percent, multiply by the improper fraction form of the percent, & put the other number over 100.

18. Pages 104 – 105 Example • Use the method that you find easier to solve the following: • 1.8% of 753 • 0.8% of 56 • 62 ½% of 176

19. Pages 104 – 105 Group Work • Use the method that you find easier to solve the following: • 2.6% of 390 • 1 ½% of 200 • 50% of 418

20. Page 108 Solving Two-Step Problems • Many applications of finding a percent of a number require two steps. • find the percent of a the number. • add it to or subtract it from the original number

21. Page 108 Example • Read each problem carefully to decide whether to add or subtract in the second step • A computer that sold for $1,200 last year is now on sale for 15% less. What is the price of the computer this year? • Elizabeth earns $576 each week. If she gets an 8% raise, how much will she take home each week?

22. Page 108 Group Work • Read each problem carefully to decide whether to add or subtract in the second step • A jacket originally selling for $48 was on sale at 20% off. Find the sale price of the jacket. • For lunch Brain bought a sandwich for $2.50. The sale tax where Brain lives is 6%. What was the price of the sandwich including sales tax? • Paul’s part-time job earns him $360 each week. His employer withholds 18% of Paul’s pay for taxes & social security. How much does Paul take home each week?

23. Pages 110 – 111 Finding What Percent One Number is of Another • To find what percent one number is of another, make a fraction by putting the part (usually the smaller number) over the whole. • Reduce the fraction & change it to a percent.

24. Pages 110 – 111 Example • Solve the following: • 792 is what percent of 200,000? • 2,600 is what percent of 10,000? • 12 is what percent of 72?

25. Pages 110 – 111 Group Work • Solve the following: • 15 is what percent of 75? • 84 is what percent of 105? • 27 is what percent of 120?

26. Page 114 Finding a Percent of Change • A common application of percent is to find a percent of change. • First, find the amount of the change. • Next, make a fraction with the change over the original (earlier) amount. • Finally, change that fraction to a percent.

27. Page 114 Example • Solve each problem. Remember to write the amount of change over the original amount. • A color TV that originally sold for $380 was on sale for $285. By what percent was the original price discounted? • Anna’s weekly salary is $500, but she takes home only $395. The deductions her employer takes out are what percent of her weekly salary?

28. Page 114 Group Work • Solve each problem. Remember to write the amount of change over the original amount. • At the beginning of the football season, 800 people attended a high school game. After the team lost several games, the attendance was down to 560 people. By what percent did the attendance drop? • Last year a town budget was $2.4 million. This year the budget will be 2.7 million. By what percent did the budget increase from last year?

29. Pages 115 – 116 Finding A Number When a Percent is Known • If a percent of a number is given & you are looking for the whole number, change the percent into either a fraction or a decimal & divide it into the number you have.

30. Pages 115 – 116 Recognizing Types of Percent Problems • Three parts of a percent problem: The part, the whole, & the percent • Three types of problems from these number • Finding the part • Finding the percent • Finding the whole

31. Pages 115 – 116 Example • Solve. • Of the 500 employees at Ajax Electronics, only 6% go to work by public transportation. How many employees at Ajax use public transportation to get to work? • The Moore family expects to spend $1,200 on their summer vacation. So far they have saved $900 toward their vacation. What percent of the cost have they saved?

32. Pages 115 – 116 Group Work • Solve. • The sales tax rate in Linda’s state is 5%. How much tax does she have to pay on a shirt that costs $29? • Juan saves 10% of his take-home pay. He puts $160 in his savings account each month. What is his monthly take-home pay? • The total bill for Paul & Dorothy’s dinner was $32. They left a tip of $4.80. The tip was what percent of the total bill?