Percents Pages 96 – 122

Understanding Percents 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 %.

Example Page 98 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.

Group Work Page 98 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.

Changing Decimals to Percents 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.

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

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

Changing Percents to Decimals 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.

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

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

Changing Fractions to Percents 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.

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

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

Changing Percents to Fractions 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.

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

Group Work Page 102 Write each percent as a common fraction. 66 2/3% 12% 90% 2/3 3/25 9/10

Finding a Percent of a Number 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.

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

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

Solving Two-Step Problems 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

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?

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?

Finding What Percent One Number is of Another 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.

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

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

Finding a Percent of Change 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.

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?

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?

Finding A Number When a Percent is Known 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.

Recognizing Types of Percent Problems 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

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?

Group Work Pages 115 – 116 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?