Chapter 8 Consumer Mathematics Section 8-1 Percents Objectives: Convert between percent, decimal, and fraction form Perform calculations involving percents Sole real-world problems involving percents Find percent increase or decrease Evaluate the validity of claims based on percents

Converting Percents to Decimals In order to change a percent to a decimal, drop the % sign and move the decimal point two places to the left.

Example 1: Changing Percents to Decimals Change each percent to a decimal. (a)84% (b)5% (c)37.5% (d)172%

Converting Percents to Fractions A percent can be converted to a fraction by dropping the percent sign and using the percent number as the numerator of a fraction whose denominator is 100. Be sure to reduce fractions to lowest terms when possible.

Example 2: Changing Percents to Fractions Change each percent to a fraction. (a)42% (b)6% (c)37.5% (d)15.8%

Converting a Decimal to a Percent To change a decimal to a percent, move the decimal point two places to the right and add a percent sign.

Example 3: Changing Decimals to Percents Change each decimal to a percent. (a)0.74 (b)0.05 (c)1.327 (d)5.463

Changing a Fraction to a Percent To change a fraction to a percent, first change the fraction to a decimal, and then change the decimal to a percent.

Example 4: Changing Fractions to Percents Convert each fraction to a percent. (a)7/8 (b)¾ (c)5/6 (d)1½

Example 5: Finding a Certain Percentage of a Whole In a class of 66 students, 32% got a B on the exam. How many students got a B? In another section of the same course, 19% of the 54 students got a B. How many students got a B?

Example 6: Finding a Percentage from a Portion Of 60 runners who started a 5K race, 45 finished the race in under 40 minutes. What percent is that? In 2008, 21 out of 50 states had a population of 5 million or higher. What percent is that?

Example 7: Finding a Whole Amount Based on a Percentage A medium-sized company reported that it had to cut its work force back to 70% of what it was last year. If it has 63 workers now, how many did it have a year ago? After a really rotten year in 2008, a baseball team won 120% as many games in 2009, which was 84 games. How many did they win in 2008?

Example 8: Calculating Sales Tax The sales tax in Allegheny County, Pennsylvania, is 7%. What is the tax on a calculator that costs $89.95? What is the total amount paid? The sales tax in Atlanta, Georgia, is 5%. Find the amount of tax and the total cost of a portable DVD player on sale for $149.

Example 9: Calculating Cost of Sale from Commission A real estate agent receives a 7% commission on all home sales. How expensive was the home if she received a commission of $5,775? A sales clerk receives a 9% commission on all sales. Find the total sales the clerk made if his commission was $486.

Percent Increase and Decrease (1)Find the amount of increase or decrease. (2)Make a fraction as shown: (3)Change the fraction to a percent.

Example 10: Finding a Percent Change A large latte at the Caffeine Connection sells at a regular price for $3.50. Today is is on sale for $3.00. Find the percent decrease in the price. A resale shop bought a guitar for $150 and then sold it for $300. What was the percent markup on the guitar?

Example 11: Recognizing Misuse of Percents in Advertising A department store advertised that certain merchandise was reduced 25%. Also, an additional 10% discount card would be given to the first 200 people who entered the store on a specific day. The advertisement then stated that this amounted to an 35% reduction in the price of an item. Is the advertiser being honest?

Example 11 Continued A department store offered a 20% discount on all TVs. They also stated that the first 50 customers would receive an additional 5% discount. Find the total percent discount.

Homework P. 428 #37, 41, 43, 45, 49, 51, 53, 59, 61