Chapter 7 Percents © 2010 Pearson Education, Inc. All rights reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved.
7.1 Basics of Percent Objectives 1. Learn the meaning of percent. 2. Write percents as decimals. 3. Write decimals as percents. 4. Understand 100%, 200%, and 300%. 5. Use 50%, 10%, and 1%. Copyright © 2010 Pearson Education, Inc. All rights reserved.

The figure has one hundred squares of equal size. Eleven of the square are shaded. The shaded portion is or 0.11 of the total figure. The shaded portion is also 11% of the total or “eleven parts out of 100 parts.” Read 11% as “eleven percent.” Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 1 Understanding Percent If 52 out of 100 chickens are hens, then 52 per 100 or , or 52% of the chickens are hens. b. If a person pays a tax of $9 on every $100 of purchases, then the tax rate is $9 per $100. The ratio is and the percent of tax is 9%. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 2 Writing Percents as Decimals Write each percent as a decimal. 32% p% = p ÷ 100 32% = 32 ÷ 100 = 0.32 78% 78% = 78 ÷ 100 = 0.78 93.4% 93.4% = 93.4 ÷ 100 = 0.934 200% 200% = 200 ÷ 100 = 2.00 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 3 Writing Percents as Decimals by Moving the Decimal Point Write each percent as a decimal by moving the decimal point two places to the left. 23% 23.% 0.23 23% = 0.23 180% 180.% = Decimal point starts at far right side Percent sign is dropped (Step 1) Decimal point is moved two places to the left. (Step 2) 180.% = 1.80 or 1.8 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 3 Writing Percents as Decimals by Moving the Decimal Point Write each percent as a decimal by moving the decimal point two places to the left. c % is attached so the decimal point can be moved two places to the left. 0.7% 0.7% = 0.007 Two zeros are attached so the decimal point can be moved two places to the left. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 4 Writing Decimals as Percents by Moving the Decimal Point Write each decimal as a percent by moving the decimal point two places to the right. 0.26 Decimal point is moved two places to the right. 0.26 = 26% b Percent sign is attached and decimal point is not written with whole number percents. = 37.6% Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 4 Writing Decimals as Percents by Moving the Decimal Point Write each decimal as a percent by moving the decimal point two places to the right. 1.83 d. 3.4 3.4 = 340% 5 5. = 5.00 so 5 = 500% = 183% = 3.40 0 is attached so the decimal point can be moved two places to the right. Attach % sign. Two zeros are attached so the decimal point can be moved two places to the right. Attach % sign. Copyright © 2010 Pearson Education, Inc. All rights reserved.

When working with percents, it is helpful to have several reference points. 100%, 200% and 300% are three such reference points. 100% means 100 parts out of 100 parts. That’s all of the parts. If 100% of the 18 people attending last week’s meeting attended this week’s meeting, then 18 people (all of them) attended this week. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 5 Finding 100%, 200%, and 300% of a Number Fill in the blanks. 100% of 24 people is _____. 100% is all of the people. 100% of 24 people is 24 people. 200% of $25 is _____. 200% is twice (2 times) as much money. 200% of $25 is 2  $25 = $50. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 5 Finding 100%, 200%, and 300% of a Number Fill in the blanks. c. 300% of 12 animals is _____. 300% is 3 times as many animals. 300% of 12 animals is 3  12 = 36 animals. Copyright © 2010 Pearson Education, Inc. All rights reserved.

50% means 50 parts out of 100 parts, which is half of the parts. So, 50% of $24 is $12 (half of the money). 10% means 10 parts out of 100. To find 10% of a number we move the decimal point one place to the left. To find 1% of a number, we move the decimal point two places to the left. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 6 Finding 50%, 10%, and 1% of a Number Fill in the blanks. 50% of 36 hours is _____. 50% is half of the hours. 50% of 36 is 18 hours. 10% of 320 pages is _____. Move the decimal point one place to the left. 10% of 320 is 32 pages. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 6 Finding 50%, 10%, and 1% of a Number Fill in the blanks. c. 1% of $780 is _____. Move the decimal point two places to the left. 1% of $780 is $7.80. Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.2 Percents and Fractions
Objectives 1. Write percents as fractions. 2. Write fractions as percents. 3. Use the table of percent equivalents. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 Writing Percents as Fractions Write each percent as a fraction or mixed number in lowest terms. The percent becomes the numerator. a. 65% Write 65% as The denominator is always 100 because percent means parts per 100. Lowest terms. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 continued Writing Percents as Fractions Write each percent as a fraction or mixed number in lowest terms. b. 84% c. 225% Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 Writing Decimal or Fraction Percents as Fractions Write each percent as a fraction in lowest terms. a % Write 20.5 over 100. To get a whole number in the numerator, multiply the numerator and denominator by 10. Now rewrite the fraction in lowest terms. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 continued Writing Decimal or Fraction Percents as Fractions Write each percent as a fraction in lowest terms. a. Write over 100. When we have a mixed number in the numerator, we must write the mixed number as an improper fraction. Reciprocals 7 = 20 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 Writing Fractions as Percents Write each fraction as a percent. Round to the nearest tenth if necessary. a. Write as a percent by solving a proportion. Find cross products and show that they are equivalent. 1 This result means that 1 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 continued Writing Fractions as Percents Write each fraction as a percent. Round to the nearest tenth if necessary. b. Write as a percent by solving a proportion. Find cross products and show that they are equivalent. 1 So, 1 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 continued Writing Fractions as Percents Write each fraction as a percent. Round to the nearest tenth if necessary. c. Start with a proportion. Find cross products and show that they are equivalent. 1 So, 1 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

The tables on the following slides show common and not so common fractions and mixed numbers and their decimal and percent equivalent. The more you work with them, the more familiar they will become. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Percent (rounded to tenths when necessary)
Percent, Decimal, and Fraction Equivalents Percent (rounded to tenths when necessary) Decimal Fraction 1% 0.01 2% 0.02 4% 0.04 5% 0.05 0.0625 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Percent, Decimal, and Fraction Equivalents Percent (rounded to tenths when necessary) Decimal Fraction 10% 0.1 0.125 0.1875 20% 0.2 25% 0.25 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Percent, Decimal, and Fraction Equivalents Percent (rounded to tenths when necessary) Decimal Fraction 30% 0.3 0.3125 0.375 40% 0.4 0.4375 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Percent, Decimal, and Fraction Equivalents Percent (rounded to tenths when necessary) Decimal Fraction 50% 0.5 0.5625 60% 0.6 0.625 0.6875 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Percent, Decimal, and Fraction Equivalents Percent (rounded to tenths when necessary) Decimal Fraction 70% 0.7 75% 0.75 80% 0.8 0.8125 0.6875 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Percent, Decimal, and Fraction Equivalents Percent (rounded to tenths when necessary) Decimal Fraction 90% 0.9 0.9375 100% 1.0 1 110% 1.1 125% 1.25 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

7.3 Using the Percent Proportion and Identifying the Components in a Percent Problem Objectives 1. Learn the percent proportion. 2. Solve for an unknown value in a percent proportion. 3. Identify the percent. 4. Identify the whole. 5. Identify the part. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 Using the Percent Proportion Use the percent proportion and solve for the unknown value. Let x represent the unknown. part = 20, percent = 80; find the whole. Find the cross products. Show that the cross products are equivalent. x • 80 20 • 100 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 Using the Percent Proportion Use the percent proportion and solve for the unknown value. Let x represent the unknown. b. part = 12, whole = 40; find the percent. The percent is written as 30%. Write the fraction in lowest terms. Find the cross products. Divide both sides by 10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 Using the Percent Proportion Use the percent proportion and solve for the unknown value. Let x represent the unknown. c. whole = 120, percent = 90; find the part. The part is 108. Write the fraction in lowest terms. Find the cross products. Divide both sides by 10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Percent Problems All percent problems involve a comparison between a part of something and the whole. Percent The percent is the ratio of a part to a whole, with 100 as the denominator. In a problem, the percent appears with the word percent or with the symbol “%” after it. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 Finding the Percent in Percent Problems Find the percent in the following. a. 20% of the 740 customers were children. Percent b. $90 is what 40 percent of what number? Percent c. What percent of 320 is 272? Percent (unknown) Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 Finding the Whole in Percent Problems Find the whole in the following. a. 14% of 600 cars were convertibles. Whole b. $200 is 30 percent of what number? Whole c. 70% of 8220 is what number? Whole Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Part The part is the portion being compared with the whole. Note: If you have trouble identifying the part, find the percent and the whole first. The remaining number is the part. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 4 Finding the Part in Percent Problems Identify the part. Then set up the percent proportion. (Do not solve.) a % of 450 animals is 270 animals. Percent; with % sign Whole Part Part Percent Whole Always 100 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 4 Finding the Part in Percent Problems Identify the part. Then set up the percent proportion. (Do not solve.) b. $240 is 10% of what number? Part Percent Whole (unknown) Part Percent Whole Always 100 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 4 Finding the Part in Percent Problems Identify the part. Then set up the percent proportion. (Do not solve.) c % of 600 is what number? Percent Whole Part (unknown) Part Percent Whole Always 100 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

7.4 Using Proportions to Solve Percent Problems
Objectives 1. Use the percent proportion to find the part. 2. Find the whole using the percent proportion. 3. Find the percent using the percent proportion. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Finding the Part Using Multiplication To find the part: Step 1 Identify the percent. Write the percent as a decimal. Step 2 Multiply this decimal by the whole. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 Find the Part Using Multiplication Use multiplication to find the part. a. Find 12% of 50 books. Step 1 Write 12% as a decimal 0.12. Step 2 Multiply 0.12 and the whole, which is 50. part = (0.12)(50) part = 6 books It is a good idea to estimate the answer to see that the exact answer is reasonable. Estimate The exact answer of 6 books is reasonable. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 continued Find the Part Using Multiplication Use multiplication to find the part. b. Find 180% of 70 dosages. The percent is 180. Written as a decimal 180% = 1.8. part = (1.80)(70) = 126 dosages You estimate by realizing that 180% is close to 200% and 2 times 70 is 140. So, 126 dosages is a reasonable answer. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 continued Find the Part Using Multiplication Use multiplication to find the part. c. Find 0.6% of 30 yards. part = (0.006)(30) = 0.18 yards Estimate by realizing that 0.6% is less than 1%. 1% of 30 yards = (0.1)30 = 0.3 yards. Our exact answer should be less than 0.3 yards, and 0.18 yards fits this requirement. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 Solving for a Part in an Application Problem MK Motors has 150 cars on the lot. Of these cars, 74% are new. How many of the cars are new? Step 1 Read the problem. The problem asks to find the number of new cars on the lot. Step 2 Work out a plan. Look for the word of as an indicator of multiplication. The total number of cars is 150, so the whole is 150. The percent is 74. To find the number of new cars, find the part. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 continued Solving for a Part in an Application Problem MK Motors has 150 cars on the lot. Of these cars, 74% are new. How many of the cars are new? Step 3 Estimate a reasonable answer. Round 74% to 75% (equivalent to 3/4) and 150 to 200. Step 4 Solve the problem. Step 5 State the answer. MK motors has 111 new cars on its lot. Step 6 Check. The exact answer, 111 cars, is close to our estimate of 150 cars. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Finding the Whole with the Percent Proportion
Parallel Example 4 Finding the Whole with the Percent Proportion 57 pages is 20% of what number of pages in a book? 57 pages is 20% of 285 pages in the book. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 5 Applying the Percent Proportion Movie Madness receives a shipment of 138 new movies. If this is 15% of their total inventory, how many movies does Movie Madness have? Step 1 Read the problem. The problem asks to find the total number of movies. Step 2 Work out a plan. From the information in the problem, the percent is 15 and the part is the number of movies in the shipment. The total inventory is the unknown. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 5 Applying the Percent Proportion Movie Madness receives a shipment of 138 new movies. If this is 15% of their total inventory, how many movies does Movie Madness have? Step 3 Estimate a reasonable answer. Round 138 to 150 and 15% to the equivalent fraction Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 5 continued Applying the Percent Proportion Movie Madness receives a shipment of 138 new movies. If this is 15% of their total inventory, how many movies does Movie Madness have? Step 4 Solve the problem. Use the percent proportion to find the whole. 1 1 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 5 continued Applying the Percent Proportion Movie Madness receives a shipment of 138 new movies. If this is 15% of their total inventory, how many movies does Movie Madness have? Step 5 State the answer. Movie Madness has 920 movies in their inventory. Step 6 Check. The exact answer, 920 movies, is close to our estimate of 1000. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 6 Using the Percent Proportion to find the Percent 18 candles is what percent of 300 candles? so or 1 1 18 candles is 6% of 300 candles. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 7 Applying the Percent Proportion A nurse gives 120 flu shots in one day. If 78 were completed in the morning, what percent were completed in the morning? Step 1 Read the problem. The problem asks to find the percent of the flu shots given in the morning. Step 2 Work out a plan. The number of shots given the entire day is the whole. The number given in the morning, 78, is the part. Step 3 Estimate a reasonable answer. Round 120 to 150 and 78 to 75. This is , so our estimate is 50%. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 7 continued Applying the Percent Proportion A nurse gives 120 flu shots in one day. If 78 were completed in the morning, what percent were completed in the morning? Step 4 Solve the problem. or 1 1 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 7 continued Applying the Percent Proportion A nurse gives 120 flu shots in one day. If 78 were completed in the morning, what percent were completed in the afternoon? Step 5 State the answer. The nurse gave 65% of the flu shots in the morning. Step 6 Check. The exact answer of 65% is a little bit more than our estimate of 50% because 120 is larger than 100. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

7.5 Using the Percent Equation
Objectives 1. Use the percent equation to find the part. 2. Find the whole using the percent equation. 3. Find the percent using the percent equation. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 Finding the Part Find 55% of $340. Write 55% as the decimal The whole, which comes after the word of, is 340. Let x represent the unknown part. part = percent • whole x = (0.55)(340) x = 187 55% of $340 is $187. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 Finding the Part b. Find 105% of 60 acres. Write 105% as the decimal The whole is 60. Let x represent the unknown part. part = percent • whole x = (1.05)(60) x = 63 105% of 60 acres is 63 acres. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 Finding the Part c. Find 0.6% of 1500 students. Write 0.6% as the decimal The whole is Let x represent the unknown part. part = percent • whole x = (0.006)(1500) x = 9 0.6% of 1500 students is 9 students. CAUTION When using the percent equations, the percent must always be changed to a decimal before multiplying. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

9 computers is 6% of what number of computers?
Parallel Example 2 Finding the Whole 9 computers is 6% of what number of computers? The part is 9 and the percent is 6% or the decimal The whole is unknown. part = percent • whole 9 = (0.06)(x) Let x represent the unknown whole. 1 Divide both sides by 0.06. 1 150 = x 9 computers is 6% of 150 computers. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 Finding the Whole b animals is 18% of what number of animals? Write18% as The part is 126. part = percent • whole 126 = (0.18)(x) Let x represent the unknown whole. 1 Divide both sides by 0.18. 1 700 = x 126 animals is 18% of 700 animals. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 Finding the Whole c of what number is 253? Write as 11.5%, or the decimal The part is 253. part = percent • whole 253 = (0.115)(x) Let x represent the unknown whole. 1 Divide both sides by 1 2200 = x 253 is 11.5% of 2200. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

7 hair stylists is what percent of 28 hair stylists?
Parallel Example 3 Finding the Percent 7 hair stylists is what percent of 28 hair stylists? Because 28 follows of, the whole is 28. The part is 7, and the percent is unknown. part = percent • whole 7 = (x)(28) Let x represent the unknown. 1 Divide both sides by 28. 1 0.25 = x 7 hair stylists is 22% of 28 hair stylists. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 Finding the Percent b. What percent of $140 is $112? The whole is 140 and the part is 112. part = percent • whole 112 = (x)(140) Let x represent the unknown. 1 Divide both sides by 40. 1 0.80 = x 80% of $140 is $112. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 Finding the Percent c. What percent of $240 is $276? The whole is 240 and the part is 276. part = percent • whole 276 = (x)(240) Let x represent the unknown. 1 Divide both sides by 240. 1 1.15 = x 115% of $240 is $276. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

7.6 Solving Applications Problems with Percent
Objectives 1. Find sales tax. 2. Find commissions. 3. Find the discount and sale price. 4. Find the percent of change. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

States, counties, and cities often collect taxes on sales to customers. The sales tax is a percent of the total sale. The following formula for finding sales tax is based on the percent equation. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 Solving for Sales Tax Sam’s Sporting Goods sells a tent for $189. If the sales tax is 5%, how much tax is paid? What is the total cost of the tent? Use the six problem-solving steps. Step 1 Read the problem. The problem asks for the total cost of the tent including the sales tax. Step 2 Work out a plan. Use the sales tax formula to find the amount of sales tax. Add the sales tax to the cost of the item to find the total cost. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 continued Solving for Sales Tax Sam’s Sporting Goods sells a tent for $189. If the sales tax is 5%, how much tax is paid? What is the total cost of the tent? Use the six problem-solving steps. Step 3 Estimate a reasonable answer. Round $189 to $200. 5% is equivalent to , so divide $200 by 20. The total estimated cost is $200 + $10 = $210. Step 4 Solve the problem. part = percent ∙ whole amount of sales tax rate of tax cost of item Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 continued Solving for Sales Tax Sam’s Sporting Goods sells a tent for $189. If the sales tax is 5%, how much tax is paid? What is the total cost of the tent? Use the six problem-solving steps. Step 4 a = (5%)($189) a = (0.05)($189) a = $9.45 Total cost equals $189 + $9.45 = $ Step 5 State the answer. The total cost of the tent is $ Step 6 Check. The exact answer, $198.45, is close to our estimate of $210. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 Finding the Sales Tax Rate The sales tax on a $580 recliner is $ Find the rate of the sales tax. Step 1 Read the problem. The problem asks for the rate of the sales tax. Step 2 Work out a plan. Use the sales tax formula. sales tax = rate of tax ∙ cost of item The cost of the recliner (the whole) is $580, and the amount of sales tax (the part) is $ Use r to represent the unknown rate of tax (the percent). Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 continued Finding the Sales Tax Rate The sales tax on a $580 recliner is $ Find the rate of the sales tax. Step 3 Estimate a reasonable answer. Round $580 to $600 and round $46.40 to $50.The sales tax is or So divide 1 by 12 to estimate the percent (rate) of sales tax. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 continued Finding the Sales Tax Rate The sales tax on a $580 recliner is $ Find the rate of the sales tax. Step 4 Solve the problem. sales tax = rate of tax ∙ cost of item $46.40 = r ∙ $580 1 1 Step 5 State the answer. The sales tax rate is 8%. Step 6 Check. The exact answer and the estimate of 8% are the same. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Many salespeople are paid by commission rather than an hourly wage. If you are paid by commission, you are paid a certain percent of your total sales dollars. The formula below for finding the commission is based on the percent equation. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 Determining the Amount of Commission Caleb Martinez had exercise equipment sales of $12,700 while working part-time last month. If his commission rate is 9%, find the amount of his commission. Step 1 Read the problem. The problem asks for the amount of commission that Martinez earned. Step 2 Work out a plan. Use the commission formula. Step 3 Estimate a reasonable answer. Round the commission rate to 10% and the sales to $10,000. $10,000 ÷ 10 = $1000 Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 continued Determining the Amount of Commission Caleb Martinez had exercise equipment sales of $12,700 while working part-time last month. If his commission rate is 9%, find the amount of his commission. Step 4 Solve the problem. Amount of commission = rate of commission ∙ amount of sales c = (9%)($12,700) c = (0.09)($12,700) c = $ Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 continued Determining the Amount of Commission Caleb Martinez had exercise equipment sales of $12,700 while working part-time last month. If his commission rate is 9%, find the amount of his commission. Step 5 State the answer. Martinez earned a commission of $1143 for selling the exercise equipment. Step 6 Check. The exact answer, $1143, is close to the estimate of $1000. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

A store will reduce prices, or discount, to attract additional customers. Use the following formula to find the discount and the sale price. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 5 Finding a Sale Price Art Designs has a painting with an original price of $620 on sale for 15% off. Find the sale price of the painting. Step 1 Read the problem. The problem asks for the sale price of the painting after a discount of 15%. Step 2 Work out a plan. First find the amount of discount by multiplying the original price by the rate of discount. Then, subtract the discount from the original price. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 5 continued Finding a Sale Price Art Designs has a painting with an original price of $620 on sale for 15% off. Find the sale price of the painting. Step 3 Estimate a reasonable answer. Round the original price to $600 and the rate of discount from 15% to 20%. Since 20% is equivalent to 1/5, the estimated discount is $600 ÷ 5 = $120. So the estimated sale price is $600 − $120 = $480. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 5 continued Finding a Sale Price Art Designs has a painting with an original price of $620 on sale for 15% off. Find the sale price of the painting. Step 4 Solve the problem. Amount of discount = rate of discount ∙ original price a = (0.15)($620) a = $93 Sale price = original price − amount of discount $620 − $93 = $527 Step 5 State the answer. The sale price of the painting is $527. Step 6 Check. The exact answer, $527, is close to the estimate of $480. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

We are often interested in looking at increases or decreases in sales, production, population, and many other items. Use the following steps to find the percent of increase. Finding the Percent of Increase Step 1 Use subtraction to find the amount of increase. Step 2 Use the percent proportion to find the percent of increase. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 6 Finding the Percent of Increase A budget had an increase from $19,600 last year to $40,060 this year. Find the percent of increase. Step 1 Read the problem. The problem asks for the percent of increase. Step 2 Work out a plan. Subtract the last year’s budget from this year. Next, use the percent proportion to find the unknown percent. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 6 continued Finding the Percent of Increase A budget had an increase from increased from $19,600 last year to $40,060 this year. Find the percent of increase. Step 3 Estimate a reasonable answer. Round $19,600 to 20,000 and $40,060 to 40,000. The amount of increase is $40,000 – $20,000 = $20,000. Since the increase is about the same as the original amount, the estimated percent increase is 100%. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 6 continued Finding the Percent of Increase A budget had an increase from increased from $19,600 last year to $40,060 this year. Find the percent of increase. Step 4 Solve the problem. $40,060 − $19,600 = $20,460 Step 5 State the answer. The percent of increase is about 104%. Step 6 Check. The exact answer, 104%, is close to the estimate of 100%. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Finding the Percent of Decrease Step 1 Use subtraction to find the amount of decrease. Step 2 Use the percent proportion to find the percent of decrease. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Finding the Percent of Decrease
Parallel Example 7 Finding the Percent of Decrease The number of minutes Rita used on her cell phone dropped this month to 798 from 840 last month. Find the percent of decease. Step 1 Read the problem. The problem asks for the percent of decrease. Step 2 Work out a plan. Subtract the number of minutes this month from last month. Then use the percent proportion. Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide

Parallel Example 7 continued Finding the Percent of Decrease The number of minutes Rita used on her cell phone dropped this month to 798 from 840 last month. Find the percent of decease. Step 3 Estimate a reasonable answer. Round 798 to 800 and 840 to So, 850 – 800 = 50. Since 50 is 1/17 of 850, our estimate is ÷ 17 ≈ 0.06 or 6%. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 7 continued Finding the Percent of Decrease The number of minutes Rita used on her cell phone dropped this month to 798 from 840 last month. Find the percent of decease. Step 4 Solve the problem. 840 − 798 = 42 Step 5 State the answer. The percent of decrease in phone minutes was 5%. Step 6 Check. The exact answer, 5%, is close to the estimate of 6%. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

When we open a savings account, we are actually lending money to the bank or credit union. The bank or credit union pays a fee to the savings account holders and charges a higher fee to it borrowers. These fees are called interest. Interest is a fee paid or a charge made for lending or borrowing money. The amount of money borrowed is called the principal. The charge for interest is often given as a percent, called the interest rate or rate of interest. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Formula for Simple Interest
Interest = principal • rate • time The formula is usually written using letters I = p • r • t Note: Simple interest is used for most short-term business loans, most real estate loans, and many automobile and consumer loans. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 1 Finding Interest for a Year Find the interest on $6000 at 8% for 1 year. The principal (p) = $6000 The interest rate (r) = 8% or 0.08 The time of the loan is 1 year. I = p • r • t The interest is $480. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 2 Finding Interest for More Than a Year Find the interest on $3400 at 6% for two and a half years. The principal (p) = $3400 The interest rate (r) = 6% or 0.06 The time of the loan is 2.5 years. I = p • r • t The interest is $510. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 3 Finding Interest for Less Than 1 Year Find the interest on $340 at 6% for 8 months. The principal (p) = $340 The interest rate (r) = 6% or 0.06 The time of the loan is 8/12 of a year. I = p • r • t The interest is $13.60. Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Parallel Example 4 Calculating the Total Amount Due A loan of $4200 was made at 5% for 6 months. Find the total amount due. Find the interest. I = p • r • t Amount due = principal + interest = = The total amount due is $ Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide

Chapter 7 Percents © 2010 Pearson Education, Inc. All rights reserved.

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Chapter 7 Percents © 2010 Pearson Education, Inc. All rights reserved.

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Presentation on theme: "Chapter 7 Percents © 2010 Pearson Education, Inc. All rights reserved."— Presentation transcript:

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