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CHAPTER 6 Percents

CHAPTER 6 Percents. Learning Outcomes. 6-1. Write a whole number, fraction or decimal as a percent. Write a percent as a whole number, fraction or decimal. Write a whole number, fraction or decimal as a percent.

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CHAPTER 6 Percents

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  1. CHAPTER 6 Percents

  2. Learning Outcomes 6-1 • Write a whole number, fraction or decimal as a percent. • Write a percent as a whole number, fraction or decimal.

  3. Write a whole number, fractionor decimal as a percent Percents are used to calculate mark-downs mark-ups, discounts and many other business applications. Hundredths and percent have the same meaning: per hundred. 100 percent is the same as 1 whole quantity. 100% = 1. When we multiply a number by 1, the producthas the same value as the original number. 6-1-1 Section 6-1 Percent Equivalents

  4. Write a whole number, fractionor decimal as a percent N x 1 = N If 1 = 100%, then ½ x 100% = 50%. If 1 = 100%, then 0.5 x 100% = 050.% = 50%. Section 6-1 Percent Equivalents In each case when we multiply by 1 in some form, the value of the product is equivalent to the value of the original number—even though the product looks different.

  5. Write a number as its percent equivalent Multiply the number by 1 in the form of 100%. The product has a % symbol. Example: Write 0.65 as a percent. 0.65 = 0.65 x 100% = 065.% = 65% The decimal point movestwo places to the right. Write a number as its percent equivalent HOW TO: Section 6-1 Percent Equivalents

  6. 0.98 x 100% = 098.% = 98% 1.52 x 100% = 152.% = 152% 0.04 x 100% = 004.% = 4% 5.00 x 100% = 500.% = 500% 0.003 x 100% = 000.3% = 0.3 Write a number as its percent equivalent HOW TO: Section 6-1 Percent Equivalents Write the decimal or wholenumber as a percent 0.98 = 1.52 = 0.04 = 5 = 0.003 =

  7. .48 = 7.16 = 0.0034 = Examples… Section 6-1 Percent Equivalents EXAMPLES 48% 716% 0.34%

  8. Examples… Section 6-1 Percent Equivalents MORE EXAMPLES For the following, change the mixed numberto an improper fraction and multiply by 100%.

  9. ⅜ = ⅞ = ¾ = Examples… Section 6-1 Percent Equivalents MORE EXAMPLES 37.5% 87.5% 75%

  10. Write a percent as a wholenumber, fraction or decimal When a number is divided by 1, the quotient has the same value as the original number. We can also use the fact that N ÷ 1 = N to change percents to numerical equivalents. 6-1-2 Section 6-1 Percent Equivalents

  11. Write a percent as a wholenumber, fraction or decimal Write the percent as a number Divide by 1 in the form of 100% or multiply by: The quotient does not have the % symbol. 37% = 37% ÷ 100% = .37 = 0.37 127% = 127% ÷ 100% = 1.27 Examples: 6-1-2 Section 6-1 Percent Equivalents • To divide by 100 mentally, move the decimal point two places to the left.

  12. Write the percent as a fraction or mixed number In multiplying fractions, reduce or cancel common factors from a numerator to a denominator. Percent signs also cancel. Division is the same as multiplying by the reciprocal of the divisor. Similarly, % ÷ % = 1 HOW TO: Section 6-1 Percent Equivalents Example:

  13. Learning Outcomes 6-2 • Identify the rate, base, and portion in percent problems. • Use the percentage formula to find the unknown value when two values are known.

  14. Identify the rate, base andportion in percent problems 6-2-1 Section 6-2 Solving Percentage Problems In the formula P = R x B: P refers to portion.It represents a portion of the base. B refers to the base.The original number or one entire quantity. R refers to rate.A percent that tells us how thebase and portion are related. To find the portion, multiply the rate by the base.

  15. 60 people are registered for this course,and 25% are Spanish-speaking. What number of students are Spanish-speaking? An Example… Section 6-2 Solving Percentage Problems What are you looking for? The number of Spanish-speaking students What do you know? The base is 60 (rate); and the rate is 25% or 0.25. Solution plan; Solve. P = 60 x 25% (or .25); P = 15 Conclusion. 15 students are Spanish-speaking. Identify the base; identify the rate. Use the solution plan to find the answer.

  16. If 40% of the registered voters in a communityof 5,600 are Democrats, how many voters are Democrats? 2,240 If 58% of the office workers prefer diet sodaand there are 600 workers, how many preferdiet soda? 348 Examples… Section 6-2 Solving Percentage Problems

  17. Identify the rate, base andportion in percent problems To find “B,” change the formula to: B= P/R. Section 6-2 Solving Percentage Problems In the formula P = R x B: To find the original number, divide the portion by the rate.

  18. Forty percent, or 90 diners preferredoutdoor seating at the new restaurant. How many diners were interviewed in all? An Example… Section 6-2 Solving Percentage Problems What are you looking for? The total number of diners surveyed. What do you know? The portion (90) and the rate (40%) Solution plan; Solve. Base =P/R; Base = 90/.40; B = 225 Conclusion. 225 diners were interviewed.

  19. 1700 dentists attending a convention last month prefer fluoride treatments for preschoolers—that’s 4 out of every 5 dentists. How many dentists attended in all? 2,125 80%, or 560, of our current clients take advantage of our cash discount program for prompt payment. What is our current client base? 700 Examples… Section 6-2 Solving Percentage Problems

  20. Identify the rate, base andportion in percent problems To find “R,” change the formula to: R= P/B. Section 6-2 Solving Percentage Problems In the formula P = R x B: To find the rate, divide theportionby the base.

  21. An Example… Section 6-2 Solving Percentage Problems 55 insurance agents were able to meet with their clients to inform them of policy changes. Of 220 agents, what percent does this represent? What are you looking for? The percent of rate of agents that talked to their clients. What do you know? The base or total number of agents, and the portion that talkedto their clients. Solution plan; Solve. R = P/B; R = 55/220; B = .25 Conclusion.25% of the agents talked to their clients.

  22. The plant foreperson reported that 873 of the 900 items tested met the quality control specifications for production. What is the rate of acceptable items? 97% In the new product focus group, 6,700 of the 8,375 customers rated the product as “very good” or “superior.” What was the rate? 80% Examples… Section 6-2 Solving Percentage Problems

  23. Identify the rate, base andportion in percent problems You may need find one of the elements—rate, base or portion—when you know the other two. “Read” the problem to identify the missing element. Section 6-2 Solving Percentage Problems Example: 30% of 70 is what number? 30% is the rate. 70 is the base. You are looking for “P” or portion. P = R x BP = 0.3 x 70 = 21

  24. Use the percentage formula to find theunknown value when two values are known. You may need find one of the elements—rate, base or portion—when you know the other two. “Read” the problem to identify the missing element. 6-2-2 Section 6-2 Solving Percentage Problems

  25. Use the percentage formula to find theunknown value when two values are known. Identify what’s missing and then solvethe problem using the correct formula. Section 6-2 Solving Percentage Problems 60 is what percent of 80? R = P/BR = 60/80 = 75% 35% of 350 is what? P = R x B P = 0.35 x 350 = 122.5 25% of what number is 125? B = P/RB = 125/.25 = 500

  26. Learning Outcomes 6-3 • Find the amount of increase or decrease in percent problems. • Find the new amount directly in percent problems. • Find the rate or the base in increase or decrease problems.

  27. Find the amount of increase ordecrease in percent problems 6-3-1 Section 6-3 Increases and Decreases Examples of increases in businessapplications include: Sales tax Raise in salary Markup on a wholesale price

  28. Amount of increase = new amt. – beg. amt. Find the amount of increase HOW TO: Section 6-3 Increases and Decreases Example: Joe’s salary has been $400 a week. Beginning next month, it will be $450 a week. The amount of increase is $50 a week.

  29. Find the amount of increase ordecrease in percent problems 6-3-1 Section 6-3 Increases and Decreases Examples of decreases include: Payroll deductions Markdowns Discounts on sale items

  30. Amount of decrease = beg. amt. – new amt. Find the amount of decrease HOW TO: Section 6-3 Increases and Decreases Example: Roxanne’s new purse originally cost $60,but was on sale when she bought it on Saturday for $39.99. The amount of decrease (or markdown) is $20.01.

  31. The amount of change is a percent of the original or beginning amount. Find the amount (increase or decrease) from a percent of change by: Identifying the original or beginning amount and the percent or rate of change. Multiplying the decimal equivalent of the rate of change by the original or beginning amount. Percent of change Section 6-3 Increases and Decreases

  32. Your company has announced a 1.5% cost ofliving raise for all employees next month.Your monthly salary is currently $2,300. Starting next month, what will your new salary be? Percent of change Section 6-3 Increases and Decreases Current salary = $2,300 a month Rate of change = 1.5% Amount of raise = Percent of change x original amount .015 x $2,300 = $34.50 a month Add $34.50 to the original amount of $2,300 to identify the new amount. New amount = $2,334.50

  33. Find the new amountdirectly in percent problems 6-3-2 Section 6-3 Increases and Decreases • Often in increase or decrease problems, we are more interested in the new amount than the amount of change. • Find the new amount by adding or subtracting|percents first. • The original or beginning amount is always considered to be the base, and is 100% of itself.

  34. Find the new amount directlyin a percent problem Find the rate of the new amount. For increase: 100% + rate of increase. For decrease: 100% - rate of decrease. Find the new amount. P = R x B New amount = rate of new amt. x original amt. HOW TO: Section 6-3 Increases and Decreases

  35. Find the new amount directlyin a percent problem Medical assistants are to receive a 9% increasein wages per hour. If they were making $15.25, what is the new per hour salary to the nearest cent? HOW TO: Section 6-3 Increases and Decreases Rate of new amount = 100% + rate of increase Rate of new amount = 100% + 9% = 109% New amount = $15.25 x 109% Change 109% to its decimal equivalent: 1.09 $15.25 x 1.09 = $16.6225 = $16.62

  36. Find the new amount directlyin a percent problem A new pair of jeans that costs$49.99 is advertised at 70% off. What is the sale price to the nearest cent of the jeans? HOW TO: Section 6-3 Increases and Decreases Rate of new amount = 100% - rate of decrease= 100% - 70% = 30% New amount = rate of new amt. x original amt. New amount = 30% x $49.99 New amount = 0.3 x $49.99 = $14.997 New amount =$15.00 (nearest cent)

  37. The property taxes at your business office willgo up 5% next year. Currently, you pay $3,400. How much will you pay next year? $3,570 A wholesaler is offering you a 20% discount if you purchase new inventory before the 15th of the month. If your normal invoice is $3,600, how much would you pay if you got the discount? $2,880 Examples… Section 6-3 Increases and Decreases

  38. Find the rate or the base inincrease or decrease problems To find the rate of increase or decrease, use the percentage formula: R = P/B Rate = amount of change ÷ original amount To find the base or original amount, use the percentage formula: B = P/R Base = amount of change ÷ rate of change 6-3-3 Section 6-3 Increases and Decreases

  39. An Example… Section 6-3 Increases and Decreases During the month of May, a graphic artist made a profitof $1,525. In June, she made a profit of $1,708. What is the percent of increase in profit? What are you looking for? What do you know?Percent of increase in profits.Original amt. = $1,525; New amt. = $1,708. Solution plan. Find amount of increase; Find percent of increase; B = .25 Solve. $1,708 – $1,525 = $183; $183 ÷ $1,525 = 0.12 = 12% Conclusion.The rate of increase in profit is 12%.

  40. A popular detergent cost $5.99 last Saturday, but today the same detergent costs a$7.50. What is the rate of increase? 25.2% Sales in the East Region were $10,800 in January and dropped to $9,700 in February. What is the rate of decrease from January to February? 10.2% Examples… Section 6-3 Increases and Decreases

  41. Exercises Set A

  42. EXERCISE SET A Write the decimal as a percent. 2. 0.82 0.82(100%) = 82% 4. 0.34 0.34(100%) = 34% 6. 1 1(100%) = 100%

  43. EXERCISE SET A Write the decimal as a percent. 8. 0.37 0.37 = 0.37(100%) = 37% 10. 4 4 = 4(100%) = 400%

  44. EXERCISE SET A Write the fraction or mixed number as a percent. Round to the nearest hundredth of a percent if necessary. 12. 14. 16.

  45. EXERCISE SET A Write the percent as a decimal. 18. 98% 20. 91.7% 22. 6%

  46. EXERCISE SET A Write the percent as a whole number, mixed number, or fraction, reduced to lowest terms. 24. 6% 26. 45%

  47. EXERCISE SET A Percent Fraction Decimal 28. 30.

  48. EXERCISE SET A Find P, R, or B using the percentage formula or one of its forms. Round decimals to the nearest hundredth and percents to the nearest whole number percent. 32. P = 25, B = 100 34. P = $835, R = 3.2%

  49. EXERCISE SET A Find P, R, or B using the percentage formula or one of its forms. Round decimals to the nearest hundredth and percents to the nearest whole number percent. 36. Find 30% of 80 38. 51.52 is what percent of 2,576?

  50. EXERCISE SET A 40. Eighty percent of one store’s customers paid with credit cards. Forty customers came in that day. How many customers paid for their purchases with credit cards? P = RB P = 0.8(40) P = 32 customers

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