1. 6-1 Percents and Their Applications Kirkwood Community College February 16, 2009 Presented by Sanh Tran, MBA, CPIM, CTL

2. McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved Chapter 6 Percents and Their Applications

3. 6-3 Convert decimals to percents (including rounding percents), percents to decimals, and fractions to percents Convert percents to fractions Percent and Their Applications #6 Learning Unit Objectives Conversions LU6.1

4. 6-4 List and define the key elements of the portion formula Solve for one unknown of the portion formula when the other two key elements are given Calculate the rate of percent decreases and increases Percent and Their Applications #6 Learning Unit Objectives Application of Percents -- Portion Formula LU6.2

5. 6-5 Table 6.1 - Bag of M&M’s Decimal Percent ColorFraction (hundredth)(hundredth) Yellow Yellow 18.33 32.73% 55 Red Red 10.18 18.18% 55 Blue Blue 9.16 16.36% 55 Orange Orange 7.13 12.73% 55 Brown Brown 6.11 10.91% 55 Green Green 5.09 9.09% 55 Total Total 55 1.00 100.00% 55 = 1

6. 6-6 Review the concept of “multiplying by 100” We have learned in Chapter 3, to multiply a certain number by 100, we do the following: Either (1) Add 2 zeros behind the “ones” place. Example: 23 x 100 = 2300 Or (2) Move the decimal point 2 places to the right. Example: 1.425 x 100 = 142.5

7. 6-7 Converting Decimals to Percents.66 66% 8 800% Step 1. Move decimal point 2 places to the right. You are multiplying by 100. If necessary add zeros. Step 2. Add a percent symbol at the end of the number

8. 6-8 Converting Decimals to Percents.425.42.5 42.5% Step 1. Move decimal point 2 places to the right. You are multiplying by 100. If necessary add zeros.

9. 6-9 Practice: Convert into Percentages 4.7 = (Move the decimal point 2 places to the right, add additional zero and place behind number ? ) % = 57.324 = (Move the decimal point 2 places to the right, and place behind number ? ) % = 41 = (Add 2 zeros behind number…)% = 0.936 = (Move the decimal point 2 places to the right, and place it behind number ? ) % =

10. 6-10 Rounding Percents.0588235 5.88% Step 1. When you convert from a fraction or decimal, be sure your answer is in percent before rounding. Step 2. Identify the specific digit. If the digit to the right of the identified digit is 5 or greater, round the identified digit. Delete digits to the right of the identified digit. 1 % 17.0588235

11. 6-11 Convention: Rounding Percentages Keep 2 digits after the decimal point. Use the 2 nd digit in the percentages as the specific digit. Look to the right and compare that digit with 5. If greater than 5, increase the previous digit. If less than 5, drop the rest of the digits. Examples: 1.3582% round up 1.36% 1.35285% round off 1.35%

12. 6-12 Practice: Convert and Round the Percentages 0.23518 = 14.78193 = 317.1729 = 2.9192 =

13. 6-13 Rounding Percents 18 55.3272727 32.73% 32.73727% 55 18.000000 = Step 1 Step 2 Step 3

14. 6-14 Convert From Fraction to Percentages (1) Change the fraction into decimals by dividing the numerator by the denominator. (2) Use the rule of changing decimals (whole number) into percentages. (3) Use the rounding rule.

15. 6-15 Converting Percents to Decimals 66%.66 8.244 824.4% Step 1. Drop the percent symbol. Step 2. Move decimal point 2 places to the left, You are dividing by 100. If necessary add zeros.

16. 6-16 Converting Percents to Decimals.95%.95.00.95.0095 Drop the percent symbol and move the decimal point 2 places to the left.

17. 6-17 Practice: Convert Percentages into Decimals 45% = (Drop % sign, place the decimal point 2 places from the ones to the left, and add zero if needed) 1.296% = (Drop % sign, place the decimal point 2 places to the left from its original place, and add 1 zero to fill the empty place before inserting the decimal)

18. 6-18 Converting Fractional Percents to Decimals.0025.0775 7 % Step 1. Convert a single fraction percent to its decimal equivalent by dividing the numerator by the denominator. Step 2. If a fractional percent is combined with a whole number ( mixed fractional percent) convert the fractional percent first. Then combine the whole number and the fractional percent. Step 3. Drop the percent symbol; move the decimal point two places to the left (this divides the number by 100). 1 % 4 3434

19. 6-19 Converting Fractional Percents to Decimals 1 % 5.20%.00.20.0020 5 1.00 = Step 1 Step 2 Step 3

20. 6-20 Practice: Convert into Percentages 1/2 % = (do the division first, and convert the result into percentage) 3 ¼% = (Convert ¼ into decimals, add to the whole number 3, and convert the result into percentage)

21. 6-21 Converting Fractions to Percents 3434 75% Step 1. Divide the numerator by the denominator to convert the fraction to a decimal. Step 2. Move decimal point 2 places to the right; add the percent symbol. 20% 1515

22. 6-22 Converting Fractions to Percents 1 20.05.05. 5% 20 1.00 = Step 1 Step 2 Step 3

23. 6-23 Practice: Convert into Percentages 4/5 = (Do the division, and convert the result into percentage) 4/5 = 0.8 = % 1/20 = (Do the division, and convert the result into percentage) 1/20 = 0.05 = %

24. 6-24 Converting a Whole Percent (or a Fractional Percent) to a Fraction 156% 1 1%81%8 Step 1. Drop the percent symbol. Step 2. Multiply the number by 1/100. Step 3. Reduce to lowest terms 1 800 14 25 56/ 100 Reduced by 4

25. 6-25 Converting a Whole Percent (or a Fractional Percent) to a Fraction 76% 76 x 1 100 76 100 19 25 Reduce to lowest terms Step 1 Step 2 Step 3 (76/100 Reduced by 4)

26. 6-26 Converting Percents to Decimals 12.5% 1818 12 1/2% Step 1. Drop the percent symbol. Step 2. Change the mixed percent to an improper fraction. Step 3. Multiply the number by 1/100 Step 4. Reduce to lowest terms Note: If you have a mixed or decimal percent, change the decimal portion to fractional equivalent and continue with Steps 1 to 4. 1818

27. 6-27 Converting a Mixed or Decimal Percent to a Fraction 22.5% 45 x 1 = 45 2 100 200 1 2 9 40 Reduce to lowest terms 22 Step 1 Step 2 Step 3

28. 6-28 Application of Percents - Portion Formula Portion (P) = Base (B) x Rate (R) Portion “is” Base “of” Rate “%” Assume you received a small bonus check of $100 and your company did not withhold any taxes. Compute taxes assuming a 20% in tax rate.

29. 6-29 Solving for Portion Sales of Milk Chocolate M&M’s® are 80% of total M&M’s® sales. Total M&M’s® sales are $400,000. What are the sales of Milk Chocolate M&M’s®? Portion (P)= Base (B) x Rate (R) P = $400,000 x.80 P = $320,000

30. 6-30 Solving for Rate Sales of Milk Chocolate M&M’s® are 320,000. Total M&M’s® sales are $400,000. What is the percent of Milk Chocolate M&M’s® sales compared to total M&M’s® sales? Rate = Portion Base R = $320, 000 $400,000 R = 80%

31. 6-31 Solving for Base Sales of Peanut and other M&M’s® chocolate candies are 20% of total M&M’s® sales. Sales of Milk Chocolate M&M’s® sales are $320,000. What are the total sales of all M&M’s®? Base = Portion Rate B = $320,000.80 B = $400,000 320,000 is 80% of base (1.00 -.20)

32. 6-32 Calculating Percent Decreases and Increases Step 1. Find the difference between amounts (such as advertising costs). Step 2. Divide step 1 by the original amount (the base): R = P / B. Be sure to express your answer in percent.

33. 6-33 Rate of Percent Decrease Rate = Portion Diff. between old and new TV price Base Old TV amount Rate = $600 $1,500 Rate =.40 or 40% Decrease Original Price $1,500 New Price $900 $1,500 – 900 = $600

34. 6-34 Rate of Percent Increase Rate = Portion Diff. between old and new TV price Base Old TV amount Rate = $200 $1,000 Rate =.20 or 20% Decrease Original Price $1,000 New Price $1,200 $1,200- 1,000 = $200

35. 6-35 Chapter 6 Homework 6.26-3 6-116-9 6-56-18 6-236-34 6-396-54

36. 6-36 Problem 6-59: Solution: $30.50 $4.50 = 6.7777 = 677.78% Do the division Convert into percentages Price sold to the antique store Original price bought

37. 6-37 Problem 6-61: Solution: $24,500 x 1.15 = $28,175 Selling price of the painting per bidding 1.15 is the bidding plus the premium add-on factor

38. 6-38 Problem 6-67: Solution: $19.95 $49.95 = 39.94% Price decrease amount: 49.95 – 30.00 = $19.95 Original selling price New selling price

39. 6-39 Reference Slater, J. (2008). Practical business math procedures (9 th ed.). New York: McGraw- Hill/Irwin