1. RATIOS & PROPORTIONS A ratio is a comparison of two numbers by division. To write ratios, use the word to, a colon, or a fraction bar. EXAMPLE #1: John read 3 books in 4 days. Write the ratio of books to days. Words: 3 to 4Colon: 3:4 Fraction: 3/4

2. RATIOS & PROPORTIONS There are 5 men and 6 women in my class. 1. What is the ratio of women to men using a fraction? 2. What is the ratio of women to students in my class (use a colon)? 3. What is the ratio of men to students in my class (use words)?

3. RATIOS & PROPORTIONS There are 5 men and 6 women in my class. 1. What is the ratio of women to men using a fraction? 2. What is the ratio of women to students in my class (use a colon)? 6:11 3. What is the ratio of men to students in my class (use words)? 5 to 11

4. RATIOS & PROPORTIONS A proportion is a statement that two ratios are equal. EXAMPLE#2: Is a proportion? Find the cross products. 30 = 30 TRUE If TRUE, the statement is a proportion.

5. RATIOS & PROPORTIONS EXAMPLE#3: Is a proportion? Find the cross products.

6. RATIOS & PROPORTIONS EXAMPLE#3: Is a proportion? Find the cross products. 20 = 21 FALSE If FALSE, the statement is NOT a proportion.

7. RATIOS & PROPORTIONS

8. FALSE – Not a proportion

9. RATIOS & PROPORTIONS

10. FALSE – Not a proportion

11. RATIOS & PROPORTIONS Are the following proportions?

12. RATIOS & PROPORTIONS TRUE – this is a proportion

13. RATIOS & PROPORTIONS EXAMPLE#4: Solve the proportion: Find the cross products. Multiply both sides of the proportion. 10 Divide both sides by 10.

14. RATIOS & PROPORTIONS Find the missing numbers to make the following proportions. 9

15. RATIOS & PROPORTIONS Find the missing numbers to make the following proportions.

16. RATIOS & PROPORTIONS Find the missing numbers to make the following proportions. 10

17. If 5 ounces of a medicine must be mixed with 8 ounces of water, how many ounces of medicine would be mixed with 36 ounces of water?

18. If 5 ounces of a medicine must be mixed with 8 ounces of water, how many ounces of medicine would be mixed with 36 ounces of water? Solution Let m represent how much medicine would be needed. 22.5 ounces of medicine would be needed. 8 8 Find the cross products. Multiply both sides of the proportion by the denominator of the fraction containing the unknown

19. Jane drives her delivery van 800 miles in 3 days. At this rate, how far will she drive in 15 days?

20. Jane would drive 4000 Miles in 15 days 3 15 Find the cross products. Multiply both sides of the proportion by the denominator of the fraction containing the unknown Distance in 3 daysDistance in 15 days time 800 x 15 = 3d 3 3 800 x 15 = 12000 3 d=4000

21. Definition Percent can be defined as “of one hundred.”

22. Slide 4- 22 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Notation for n % Percent notation, n%, can be expressed using: ratio  n% = the ratio of n to 100 = fraction notation  decimal notation 

23. Slide 4- 23 To solve a problem involving percents, it is helpful to translate first to an equation. For example, “23% of 5 is what?” “Of” translates to “  ” or “  ”.multiplication “Is” translates to “=”.equal “What” translates to any letter. “%” translates to

24. How to Find the Percent of a Whole Number What number is 75% of 4? 3 is what percent of 4? Using the PROPORTION METHOD, the set-up is always the same:

25. PERCENT-- the number with the percent sign (%). PART-- the number with the word is. WHOLE -- the number with the word of. What number is 75% of 4? 3 is what percent of 4?

26. NOW, to change a percentage into a decimal, you can divide by 100 or replace the percent symbol with  0.01, and 35%/ 100 35x0.01 0.35.35

27. Slide 4- 27 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write an equivalent decimal for 67.34%.

28. Slide 4- 28 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write an equivalent decimal for 67.34%. a) Replace the % symbol with * 0.01. 67.34 * 0.01 b) Multiply to move the decimal point two places to the left.0.67.34 67.34% = 0.6734. or Divide 67.34%/100=0.6734

29. To change decimal into a percentage DecimalPercentage To change a decimal into a percentage, you X by 100 0.23 23% X 100

30. To change decimal into a percentage DecimalPercentage To change a decimal into a percentage, you X by 100 0.45 ? X 100

31. Slide 4- 31 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To convert from fraction notation to percent notation, a) find decimal notation by division, and b) convert the decimal notation to percent notation. 0.6 = 0.60 = 60% Percent notation

32. Slide 4- 32 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find the percent notation

33. Slide 4- 33 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley a) Find decimal notation by division. b) Convert the decimal notation to percent notation. To do so, multiply by 100 to move the decimal point two places to the right, and write a % symbol.

34. Slide 4- 34 Translate: What is 19% of 82? What is 19% of 82?  | | | |  a = 19% x 82  19/100 =.19 .19 x 82 = 15.58

35. Slide 4- 35 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example B Translate: 7 is 10% of what? 7 is 10% of what? | | | | | 7 = 10% x b

36. Slide 4- 36 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example B Translate: 7 is 10% of what? 7 is 10% of what? | | | | | 7 = 10% x b 7 /.10 = 70

37. Try these 25% of 32

38. .25 x 32 = 8

39. 75% of 36

40. 75% of 36 = 27

41. Slide 4- 41 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The sales tax rate in Ohio is 6%. How much tax is charged on the purchase of 4 books at $15.95 each? What is the total price?

42. Slide 4- 42 The sales tax rate in Ohio is 6%. How much tax is charged on the purchase of 4 books at $15.95 each? What is the total price? Solution a) We first find the cost of the books. 4 × $15.95 = $63.80 b) The sales tax on items costing $63.80 is Sales tax rate × Purchase price 0.06 × $63.80 or $3.83

43. Slide 4- 43 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley A person’s sales commission is 8%. What is the commission from the sale of $73,230 worth of new car sales? Commission = Commission rate × Sales

44. Slide 4- 44 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley A person’s sales commission is 8%. What is the commission from the sale of $73,230 worth of new car sales? Commission = Commission rate × Sales C = 8% × 73,230 C = 0.08 × 73,230 C = 5858.40 The commission is $5858.40.

45. Monica Yuskaitis Credits Clipart from “Microsoft Clip Gallery” located on the Internet at http://cgl.microsoft.com/http://cgl.microsoft.com/ clipgallerylive/default.asp Pearson Education, Inc. Publishing as Pearson Addison-Wesley