2. Ratio —comparison of 2 quantities by division Written using to, :, fraction Ex: 10 to 15, 10:15, 10/15

3. Rate —ratio that compares quantities in different units Unit Rate- -denominator of 1 Can be used when finding the “best buy” Ex: miles/gallon

4.  Ex: 2 L of soda for $1.98, how much for 1 L? 1.98 = 0.99 2 1

5. Fractions, Decimals, Percents

6. Percent to Fraction Write each percent as a fraction and reduce Ex: 5 % = 5 = 1 100 20 Ex: 125 % = 125 = 5 = 1 ¼ 100 4

7. Fraction to Percent Divide numerator by denominator Then move decimal point 2 places to the right Ex: 5 = 0.3125 = 31.25 % 16 Ex: 3 = 0.27 = 27 % 11

8. Percent to Decimal Move decimal point 2 places to left Ex: 16 % = 0.16 Ex: 9.7 % = 0.097 add a zero in front of the 9 for extra place

9. Decimal to Percent Move decimal point 2 places to right Ex: 0.33 = 33 % Ex: 0.023 = 2.3 %

11.  Proportion—equation with 2 equal ratios  Cross Product—the product of the numerator in one ratio and the denominator in the other ratio  Cross Products are used to find a missing quantity in a proportion  When the two ratios are equal, then the cross products are equal  You can use cross products to find out if 2 ratios form a proportion

12.  Ex: x = 4 9 6 6x = 9 * 4 6x = 36 6 6 x = ?

13.  Ex: h = 2 9 3 3h = 2 * 9 3h = 18 3 3 h = ?

14.  Ex: Do the ratios 6/9 and 4/6 form a proportions? 6 = 4 9 6 6 * 6 = 9 * 4 ? = ?

16.  *Remember* a percent is part of a whole and is out of 100  To solve:  Multiply the number by the percent

17.  1.) 15% of 40  2.) 80% of 460  3.) 20% of 25  4.) 49% of 300  5.) 11% of 720

18.  Use a proportion to solve  Don’t forget that % are out of 100  Remember: is/of for the correct placement of numbers in the proportion  Always: Part/whole

19.  Finding the Percent Ex: What % of 40 is 6? n = 6 part 100 40 whole

20.  Finding the Part: Ex: What is 15% of 40? 15 = n part 100 40 whole

21.  Finding the Whole Ex: 6 is 15% of what number? 15 = 6 part 100 x whole

22.  Ex: What percent of 250 is 138?

23.  Ex: 207 is 46 % of what number?

24.  Ex: What percent of 60 is 52?

25.  Ex: What is 85% of 62?

26.  Ex: 0.96 is what percent of 10?

27.  Ex: 19.2 is 32 % of what?

28.  Ex: What percent of 48 is 54?

29.  Ex: What is 145.5% of 20? 

30.  Ex: 380 is 125% of what number?

32.  Tax = % times purchase price  To find the total, add the answer back to the price  Ex: $159.99 desk sales tax 6% 159.99 x 6% =9.5994 (9.60)

33.  Tip = % times the price  To find the total, add the tip amount back to the price Ex: $9.68 meal, 7% tip 9.68 x 7% = 0.6776 (0.68) 9.68 + 0.68 = 10. 36

34.  Commission= % times the price  Ex: $500 with 12.5% commission 500 x 12.5% = 62.50

35.  1st method:  Discount = percent of discount * regular price  Subtract answer from regular price  Ex: A pair of shoes costs $85.99 and are on sale for 20% off. Find the discount. 20% * 85.99 0.20 * 85.99 = 17.20 85.99 – 17.20 = $68.79

36.  2 nd method:  Subtract the percent from 100  then multiply new % to regular price Ex: A video game costs $39.95 and is on sale for 20% off. What is the sale price? 100 – 20 = 80% 80% * 39.95 = $31.96

37.  Ex: A pair of pants cost $21.99 and are marked 15% off. Find the discount. 100 – 15 = 85% 85% x 21.99 = $18.70 15% x 21.99 = 3.30 21.99 – 33.30= 18.70

38.  Ex: A book cost $21.99 and is on sale for 25% off. What is the sale price? 100 – 25 = 75% 75% x 21.99 = 16.50

39.  Ex: A singer receives a 5% royalty on each CD sale. Find the royalty for a $16.99 CD.  C = 5% * 16.99  C = 0.05 * 16.99  C = ?

40.  Ex: How many people were surveyed if 1023 people is 93% of the population?  1023 = 93% * n  1023 = 0.93 * n  ? = n

41.  Ex: In a survey, 922 people or 68.6% preferred smooth peanut butter. How many people were surveyed?  922 = 68.6% * p  922 = 0.686 * p  ? = p

43.  Percent a quantity increases or decreases from its original amount  Percent of change = amount of change original amount

44.  Percent of increase = amount of change original amount Ex: Find percent of increase from 4 to 7.5 7.5 – 4 = 3.5 = 3.5 4

45.  Ex: from 100 to 114  114 – 100 = 14  14 =  100

46.  Ex: from 2.0 to 3.2  3.2 – 2.0 = 1.2  1.2 =  2.0

47.  Ex: from 4000 to 8500  8500 – 4000 = 4500  4500 =  4000

48.  Percent of decrease = amount of change  original amount  Ex: Find percent of decrease from 1500 to 1416  1500 – 1416 = 84 = 84  1500

49.  Ex: from 9.6 to 4.8  9.6 – 4.8 = 4.8  4.8 = 9.6

50.  Ex: from 202 to 192  202 – 192 = 10  10 =  202

51.  Ex: from 854.5 to 60.6  854.5 – 60.6 = 793.9  793.9 =  854.5

53.  Selling price– store’s cost plus the markup  Multiply the cost to the % then add back to the original cost to find the selling price  Ex: $5.25 with 10% mark-up 5.25 x 10 % = ? 5.25 + ? = ?

54.  Ex: Percent mark-up for a music store is 67% and the CD costs $10.15. Find the mark-up.

55.  Ex: A jacket costs $56 and the percent mark-up is 75%. Find the mark-up.

56.  Ex: A computer store pays $6 for a mouse and the percent mark-up is 75%. What is the selling price?

57.  Ex: A $5 hat has a 70% mark-up. Find the selling price.

58.  Ex: A bike that cost $525 a year ago is now worth $472.50. What is the percent decrease?

59.  Ex: A $70 coat is now worth $59. What is the percent decrease?

60.  Ex: A new stereo cost $425 now costs $382.50. What is the percent discount?