Percent of a number

1. Percent of a number Lesson 1

2. Find the Percent of a Number To find the percent of a number, choose one of the methods 1. Write percent as a fraction and then multiply. OR 2. Write percent as a decimal and then multiply.

3. Example 1 Find 5% of 300 by writing the percent as a fraction. 5% = of 300 = x 300 x = = = 15 So, 5% of 300 is 15.

4. Example 2 Find 25% of 180 by writing the percent as a decimal. 25% = 0.25 0.25 of 180 = 0.25 x 180 Solve this without a calculator. So, 25% of 180 is 45.

5. Got it? Find the percent of each number. a. 40% of 70 b. 15% of 100 c. 55% of 160 d. 75% of 280 28 15 88 210

6. Use Percents Greater Than 100% 150% = = = 1 = 1.5

7. Example 3 Find 120% of 75 by writing the percent as a fraction. Write 120% as of . of 75 = x x = x 6 x 15 = 90 So, 120% of 75 is 90.

8. Example 4 Find 150% of 28 by writing the percent as a decimal. Write 150% as . of 28 1.5 x 28 = 42 So, 150% of 28 is 45.

9. Got it? Find each number. a. 150% of 20 b. 160% of 35 30 56

10. Example 5 Refer to the graph. If 275 students took the survey, how many can be expected to have 3 TV’s in each of their houses? 23% of 275 0.23 x 275 = 63.25 So, about 63 students can be expected to have a 3 TV’s in their house.

11. Percent and estimation Lesson 2

12. Estimate the Percent of a Number Sometimes an exact answer is not needed when using percents. Take 70%. 70% = 70% = 7 x 10%

13. Example 1 Jodi has paid 62% of the $500 she owes for her loan. Estimate 62% of 500. 62% of 500 60% of 500 60% = 0.6 0.6 x 500 = 300 So, 62% of $500 is about $300.

14. Example 2 Marita and four of her friends ordered a pizza that cost $14.72. She is responsible for 20% of the bill. About how much money will she need to pay? $14.72 is close to $15. Find 10% of 15, which is $1.5. Multiply $1.5 by 2, since 20% is twice as much as 10%. $1.5 x 2 = $3.00 Maritashould pay about $3.00.

15. Got it? • Estimate 42% of 120. • Dante plans to put 80% of his paycheck into a savings account and spend the other 20%. His paycheck this week is $295. About how much will he put into his savings account? 48 About $240

16. Example 3 Estimate 122% of 50. 122% = 100% + 22% 100% of 50 + 22% of 50 (1 x 50) + (20% x 50) 50 + ( x 50) 50 + 10 = 60 So, 122% of 50 is about 60.

17. Example 4 There are 789 seventh grader students at Washington Middle School. About of the 7th grade students have traveled overseas. What is the approximate number of 7th graders that have traveled overseas? Explain. % can be estimated to 1%. 789 can be estimated to 800. 1% x 800 = 0.01 x 800 = 8 8 x = 2 So, about 2 seventh graders have traveled overseas.

18. Got it? A country receives of a sales tax. About how much money would a country receive from the sale of a computer that costs $1,020? % can be estimated to 1%. 1,020 can be estimated to 1000. 1% x 1000 = 0.01 x 1000 = 10 10 x = 7.5 So, it would cost about $7.50 in tax.

19. Example 5 Last year, 639 students attended summer camp. Of those who attended this year, 0.5% also attended camp last year. About how many students attended the summer camp two years in a row? 0.5% is half of 1%. 1% of 639 6 So, 0.5% of 639 is half of 6 or 3. About 3 students attended summer camp two years in a row.

20. The Percent Proportion Lesson 3

21. Use the Percent Proportion 4 out of 5 is 80% = =

22. Example 1 What percent $15 is $9? Ask: What type of percent proportion do you use? Find the percent. Let n represent the percent. In the table, the first number is the denominator and the second number in the numerator. 9(100) = 15n 900 = 15n Divide 900 and 15. n = 60

23. Got it? a. What percent of 25 is 20? 80% b. $12.75 is what percent of 4? 25.5%

24. Example 2 What number is 40% of 120? p • 100 = 120 • 40 100p = 4800 p = 48 So, 48 is 40% of 120.

25. Got it? a. What number is 5% of 60? 3 b. 12% of 85 is what number? 112

26. Example 3 18 is 25% of what number? w • 25 = 18 • 100 25w = 1800 w = 72 So, 18 is 25% of 72.

27. Got it? a. 40% of what number is 26? 65 b. 84 is 75% of what number? 112

28. Example 4 The average adult male Western Lowland gorilla eats about 33.5 pounds of fruit each day. How much food does the average adult male gorilla eat each day? 33.5 •100 = w • 67 3350 = 67w 50 = w So, an average male gorilla eats 50 pounds of food each day.

29. The Percent Equation Lesson 4

30. Percent Equation Part = percent • whole whole = percent • _____________ ____________ = percent • whole percent whole part

31. Use the Percent Equation 3 = n • 6 p = 0.5 • 6 3 = 0.5 • w 3 is 50% of 6 3 = 0.5 x 6 part percent whole

32. Example 1 What number is 12% of 150? Do you need to find percent, part or whole? ________ part = 0.12 • 150 p = 18 So, 18 is 12% of 150. part

33. Got it? 1 Write an equation and solve. a. What is 6% of 200? p = 0.06 • 200 p = 12 c. What is 14% of 150 p = 0.14 • 150 p = 21 b. Find 72% of 50. p = 0.72 • 50 p = 36 d. Find 50% of 70. p = 0.5 • 70 p = 35

34. Example 2 21 is what percent of 40? Do you need to find percent, part or whole? ________ 21 = n • 40 = n 0.525 = n So, 21 is 52.5% of 40. percent

35. Got it? 2 Write an equation and solve. a. What percent of 40 is 9? 9 = n • 40 22.5% = n b. 27 is what percent of 150? 27 = n • 150 18% = n

36. Example 3 13 is 26% of what number? Do you need to find percent, part or whole? ________ 13 = 0.26 • w = w 50 = w So, 13 is 26% of 50. whole

37. Got it? 3 Write an equation and solve. a. 39 is 84% of what number? 39 = 0.84 • w 46.4= w b. 26% of what number is 45? .26 = w• 45 173.1 = w

38. Example 4 A survey found that 25% of people aged 18-24 gave up their home phone and only use a cell phone. If 3264 people only used a cell phone, how many people were surveyed? Do you need to find percent, part or whole? ________ 3,264 = 0.25w 13,056 = w About 13,056 people were surveyed. whole

39. Percent of Change Lesson 5

40. Percent of Change Words: A percent of change is the ratio that compares the change in quantity to the original amount. Equation: percent of change =

41. Percent of Increase and Decrease Increase: percent of increase = Decrease: percent of decrease =

42. Example 1 Find the percent of change in the cost of gasoline from 1970 to 2010. Round to the nearest whole percent if necessary. This is a percent increase. It increased $1.65. percent of increase = = ≈ 1.27 or 127% The cost of gasoline increase by about 127% from 1970 to 2010.

43. Example 2 Yusuf bought a DVD recorder for $280. Now it is on sale for $220. Find percent of change in the price. Round to the nearest whole percent if necessary. This is a percent decrease. It decreased by $60. percent of decrease = = ≈ 0.21 or 21% The price of the DVD recorder decreased by about 21%.

44. Got it? 1 & 2 a. Find the percent of change from 10 yards to 13 yards. 30% increase b. The price of a radio was $20. It is on sale for $15. What is the percent of change in the price of a radio? 25% decrease

45. Percent Error Words: A percent error is a ratio that compares the inaccuracy of an estimate, or amount of error, to the actual amount. Equation: percent error = Suppose you guess there are 300 gum balls in the jar, and you guessed 400. =

46. Example 3 Ahmed wants to practice free-throws. He estimates the distance from the free-throw line to the hoop and marks it with chalk. Ahmed’s estimate was 13.5 feet. The actual distance should be 15 feet. Find the percent error. = The percent error is 10%.

47. Sales Tax, Tips, and Markups Lesson 6

48. Example 1 – Sales Tax Drew wants to buy exercise equipment that cost $140 and the sales take is 5.75%. What is the total cost? Add sales tax to the regular price. First, find the sales tax. Let t represent sales tax. t = 0.0575 x 140 t = 8.05 Next, add the sales tax to the regular price. $8.05 + 140 = $148.05

49. Example 1 – Sales Tax Drew wants to buy exercise equipment that cost $140 and the sales take is 5.75%. What is the total cost? Add the percent of tax to 100%. 100% + 5.75% = 105.75% Let t represent sales tax. t = 1.0575 x 140 t = $148.05 The total cost of the exercise equipment is $148.05.

50. Got it? 1 What is the total cost of a sweatshirt if the regular price is $42 and the sales tax is 5%? $44.31