6 2 Estimating with Percents Warm Up Problem
6 -2 Estimating with Percents Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
6 -2 Estimating with Percents Warm Up Write each percent as a fraction. 1. 33. 3% 1 3 2. 75% 3 4 1 5 4. 60% 3 5 3. 20%
6 -2 Estimating with Percents Problem of the Day If you enlarge a picture by 25%, by what percent do you need to reduce it to return it to its original size? (Hint: Try using a simple number for the original area of the picture. ) 20%
6 -2 Estimating with Percents Sunshine State Standards Prep for MA. 8. A. 6. 4 Perform operations on real numbers (including…percents…)… Review MA. 6. A. 5. 3, Review MA. 7. A. 1. 2
6 -2 Estimating with Percents Vocabulary estimate compatible numbers benchmark
6 -2 Estimating with Percents An estimate is a useful answer that is close to the exact answer. Estimates involving percents and fractions can be found by using compatible numbers, numbers that go well together because they have common factors.
6 -2 Estimating with Percents When estimating with percents, it helps to know some benchmarks. Benchmarks are common numbers that serve as points of reference. Some common benchmarks for percents are shown in the table.
6 -2 Estimating with Percents Additional Example 1 A: Estimating with Percents Estimate. 21% of 66 21% ≈ 20% ≈ 1 5 Use a benchmark close to 21%. Write 20% as a fraction. 66 ≈ 65 Use compatible numbers, 65 and 5. 65 = 13 Use mental math: 65 ÷ 5. So 21% of 66 is about 13.
6 -2 Estimating with Percents Additional Example 1 B: Estimating with Percents Estimate. 36% of 120 Instead of computing the exact answer of 36% 120, estimate. 36% 35% Round. 30% + 5% 3 35% Break down the percent into smaller parts. 10% + 5% 120 = (3 10% + 5%) 120 Set up an equation.
6 -2 Estimating with Percents Additional Example 1 B Continued =3 10% = 36 + 6 120 + 5% 120 Use Distributive Property. 10% of 120 is 12, so 5% of 120 is 6. = 42 So 36% of 120 is about 42.
6 -2 Estimating with Percents Check It Out: Example 1 A Estimate. 29% of 86 29% ≈ 30% ≈ 3 10 86 ≈ 90 3 10 90 = 27 Use a benchmark close to 29%. Write 30% as a fraction. Use compatible numbers, 90 and 10. Use mental math: 90 ÷ 10. So 29% of 86 is about 27.
6 -2 Estimating with Percents Check It Out: Example 1 B Estimate. 44% of 130 Instead of computing the exact answer of 44% 130, estimate. 44% 45% Round. 40% + 5% 4 45% Break down the percent into smaller parts. 10% + 5% 130 = (4 10% + 5%) 130 Set up an equation.
6 -2 Estimating with Percents Check It Out: Example 1 B Continued =4 10% = 52 + 6. 5 = 58. 5 130 + 5% 130 Set up an equation. 10% of 130 is 13, so 5% of 130 is 6. 5. So, 44% of 130 is about 58. 5.
6 -2 Estimating with Percents Additional Example 2: Problem Solving Application Maria took her mother out to lunch for her birthday. The total cost of their food, drinks, and dessert was $20. 15. if the sales tax was 7% and Maria wants to leave a 15% tip, about how much should she pay?
6 -2 Estimating with Percents Additional Example 2 Continued 1 Understand the Problem The answer is the total amount Maria should pay for their lunch. List the important information: • The total cost of food, drinks, and dessert was $20. 15. • The sales tax is 7%. • Maria wants to leave a 15% tip.
6 -2 Estimating with Percents Additional Example 2 Continued 2 Make a Plan Think: Sales tax and tip together are 22% of Maria and her mother’s lunch total (7% + 15% = 22%). The numbers $20. 15 and 22% are difficult to work with. Use compatible numbers: $20. 12 is close to $20. 00; 22% is close to 20%.
6 -2 Estimating with Percents Additional Example 2 Continued 3 Solve $20. 00 20% = $20. 00 = $4. 00 $20. 15 + $4. 00 = $24. 15. Maria should pay $24. 15. 0. 20
6 -2 Estimating with Percents Additional Example 2 Continued 4 Look Back To determine whether $24. 15 is a reasonable estimate of what Maria should pay; use a calculator to find the tax and the tip for $20. 15 1. 22 = $24. 58, so $24. 15 is a reasonable estimate.
6 -2 Estimating with Percents Check It Out: Example 2 Fred and Claudia went out to lunch. The total cost of their food and drinks, was $24. 85. If the sales tax was 8. 5% and they want to leave a 16% tip, about how much should they pay?
6 -2 Estimating with Percents Check It Out: Example 2 Continued 1 Understand the Problem The answer is the total amount Fred and Claudia should pay for their lunch. List the important information: • The total cost of food, drinks, and dessert was $24. 85. • The sales tax is 8. 5%. • They wants to leave a 16% tip.
6 -2 Estimating with Percents Check It Out: Example 2 Continued 2 Make a Plan Think: Sales tax and tip together are 24. 5% of Fred and Claudia’s lunch total (8. 5% + 16% = 24. 5%). The numbers $24. 85 and 24. 5% are difficult to work with. Use compatible numbers: $24. 85 is close to $25. 00; 24. 5% is close to 25%.
6 -2 Estimating with Percents Check It Out: Example 2 Continued 3 Solve $25. 00 25% = $25. 00 0. 25 = $6. 25 $24. 85 + $6. 25 = $31. 10. Fred and Claudia should pay $31. 10.
6 -2 Estimating with Percents Check It Out: Example 2 Continued 4 Look Back To determine whether $31. 10 is a reasonable estimate of what Fred and Claudia should pay; use a calculator to find the tax and the tip for $24. 85 1. 245 = $30. 94, so $31. 10 is a reasonable estimate.
6 -2 Estimating with Percents Additional Example 3: Printing Application A printing company has determined that approximately 6% of the books it prints have errors. Out of a printing run of 2050 books, the production manager estimates that 250 books have errors. Estimate to see if the manager’s number is reasonable. Explain. 6% 2050 ≈ 5% 2000 Use compatible numbers. ≈ 0. 05 ≈ 100 2000 Write 5% as a decimal. Multiply. The manager’s number is not reasonable. Only about 100 books have errors. 250 is much greater that 100.
6 -2 Estimating with Percents Check It Out: Example 3 A clothing company has determined that approximately 9% of the sheets it makes are irregular. Out of a shipment of 4073, the company manager estimates that 397 sheets are irregular. Estimate to see if the manager’s number is reasonable. Explain. 9% 4073 ≈ 10% 4000 Use compatible numbers. ≈ 0. 10 4000 Write 10% as a decimal. ≈ 400 Multiply. Because 397 is close to 400, the manager’s number is reasonable.
6 -2 Estimating with Percents Lesson Quizzes Standard Lesson Quiz for Student Response Systems
6 -2 Estimating with Percents Lesson Quiz: Part I Estimate. Possible answers: 1. 34% of 12 4 2. 113% of 80 90 3. Ian had dinner with some friends at a restaurant. His food and drink cost $10. 25. If the sales tax is 8. 25% and he wants to leave a 20% tip, about how much should Ian pay? $13. 00
6 -2 Estimating with Percents Lesson Quiz: Part II 4. Approximately 8% of each batch of jeans produced at one factory is defective. Ms. Fleming said that in a batch of 400 jeans, about 35 jeans would be defective. Estimate to determine if her number is reasonable. Explain. Yes, it is reasonable because 8% of 400 is a little less than 10% of 400 is 40, and 35 is a little less than 40.
6 -2 Estimating with Percents Lesson Quiz for Student Response Systems 1. Estimate. 26% of 35 A. 8 B. 9 C. 17 D. 26
6 -2 Estimating with Percents Lesson Quiz for Student Response Systems 2. Smith bought a book at an online store. The cost of the book was $12. 25. If the sales tax rate is 7. 75% and the shipping charges are 10% of the cost of the book, about how much should he pay? A. $13. 00 B. $14. 50 C. $15. 25 D. $16. 50
6 -2 Estimating with Percents Lesson Quiz for Student Response Systems 3. On an average 9% of the CDs produced by a company are defective. The Quality Control Manager states that out of 1300 CDs produced, 121 are defective. Estimate to determine if his number is reasonable. Explain. A. yes; because 9% of 1300 is a little less than 10% of 1300 is 130 and 121 is a little less than 130. B. no: because 9% of 1300 is a little greater than 10% of 1300 is 130 which is greater than 121.
- Slides: 31