1. Course 3 6-2 Estimate with Percents 6-2 Estimate with Percents Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Course 3 6-2 Estimate with Percents Warm Up Write each percent as a fraction. 1. 33%2. 75% 3. 20%4. 60% 1 3 3 4 1 5 3 5

3. Course 3 6-2 Estimate 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%

4. Course 3 6-2 Estimate with Percents Learn to estimate with percents.

5. Course 3 6-2 Estimate with Percents Vocabulary estimate compatible numbers benchmark

6. Course 3 6-2 Estimate with Percents Some problems require only an estimate. Estimates involving percents and fractions can be found by using compatible numbers, numbers that go well together because they have common factors. 12 24  compatible 13 24 not compatible

7. Course 3 6-2 Estimate 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. PercentDecimalFraction 5%0.05 10%0.1 25%0.25 50%0.5 66.6%0.6 100%11 1 20 1 10 1414 1212 2323

8. Course 3 6-2 Estimate with Percents Estimate. 21% of 66 Additional Example 1A: Estimating with Percents 21% ≈ 20%Use a benchmark close to 21%. ≈ 1 5 Write 20% as a fraction. 66 ≈ 65 Use compatible numbers, 65 and 5. 1 5  65 = 13 Use mental math: 65 ÷ 5. So 21% of 66 is about 13.

9. Course 3 6-2 Estimate with Percents Estimate. 36% of 120 Additional Example 1B: Estimating with Percents Instead of computing the exact answer of 36%  120, estimate. 36%  35%Round.  30% + 5%Break down the percent into smaller parts.  3  10% + 5% 35%  120 = (3  10% + 5%)  120 Set up an equation.

10. Course 3 6-2 Estimate with Percents Additional Example 1B Continued = 36 + 610% of 120 is 12, so 5% of 120 is 6. = 42 So 36% of 120 is about 42. = 3  10%  120 + 5%  120 Use Distributive Property.

11. Course 3 6-2 Estimate with Percents Estimate. 29% of 86 Check It Out: Example 1A 29% ≈ 30%Use a benchmark close to 29%. ≈ 3 10 Write 30% as a fraction. 86 ≈ 90 Use compatible numbers, 90 and 10. 3 10  90 = 27 Use mental math: 90 ÷ 10. So 29% of 86 is about 27.

12. Course 3 6-2 Estimate with Percents Estimate. 44% of 130 Instead of computing the exact answer of 44%  130, estimate. 44%  45%Round.  40% + 5%Break down the percent into smaller parts.  4  10% + 5% 45%  130 = (4  10% + 5%)  130 Set up an equation. Check It Out: Example 1B

13. Course 3 6-2 Estimate with Percents = 52 + 6.5 10% of 130 is 13, so 5% of 130 is 6.5. = 58.5 So, 44% of 130 is about 58.5. = 4  10%  130 + 5%  130 Set up an equation. Check It Out: Example 1B Continued

14. Course 3 6-2 Estimate with Percents 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? Additional Example 2: Problem Solving Application

15. Course 3 6-2 Estimate 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.

16. Course 3 6-2 Estimate with Percents 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%. Additional Example 2 Continued

17. Course 3 6-2 Estimate with Percents Solve 3 $20.00  20% = $20.00  0.20 = $4.00 $20.15 + $4.00 = $24.15. Additional Example 2 Continued Maria should pay $24.15.

18. Course 3 6-2 Estimate with Percents Look Back4 Additional Example 2 Continued 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. $20.15  1.22 = $24.58, so $24.15 is a reasonable estimate.

19. Course 3 6-2 Estimate with Percents 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? Check It Out: Example 2

20. Course 3 6-2 Estimate 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.

21. Course 3 6-2 Estimate with Percents 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%. Check It Out: Example 2 Continued

22. Course 3 6-2 Estimate with Percents Solve 3 $25.00  25% = $25.00  0.25 = $6.25 $24.85 + $6.25 = $31.10. Check It Out: Example 2 Continued Fred and Claudia should pay $31.10.

23. Course 3 6-2 Estimate with Percents Look Back4 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. $24.85  1.245 = $30.94, so $31.10 is a reasonable estimate. Check It Out: Example 2 Continued

24. Course 3 6-2 Estimate 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%  2000Use compatible numbers. ≈ 0.05  2000Write 5% as a decimal. Multiply. ≈ 100 The manager’s number is not reasonable. Only about 100 books have errors. 250 is much greater that 100.

25. Course 3 6-2 Estimate 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%  4000Use compatible numbers. ≈ 0.10  4000Write 10% as a decimal. Multiply. ≈ 400 Because 397 is close to 400, the manager’s number is reasonable.

26. Course 3 6-2 Estimate with Percents Lesson Quiz: Part 1 Estimate. 1. 34% of 12 2. 113% of 80 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? 4 90 $13.23 Possible answers:

27. Course 3 6-2 Estimate with Percents Lesson Quiz: Part 2 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. 10% of 400 is 40, and 35 is a little less than 40.