1. 3-1 Estimating with Decimals Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes Objective: Students estimate decimal sums, differences, products, and quotients

2. 3-1 Estimating with Decimals Warm Up Estimate. 1. 27 30 2. 85 92 3. 12 28 4. 185 201 900 8,100 300 40,000

3. 3-1 Estimating with Decimals Problem of the Day I am a two-digit decimal greater than 0.25 and less than. My hundredths digit is 3 times my tenths digit. What number am I? 0.26 or 0.39 5 2

4. 3-1 Estimating with Decimals Learn to estimate decimal sums, differences, products, and quotients.

5. 3-1 Estimating with Decimals Vocabulary compatible numbers

6. 3-1 Estimating with Decimals Jessie earned $26.00 for baby-sitting. She wants to use the money to buy a ticket to a water park for $14.75 and a souvenir T-shirt for $13.20. To find out if Jessie has enough money to buy both items, you can use estimation. To estimate the total cost of the ticket and the T-shirt, round each price to the nearest dollar, or integer. Then add the rounded values.

7. 3-1 Estimating with Decimals $14.7577 > 5, so round to $15$15 $13.202 2 < 5, so round to $13 $13 + $28 The estimated cost is $28, so Jessie does not have enough money to buy both items. To estimate decimal sums and differences, round each decimal to the nearest integer and then add or subtract.

8. 3-1 Estimating with Decimals To round to the nearest integer, look at the digit in the tenths place. If it is greater than or equal to 5, round to the next integer. If it is less than 5, keep the same integer. Remember!

9. 3-1 Estimating with Decimals Estimate by rounding to the nearest integer. 4.5 + 8.9 55 ≥ 5, so round to 5. 9 > 5, so round to 9. 4.5 +8.9 14 Estimate +9 Additional Example 1A: Estimating Sums and Differences of Decimals

10. 3-1 Estimating with Decimals Estimate by rounding to the nearest integer. 28.3 – 11.7 283 < 5, so round to 28. 7 > 5, so round to 12. 28.3 –11.7 16 Estimate –12 Additional Example 1B: Estimating Sums and Differences of Decimals

11. 3-1 Estimating with Decimals Estimate by rounding to the nearest integer. 57.2 + (–23.72) 572 < 5, so round to 57. 7 > 5, so round to –24. 57.2 + (–23.72) 33Estimate + (–24) Additional Example 1C: Estimating Sums and Differences of Decimals

12. 3-1 Estimating with Decimals Estimate by rounding to the nearest integer. 6.7 + 4.9 78 ≥ 5, so round to 7. 9 > 5, so round to 5. 6.8 +4.9 12 Estimate +5 Check It Out: Example 1A

13. 3-1 Estimating with Decimals Estimate by rounding to the nearest integer. 19.2 – 13.6 192 < 5, so round to 19. 6 > 5, so round to –14. 5 Estimate –14 Check It Out: Example 1B 19.2 –13.6

14. 3-1 Estimating with Decimals Estimate by rounding to the nearest integer. 61.3 + (–18.84) 613 < 5, so round to 61. 8 > 5, so round to –19. 61.3 + (–18.84) 42Estimate + (–19) Check It Out: Example 1C

15. 3-1 Estimating with Decimals Compatible numbers are numbers that replace the numbers in the problem and are easier to use. You can use compatible numbers when estimating.

16. 3-1 Estimating with Decimals Guidelines for Using Compatible Numbers When multiplying... round numbers to the nearest nonzero integer or to numbers that are easy to multiply. When dividing... round numbers so that they divide without leaving a remainder.

17. 3-1 Estimating with Decimals Use compatible numbers to estimate. 45.99 · 2.31 50 Round to the nearest multiple of 10. 100 Estimate  2 Additional Example 2A: Estimating Products and Quotients of Decimals 3 < 5, so round to 2. 45.99  2.31

18. 3-1 Estimating with Decimals Use compatible numbers to estimate. 51.33 ÷ (–7.98) 51.33 48 51 is prime, so round to 48. –8 –8 divides into 48 without a remainder. –7.98 Estimate Additional Example 2B: Estimating Products and Quotients of Decimals 48 ÷ –8 = –6 A prime number has exactly two factors. 1 and itself. So the factors of 51 are 1 and 51. Remember!

19. 3-1 Estimating with Decimals Use compatible numbers to estimate. 39.62 · 4.99 40 Round to the nearest multiple of 10. 200 Estimate  5 Check It Out: Example 2A 9 > 5, so round to 5. 39.62  4.99

20. 3-1 Estimating with Decimals Use compatible numbers to estimate. 19.42 ÷ (–4.88) 19.42 20 19 is prime, so round to 20. –5 –5 divides into 20 without a remainder. –4.88 Estimate Check It Out: Example 2B 20 ÷ –5 = –4

21. 3-1 Estimating with Decimals Cara spent $58.80 on 4.8 pounds of lobster. Use estimation to check whether it is reasonable to spend $12 per pound on lobster. $58.80 $60 Round to the nearest multiple of 10. 5 4.85 Estimate Additional Example 3: Application 60 ÷ 5 = 12 8 > 5, so round to 5. The estimate is the same as Cara’s calculation, so $12 per pound for lobster is a reasonable answer.

22. 3-1 Estimating with Decimals Clem spent $18.43 on 11.7 pounds of apples. Use estimation to check whether it is reasonable to spend about $4 per pound on apples? 18.43 $20 Round to the nearest multiple of 10. 10 11.7 Estimate Check It Out: Example 3 20 ÷ 10 = 2 10 divides evenly into 20 without a remainder. The estimate is more than Clem’s calculation, so it is not reasonable to spend $4 per pound of apples.

23. 3-1 Estimating with Decimals Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

24. 3-1 Estimating with Decimals Lesson Quiz: Part I Estimate by rounding to nearest integer. 1. 68.4 + 29.5 2. 7.24 + (–10.5) Use compatible numbers to estimate. 3. 48.27  4.67 4. 54.37  5.67 –4 98 250 9 Possible answers:

25. 3-1 Estimating with Decimals Lesson Quiz: Part II Use compatible numbers to estimate. 5. Ray is catering a party for 60 people. He needs to have 30 pounds of potato salad. He has made 6.21 pounds and 22.68 pounds. Estimate to check whether he has enough for the party? No; The estimate is 29 pounds.

26. 3-1 Estimating with Decimals 1. Estimate by rounding to the nearest integer. 77.3 + 28.6 A. 90 B. 100 C. 105 D. 106 Lesson Quiz for Student Response Systems

27. 3-1 Estimating with Decimals 2. Estimate by rounding to the nearest integer. 8.32 + (–12.6) A. –10 B. –5 C. –4 D. –2 Lesson Quiz for Student Response Systems

28. 3-1 Estimating with Decimals 3. Use compatible numbers to estimate. 58.36 · 5.72 A. 360 B. 348 C. 290 D. 250 Lesson Quiz for Student Response Systems

29. 3-1 Estimating with Decimals 4. Use compatible numbers to estimate. 64.46 ÷ 3.72 A. 15 B. 16 C. 20 D. 21 Lesson Quiz for Student Response Systems

30. 3-1 Estimating with Decimals 5. Patricia and Jennifer decide to give a watch to their friend on her birthday. Patricia has $35.91, and Jennifer has $20.25. The cost of a watch is $60. Estimate to check whether they have enough money to buy the watch. A. Yes; the estimate is $60. B. Yes; the estimate is $59. C. No; the estimate is $55. D. No; the estimate is $56. Lesson Quiz for Student Response Systems