1. Pre-Algebra Objectives: 1. To round decimals 2. To estimate sums and differences Rounding and Estimating Lesson 3-1

2. Pre-Algebra Tip: ≈ means approximately equal to Rounding and Estimating Lesson 3-1

3. Pre-Algebra Rounding and Estimating Lesson 3-1 a. Round 8.7398 to the nearest tenth. 8.7398 tenths place less than 5 8.7 Round down to 7. Additional Examples

4. Pre-Algebra (continued) Rounding and Estimating Lesson 3-1 b. Round 8.7398 to the nearest integer. 8.7398 nearest integer is ones place 5 or greater 9 Round up to 9. Additional Examples

5. Pre-Algebra Estimate to find whether each answer is reasonable. Rounding and Estimating Lesson 3-1 a. Calculation +$ 59.98 $ 83.21 $115.67 $258.86 +$ 60 $ 80 $120 Estimate $260 The answer is close to the estimate. It is reasonable. Additional Examples

6. Pre-Algebra (continued) Rounding and Estimating Lesson 3-1 b. Calculation –$ 39.34 $176.48 $137.14 Estimate –$ 40 $180 $140 The answer is not close to the estimate. It is not reasonable. Additional Examples

7. Pre-Algebra Add the front-end digits. You are buying some fruit. The bananas cost $1.32, the apples cost $2.19, and the avocados cost $1.63. Use front-end estimation to estimate the total cost of the fruit. Rounding and Estimating Lesson 3-1 5.10= The total cost is about $5.10. + Estimate by rounding..60.20.30 1.10 Additional Examples

8. Pre-Algebra Estimate the total electricity charge: March: $81.75; April: $79.56; May: $80.89. Rounding and Estimating Lesson 3-1 240= The total electricity charge is about $240.00. The values cluster around $80. 80 3 months 3 Additional Examples

9. Pre-Algebra Objectives: 1.To estimate products 2. To estimate quotients Estimating Decimal Products and Quotients Lesson 3-2

10. Pre-Algebra Tips: On multiple choice questions, sometimes you can eliminate answers by estimating. Estimating Decimal Products and Quotients Lesson 3-2

11. Pre-Algebra Estimate 6.43 4.7. Estimating Decimal Products and Quotients Lesson 3-2 Multiply.6 5 = 30 6.4364.75Round to the nearest integer. 6.43 4.7 30 Additional Examples

12. Pre-Algebra Joshua bought 3 yd of fabric to make a flag. The fabric cost $5.35/yd. The clerk said his total was $14.95 before tax. Did the clerk make a mistake? Explain. Estimating Decimal Products and Quotients Lesson 3-2 Multiply 5 times 3, the number of yards of fabric. 5 3 = 15 5.355Round to the nearest dollar. The sales clerk made a mistake. Since 5.35 > 5, the actual cost should be more than the estimate. The clerk should have charged Joshua more than $15.00 before tax. Additional Examples

13. Pre-Algebra The cost to ship one yearbook is $3.12. The total cost for a shipment was $62.40. Estimate how many books were in the shipment. Estimating Decimal Products and Quotients Lesson 3-2 3.123Round the divisor. The shipment is made up of about 20 books. 62.4060 Round the dividend to a multiple of 3 that is close to 62.40. 60 ÷ 3 = 20Divide. Additional Examples

14. Pre-Algebra Is 3.29 a reasonable quotient for 31.423 ÷ 5.94? Estimating Decimal Products and Quotients Lesson 3-2 Since 3.29 is not close to 5, it is not reasonable. 5.946Round the divisor. 31.42330 Round the dividend to a multiple of 6 that is close to 31.423. 30 ÷ 6 = 5Divide. Additional Examples

15. Pre-Algebra Objectives: 1.To find mean, median, mode, and range of a set of data. 2. To choose the best measure of central tendency. Mean, Median, and Mode Lesson 3-3

16. Pre-Algebra New Terms: 1 Measures of Central Tendency – mean, median, mode of a collection of data. 2. Mean – is the sum of the data values divided by the number of data values, average. 3. Median – is the middle number when data values are written in order and there is an odd number of data values. For an even number of data values, the median is the mean of the two middle numbers. 4. Mode – is the data item that occurs most often. There can be one mode, more than one, or none. 5. Range – the difference between the greatest and least values in the data set. 6. Outlier – a data value that is much greater or less than the other data values. Mean, Median, and Mode Lesson 3-3

17. Pre-Algebra Six elementary students are participating in a one-week Readathon to raise money for a good cause. Use the graph. Find the (a) mean, (b) median, and (c) mode of the data if you leave out Latana’s pages. Mean, Median, and Mode Lesson 3-3 a. Mean: 40 + 45 + 48 + 50 + 50 5 = 233 5 = 46.6= The mean is 46.6. sum of data values number of data values Additional Examples

18. Pre-Algebra (continued) Mean, Median, and Mode Lesson 3-3 b. Median: 40 45 48 50 50 Write the data in order. The median is the middle number, or 48. c. Mode: Find the data value that occurs most often. The mode is 50. Additional Examples

19. Pre-Algebra Mean, Median, and Mode Lesson 3-3 a. $1.10 $1.25 $2.00 $2.10 $2.20 $3.50 No values are the same, so there is no mode. b. 1 3 4 6 7 7 8 9 10 12 12 13 How many modes, if any, does each have? Name them. c. tomato, tomato, grape, orange, cherry, cherry, melon, cherry, grape There is one mode. Both 7 and 12 appear more than the other data values. Cherry appears most often. Since they appear the same number of times, there are two modes. Additional Examples

20. Pre-Algebra Mean, Median, and Mode Lesson 3-3 a. Which data value is an outlier? Use the data: 7%, 4%, 10%, 33%, 11%, 12%. The data value 33% is an outlier. It is an outlier because it is 21% away from the closest data value. b. How does the outlier affect the mean? The outlier raises the mean by about 4 points. 12.8 – 8.8 = 4 Find the mean with the outlier. 77 6 12.8 Find the mean without the outlier. 44 5 8.8 Additional Examples

21. Pre-Algebra Mean, Median, and Mode Lesson 3-3 a. the monthly amount of rain for a year Which measure of central tendency best describes each situation? Explain. since the average monthly amount of rain for a year is not likely to have an outlier, mean is the appropriate measure. Mean; b. most popular color of shirt Mode; When the data have no outliers, use the mean. When determining the most frequently chosen item, or when the data are not numerical, use the mode. since the data are not numerical, the mode is the appropriate measure. Additional Examples

22. Pre-Algebra Mean, Median, and Mode Lesson 3-3 c. times school buses arrive at school (continued) since one bus may have to travel much farther than other buses, the median is the appropriate measure. Median; When an outlier may significantly influence the mean, use the median. Additional Examples

23. Pre-Algebra Objectives: 1.To substitute into formulas 2. To use the formula for the perimeter of a rectangle Using Formulas Lesson 3-4

24. Pre-Algebra New Terms: 1. Formula – an equation that shows a relationship between quantities that are represented by variables. 2. Perimeter – the distance around a figure. Using Formulas Lesson 3-4

25. Pre-Algebra Using Formulas Lesson 3-4 Suppose you ride your bike 18 miles in 3 hours. Use the formula d = r t to find your average speed. d = r tWrite the formula. 18 = (r )(3)Substitute 18 for d and 3 for t. Divide each side by 3. 18 3 = 3r33r3 Simplify.6 = r Your average speed is 6 mi/h. Additional Examples

26. Pre-Algebra Use the formula F = + 37, where n is the number of chirps a cricket makes in one minute, and F is the temperature in degrees Fahrenheit. Estimate the temperature when a cricket chirps 76 times in a minute. Using Formulas Lesson 3-4 n4n4 The temperature is about 56°F. F = + 37 n4n4 Write the formula. F = + 37 76 4 Replace n with 76. F = 19 + 37Divide. F = 56Add. Additional Examples

27. Pre-Algebra Find the perimeter of a rectangular tabletop with a length of 14.5 in. and width of 8.5 in. Use the formula for the perimeter of a rectangle, P = 2 + 2w. Using Formulas Lesson 3-4 The perimeter of the tabletop is 46 in. P = 2 + 2wWrite the formula. P = 46Add. P = 2(14.5) + 2(8.5)Replace with 14.5 and w with 8.5. P = 29 + 17Multiply. Additional Examples

28. Pre-Algebra Solving Equations by Adding or Subtracting Decimals Lesson 3-5 Objectives: 1. To solve one-step decimal equations involving addition 2. To solve one-step decimal equations involving subtraction

29. Pre-Algebra Solve 6.8 + p = –9.7. Solving Equations by Adding or Subtracting Decimals Lesson 3-5 6.8 + p = –9.7 6.8 – 6.8 + p = –9.7 – 6.8Subtract 6.8 from each side. p = –16.5Simplify. Check:6.8 + p = –9.7 6.8 + (–16.5) –9.7Replace p with –16.5. –9.7 = –9.7 Additional Examples

30. Pre-Algebra Ping has a board that is 14.5 ft long. She saws off a piece that is 8.75 ft long. Use the diagram below to find the length of the piece that is left. Solving Equations by Adding or Subtracting Decimals Lesson 3-5 The length of the piece that is left is 5.75 ft. x = 5.75Simplify. x + 8.75 – 8.75 = 14.5– 8.75 Subtract 8.75 from each side. x + 8.75 = 14.5 Additional Examples

31. Pre-Algebra Solve –23.34 = q – 16.99. Solving Equations by Adding or Subtracting Decimals Lesson 3-5 –23.34 = q – 16.99 –23.34 + 16.99 = q – 16.99 + 16.99Add 16.99 to each side. –6.35 = qSimplify. Additional Examples

32. Pre-Algebra Alejandro wrote a check for $49.98. His new account balance is $169.45. What was his previous balance? Solving Equations by Adding or Subtracting Decimals Lesson 3-5 Alejandro had $219.43 in his account before he wrote the check. Simplify.p = 219.43 Add 49.98 to each side.p – 49.98 + 49.98 = 169.45 + 49.98 p – 49.98 = 169.45 Equation p – 49.98= 169.45 Let p = previous balance. Words previous balance minus check is new balance Additional Examples

33. Pre-Algebra Objectives: 1. To solve one-step decimal equations involving multiplication 2. To solve one-step decimal equations involving division Solving Equations by Multiplying or Dividing Decimals Lesson 3-6

34. Pre-Algebra Solve –6.4 = 0.8b. Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 –6.4 = 0.8b –6.4 0.8 0.8b 0.8 = Divide each side by 0.8. –8 = bSimplify. Check:–6.4 = 0.8b –6.4 0.8(–8)Replace b with –8. –6.4 = –6.4 Additional Examples

35. Pre-Algebra Every day the school cafeteria uses about 85.8 gallons of milk. About how many days will it take for the cafeteria to use the 250 gallons in the refrigerator? Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 Let x = number of days. number of days Words timesis250 gallons daily milk consumption Equation=85.8 x250 Additional Examples

36. Pre-Algebra (continued) Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 85.8x = 250 The school will take about 3 days to use 250 gallons of milk. x = 2.914...Simplify. x3Round to the nearest whole number. 85.8x 85.8 = 250 85.8 Divide each side by 85.8. Additional Examples

37. Pre-Algebra Solve –37.5 =. Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 c –1.2 –37.5 = c –1.2 Multiply each side by –1.2.–37.5(–1.2) = (–1.2) c –1.2 45 = cSimplify. Additional Examples

38. Pre-Algebra A little league player was at bat 15 times and had a batting average of 0.133 rounded to the nearest thousandth. The batting average formula is batting average (a) =. Use the formula to find the number of hits made. Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 hits (h) times at bat (n) a = hnhn 0.133 = h 15 Replace a with 0.133 and n with 15. Additional Examples

39. Pre-Algebra (continued) Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 0.133(15) = (15) h 15 Multiply each side by 15. Simplify. 1.995 = h 2 hSince h (hits) represents an integer, round to the nearest integer. The little league player made 2 hits. Additional Examples

40. Pre-Algebra Using the Metric System Lesson 3-7 Objectives: 1.To identify appropriate metric measures 2. To convert metric units

41. Pre-Algebra Choose an appropriate metric unit. Explain your choice. Using the Metric System Lesson 3-7 a. the width of this textbook b. the mass of a pair of glasses c. the capacity of a thimble Milliliter; a thimble will hold only a small amount of water. Gram; glasses have about the same mass as many paperclips, but less than this textbook. Centimeter; the width of a textbook is about two hands, or ten thumb widths, wide. Additional Examples

42. Pre-Algebra Choose a reasonable estimate. Explain your choice. Using the Metric System Lesson 3-7 a. capacity of a drinking glass: 500 L or 500 mL b. length of a hair clip: 5 m or 5 cm c. mass of a pair of hiking boots: 1 kg or 1 g 1 kg; the mass is about one half the mass of your math book. 5 cm; the length of a hair clip would be about 5 widths of a thumbnail. 500 mL; a drinking glass holds less than a quart of milk. Additional Examples

43. Pre-Algebra Complete each statement. Using the Metric System Lesson 3-7 a. 7,603 mL = L 7,603 ÷ 1,000 = 7.603To convert from milliliters to liters, divide by 1,000. 7,603 mL = 7.603 L 4.57 m = 457 cm To convert meters to centimeters, multiply by 100. 4.57  100 = 457 cm b. 4.57 m = cm Additional Examples

44. Pre-Algebra A blue whale caught in 1931 was about 2,900 cm long. What was its length in meters? Using the Metric System Lesson 3-7 Words centimeters per meter length in centimeters ÷ length in meters = 2,900Equation 10029 ÷= The whale was about 29 m long. Additional Examples

45. Pre-Algebra Objectives: 1.To solve complex problems by first solving simpler cases Problem Solving Strategy: Act It Out Lesson 3-8

46. Pre-Algebra Marta gives her sister one penny on the first day of October, two pennies on the second day, and four pennies on the third day. She continues to double the number of pennies each day. On what date will Marta give her sister $10.24 in pennies? Problem Solving Strategy: Act It Out Lesson 3-8 1 2 2 2 = 4 4 2 = 8 8 2 = 16 16 2 = 32 Number of pennies Days after the first 012345012345 Amount $0.01 $0.02 $0.04 $0.08 $0.16 $0.32 Additional Examples

47. Pre-Algebra (continued) Problem Solving Strategy: Act It Out Lesson 3-8 2 2 2 2 2 2 2 2 2 2 = 1024 You can tell from the pattern in the chart that you just need to count the number of 2’s multiplied until you reach 1,024, which is $10.24 in pennies. Marta will give her sister $10.24 in pennies on October 11. 10 twos = 10 days after the first penny is given Additional Examples