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Rounding and Estimating

Rounding and Estimating. PRE-ALGEBRA LESSON 3-1. Round each number to the underlined place value. a. 89.63. c. 0.83476. b. 579,122. 90. 600,000. 0.8348. 3-1. Rounding and Estimating. PRE-ALGEBRA LESSON 3-1. (For help, go to Skills Handbook page 727.).

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Rounding and Estimating

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  1. Rounding and Estimating PRE-ALGEBRA LESSON 3-1 Round each number to the underlined place value. a. 89.63 c. 0.83476 b. 579,122 90 600,000 0.8348 3-1

  2. Rounding and Estimating PRE-ALGEBRA LESSON 3-1 (For help, go to Skills Handbook page 727.) Use the number 27.3865. Write the value of the given digit. 1. 2 2. 3 3. 8 4. 6 Check Skills You’ll Need 3-1

  3. Rounding and Estimating PRE-ALGEBRA LESSON 3-1 Solutions 1. 27.3865; 2 tens 2. 27.3865; 3 tenths 3. 27.3865; 8 hundredths 4. 27.3865; 6 thousandths 3-1

  4. tenths place less than 5 Round down to 7. 8.7 Rounding and Estimating PRE-ALGEBRA LESSON 3-1 a. Round 8.7398 to the nearest tenth. 8.7398 3-1

  5. nearest integer is ones place 5 or greater Round up to 9. 9 Rounding and Estimating PRE-ALGEBRA LESSON 3-1 (continued) b. Round 8.7398 to the nearest integer. 8.7398 Quick Check 3-1

  6. Estimate $120 $ 80 +$ 60 $260 Rounding and Estimating PRE-ALGEBRA LESSON 3-1 Estimate to find whether each answer is reasonable. a.  Calculation $115.67 $ 83.21 +$ 59.98 $258.86 The answer is close to the estimate. It is reasonable. 3-1

  7. Estimate $176.48 $180 –$ 39.34 –$ 40 $147.14 $140 Rounding and Estimating PRE-ALGEBRA LESSON 3-1 (continued) b.  Calculation The answer is not close to the estimate. It is not reasonable. Quick Check 3-1

  8. .30 Add the front-end digits. Estimate by rounding. .20 .60 1.10 = 5.10 + Rounding and Estimating PRE-ALGEBRA LESSON 3-1 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. The total cost is about $5.10. Quick Check 3-1

  9. 3 months 80 • 3 = 240 Rounding and Estimating PRE-ALGEBRA LESSON 3-1 Estimate the total electricity charge: March: $81.75; April: $79.56; May: $80.89. The values cluster around $80. The total electricity charge is about $240.00. Quick Check 3-1

  10. Rounding and Estimating PRE-ALGEBRA LESSON 3-1 Round to the underlined place. 1. 6.557 2. 3.0448 Estimate. 3. $4.95 + $.89 4. 4.589 + 5.098 + 5.179 6.6 3.04 about $6.00 about 15 3-1

  11. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 Round to the nearest whole number and to the nearest tenth. a. 4.07 c. 364.825 b. 0.708 4, 4.1 1, 0.7 365, 364.8 3-2

  12. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 (For help, go to Lesson 3-1.) Round to the nearest one. 1. 145.89 2. 199.27 3. 101.06 4. 28.45 Check Skills You’ll Need 3-2

  13. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 Solutions nearest integer nearest integer 1. 145.89 2. 199.27 5 or greater; round up to 6 less than 5; do not change 146 199 nearest integer nearest integer 3. 101.06 4. 28.45 less than 5; do not change less than 5; do not change 101 28 3-2

  14. 6.43 6 4.7 5 Round to the nearest integer. 6 • 5 = 30 Multiply. 6.43 • 4.7 30 Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 Estimate 6.43 • 4.7. Quick Check 3-2

  15. 5.35 5 Round to the nearest dollar. 5 • 3 = 15 Multiply 5 times 3, the number of yards of fabric. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 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. 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. Quick Check 3-2

  16. 3.12 3 Round the divisor. Round the dividend to a multiple of 3 that is close to 62.40. 62.40 60 60 ÷3 = 20 Divide. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 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. The shipment is made up of about 20 books. Quick Check 3-2

  17. 5.94 6 Round the divisor. Round the dividend to a multiple of 6 that is close to 31.423. 31.423 30 30 ÷6 = 5 Divide. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 Is 3.29 a reasonable quotient for 31.423 ÷ 5.94? Since 3.29 is not close to 5, it is not reasonable. Quick Check 3-2

  18. Estimating Decimal Products and Quotients PRE-ALGEBRA LESSON 3-2 Estimate each product or quotient. 1. $4.78 ÷ 0.891 2. 983.24 • 2.41 3. –5.89 ÷ (–2.7) 4. 24.69 • 0.7 5. 20.498 • 4.908 about $5 about 2,000 about 2 about 25 about 100 3-2

  19. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 Order from greatest to least: 0.677, 0.855, 0.760, 0.078, 0.541 0.855, 0.760, 0.677, 0.541, 0.078 3-3

  20. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 (For help, go Skills Handbook page 723.) Write the numbers from least to greatest. 1. 8, 6, 4, 9, 3, 5, 6 2. 72, 68, 69, 71, 72 3. 112, 101, 98, 120, 101 4. 3.74, 3, 3.7, 3.3, 37 Check Skills You’ll Need 3-3

  21. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 Solutions 1. 3, 4, 5, 6, 6, 8, 9 2. 68, 69, 71, 72, 72 3. 98, 101, 101, 112, 120 4. 3, 3.3, 3.7, 3.74, 37 3-3

  22. sum of data values number of data values 40 + 45 + 48 + 50 + 50 5 = = = 46.6 233 5 Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 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. a. Mean: The mean is 46.6. 3-3

  23. 40 45 48 50 50   Write the data in order. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 (continued) b. Median:  The median is the middle number, or 48. c. Mode:  Find the data value that occurs most often. The mode is 50. Quick Check 3-3

  24. Both 7 and 12 appear more than the other data values. Cherry appears most often. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 How many modes, if any, does each have? Name them. 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 Since they appear the same number of times, there are two modes. c. tomato, tomato, grape, orange, cherry, cherry, melon, cherry, grape There is one mode. Quick Check 3-3

  25. 77 6 12.8 Find the mean with the outlier. 44 6 7.3 Find the mean without the outlier. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 Use the data: 7%, 4%, 10%, 33%, 11%, 12%. a. Which data value is an outlier? 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? 12.8 – 7.3 = 5.5 The outlier raises the mean by about 5.5 points. Quick Check 3-3

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

  27. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 (continued) c. times school buses arrive at school Median; since one bus may have to travel much farther than other buses, the median is the appropriate measure. When an outlier may significantly influence the mean, use the median. Quick Check 3-3

  28. Mean, Median, and Mode PRE-ALGEBRA LESSON 3-3 Which measure of central tendency best describes each situation? 1. numbers of legs on the animals in a zoo 2. favorite digits (from 0 to 9) of the students in a class 3. numbers of days-per-student that students are absent from school 4. test scores mode mode median mean 3-3

  29. Using Formulas PRE-ALGEBRA LESSON 3-4 Evaluate each expression for r = 4, s = 6, t = 2. a. 4r b. 18 ÷s +t c. (r + s) • 2 20 16 5 3-4

  30. x + y 2 Using Formulas PRE-ALGEBRA LESSON 3-4 (For help, go to Lesson 1-3.) Evaluate each expression for x = 3 and y = 4. 1. 2x + 2y2. 2x + y 3. 2(x + y) 4. Check Skills You’ll Need 3-4

  31. 3 + 4 2 x + y 2 7 2 Using Formulas PRE-ALGEBRA LESSON 3-4 Solutions 1. 2x + 2y = 2(3) + 2(4) 2. 2x + y = 2(3) + (4) = 6 + 8 = 6 + 4 = 14 = 10 3. 2(x + y) = 2(3 + 4) 4. = = 2(7) = 14 = = 3.5 3-4

  32. d = rt Write the formula. 18 = (r)(3) Substitute 18 for d and 3 for t. 18 3 3r 3 = Divide each side by 3. 6 = r Simplify. Using Formulas PRE-ALGEBRA LESSON 3-4 Suppose you ride your bike 18 miles in 3 hours. Use the formula d = rt to find your average speed. Your average speed is 6 mi/h. Quick Check 3-4

  33. Write the formula. F = + 37 F = + 37 76 4 n 4 n 4 Replace n with 76. F = 19 + 37 Divide. F = 56 Add. Using Formulas PRE-ALGEBRA LESSON 3-4 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. The temperature is about 56°F. Quick Check 3-4

  34. P = 2 + 2w Write the formula. P = 2(14.5) + 2(8.5) Replace with 14.5 and w with 8.5. P = 29 + 17 Multiply. P = 46 Add. Using Formulas PRE-ALGEBRA LESSON 3-4 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. The perimeter of the tabletop is 46 in. Quick Check 3-4

  35. Using Formulas PRE-ALGEBRA LESSON 3-4 Use the formula P = 4s to find the perimeter of a square with side s. 1.s = 5.6 m 2.s = 9.3 in. 3. Find the side of a square with a perimeter of 164 yd. 22.4 m 37.2 in. 41 yd 3-4

  36. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Separate the digits 1 through 9 into three groups that have the same sum. 1, 5, 9; 2, 6, 7; 3, 4, 8 3-5

  37. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 (For help, go to Skills Handbook page 730.) Simplify. 1. 2.8 + 7.06 2. 0.65 + 1.8 3. 4.52 – 2.48 4. 3.7 – 0.62 Check Skills You’ll Need 3-5

  38. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Solutions 1. 2.80 2. 0.65 + 7.06 + 1.80 9.86 2.45 3. 4.52 4. 3.70 – 2.48 – 0.62 2.04 3.08 3-5

  39. 6.8 – 6.8 + p = –9.7 – 6.8 Subtract 6.8 from each side. p = –16.5 Simplify. Check 6.8 + p = –9.7 Replace p with –16.5. 6.8 + (–16.5) –9.7 –9.7 = –9.7 Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Solve 6.8 + p = –9.7. 6.8 + p = –9.7 Quick Check 3-5

  40. x + 8.75 – 8.75 = 14.5 – 8.75 Subtract 8.75 from each side. x = 5.75 Simplify. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 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. x + 8.75 = 14.5 The length of the piece that is left is 5.75 ft. Quick Check 3-5

  41. –23.34 + 16.99 = q – 16.99 + 16.99 Add 16.99 to each side. –6.35 = q Simplify. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Solve –23.34 = q – 16.99. –23.34 = q – 16.99 Quick Check 3-5

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

  43. Solving Equations by Adding or Subtracting Decimals PRE-ALGEBRA LESSON 3-5 Solve each equation. 1.a + 10 = 7.9 2. –1.01 = c – 9 3.s – (–2.6) = 1.6 4. 3.02 + d = 2.91 5. –23.7 = 13.3 + g – 2.1 7.99 – 1 – 0.11 – 37 3-5

  44. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 Lucinda buys 12 gal of gasoline at $1.95 per gallon. How much does the gas cost? $23.40 3-6

  45. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 (For help, go to Skills Handbook page 765.) Find each product. 1. 2.6(4.5) 2. 3.2(0.15) 3. 11.03(0.6) 4. 8.003(0.6) Check Skills You’ll Need 3-6

  46. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 Solutions 1. 2.6 2. 0.15  4.5  3.2 130 30 + 1040 + 450 11.70 = 11.7 0.480 = 0.48 3. 11.03 4. 8.003  0.6  0.6 6.618 4.8018 3-6

  47. Divide each side by 0.8. –6.4 0.8 0.8b 0.8 = –8 = b Simplify. Check –6.4 = 0.8b –6.4 0.8(–8) Replace b with –8. –6.4 = –6.4 Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 Solve –6.4 = 0.8b. –6.4 = 0.8b Quick Check 3-6

  48. daily milk consumption numberof days Words times is 250 gallons Let x = number of days. 250 x Equation • = 85.8 Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 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? 3-6

  49. 85.8x 85.8 250 85.8 = Divide each side by 85.8. x = 2.914 . . . Simplify. x 3 Round to the nearest whole number. Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 (continued) 85.8x = 250 The school will take about 3 days to use 250 gallons of milk. Quick Check 3-6

  50. –37.5 = Multiply each side by –1.2. –37.5(–1.2) = (–1.2) 45 = c Simplify. c –1.2 c –1.2 c –1.2 Solving Equations by Multiplying or Dividing Decimals PRE-ALGEBRA LESSON 3-6 Solve –37.5 = . Quick Check 3-6

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