Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Rounding and Estimating Lesson 3-1 Pre-Algebra Objectives: 1. To round decimals 2. To estimate sums and differences Rounding and Estimating Lesson 3-1 Pre-Algebra Tip: ≈ means approximately equal to Rounding and Estimating Lesson 3-1 Additional Examples a. Round 8.7398 to the nearest tenth. tenths place 8.7398 less than 5 Round down to 7. 8.7 Pre-Algebra Rounding and Estimating Lesson 3-1 Additional Examples (continued) b. Round 8.7398 to the nearest integer. nearest integer is ones place 8.7398 5 or greater Round up to 9. 9 Pre-Algebra Rounding and Estimating Lesson 3-1 Pre-Algebra Additional Examples Estimate to find whether each answer is reasonable. a. Calculation $115.67 $ 83.21 +$ 59.98 $258.86 Estimate $120 $ 80 +$ 60 $260 The answer is close to the estimate. It is reasonable. Rounding and Estimating Lesson 3-1 Pre-Algebra Additional Examples (continued) b. Calculation $176.48 –$ 39.34 $137.14 Estimate $180 –$ 40 $140 The answer is not close to the estimate. It is not reasonable. Rounding and Estimating Lesson 3-1 Pre-Algebra Additional Examples 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. Add the front-end digits. + The total cost is about $5.10. .30 Estimate by rounding. .20 .60 1.10 = 5.10 Rounding and Estimating Lesson 3-1 Pre-Algebra Additional Examples Estimate the total electricity charge: March: $81.75; April: $79.56; May: $80.89. 3 months The values cluster around $80. 80 • 3 = 240 The total electricity charge is about $240.00. Estimating Decimal Products and Quotients Lesson 3-2 Pre-Algebra Objectives: 1. To estimate products 2. To estimate quotients Estimating Decimal Products and Quotients Lesson 3-2 Pre-Algebra Tips: On multiple choice questions, sometimes you can eliminate answers by estimating. Estimating Decimal Products and Quotients Lesson 3-2 Pre-Algebra Additional Examples Estimate 6.43 • 4.7. 6.43 6 4.7 6 • 5 = 30 6.43 • 4.7 30 5 Round to the nearest integer. Multiply. Estimating Decimal Products and Quotients Lesson 3-2 Pre-Algebra Additional Examples 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. 5.35 5 5 • 3 = 15 Round to the nearest dollar. Multiply 5 times 3, the number of yards of fabric. 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. Estimating Decimal Products and Quotients Lesson 3-2 Pre-Algebra Additional Examples 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. 3.12 3 Round the divisor. 62.40 60 Round the dividend to a multiple of 3 that is close to 62.40. 60 ÷ 3 = 20 Divide. The shipment is made up of about 20 books. Estimating Decimal Products and Quotients Lesson 3-2 Pre-Algebra Additional Examples Is 3.29 a reasonable quotient for 31.423 ÷ 5.94? 5.94 31.423 6 Round the divisor. 30 Round the dividend to a multiple of 6 that is close to 31.423. 30 ÷ 6 = 5 Divide. Since 3.29 is not close to 5, it is not reasonable. Mean, Median, and Mode Lesson 3-3 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 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 Additional Examples 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. a. Mean: sum of data values number of data values = 40 + 45 + 48 + 50 + 50 5 = 233 5 = 46.6 The mean is 46.6. Mean, Median, and Mode Lesson 3-3 Pre-Algebra Additional Examples (continued) 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. Mean, Median, and Mode Lesson 3-3 Additional Examples Pre-Algebra 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 Both 7 and 12 appear more than the other data values. Since they appear the same number of times, there are two modes. c. tomato, tomato, grape, orange, cherry, cherry, melon, cherry, grape Cherry appears most often. There is one mode. Mean, Median, and Mode Lesson 3-3 Pre-Algebra Additional Examples 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? 77 6 12.8 Find the mean with the outlier. 44 5 8.8 Find the mean without the outlier. 12.8 – 8.8 = 4 The outlier raises the mean by about 4 points. Mean, Median, and Mode Lesson 3-3 Additional Examples Pre-Algebra 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. Mean, Median, and Mode Lesson 3-3 Additional Examples Pre-Algebra (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. Using Formulas Lesson 3-4 Pre-Algebra Objectives: 1. To substitute into formulas 2. To use the formula for the perimeter of a rectangle Using Formulas Lesson 3-4 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 Pre-Algebra Additional Examples Suppose you ride your bike 18 miles in 3 hours. Use the formula d = r t to find your average speed. d = rt Write the formula. 18 = (r )(3) Substitute 18 for d and 3 for t. 18 3r = 3 3 Divide each side by 3. 6=r Simplify. Your average speed is 6 mi/h. Using Formulas Lesson 3-4 Pre-Algebra Additional Examples Use the formula F = n + 37, where n is the number 4 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. n F = 4 + 37 76 Write the formula. F = 4 + 37 Replace n with 76. F = 19 + 37 Divide. F = 56 Add. The temperature is about 56°F. Using Formulas Lesson 3-4 Pre-Algebra Additional Examples 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. P = 2 + 2w Write the formula. P = 2(14.5) + 2(8.5) Replace P = 29 + 17 Multiply. P = 46 Add. with 14.5 and w with 8.5. The perimeter of the tabletop is 46 in. Solving Equations by Adding or Subtracting Decimals Lesson 3-5 Pre-Algebra Objectives: 1. To solve one-step decimal equations involving addition 2. To solve one-step decimal equations involving subtraction Solving Equations by Adding or Subtracting Decimals Lesson 3-5 Pre-Algebra Additional Examples Solve 6.8 + p = –9.7. 6.8 + p = –9.7 6.8 – 6.8 + p = –9.7 – 6.8 p = –16.5 Check: Subtract 6.8 from each side. Simplify. 6.8 + p = –9.7 6.8 + (–16.5) –9.7 –9.7 = –9.7 Replace p with –16.5. Solving Equations by Adding or Subtracting Decimals Lesson 3-5 Pre-Algebra Additional Examples 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 x + 8.75 – 8.75 = 14.5 – 8.75 x = 5.75 Subtract 8.75 from each side. Simplify. The length of the piece that is left is 5.75 ft. Solving Equations by Adding or Subtracting Decimals Lesson 3-5 Pre-Algebra Additional Examples Solve –23.34 = q – 16.99. –23.34 = q – 16.99 –23.34 + 16.99 = q – 16.99 + 16.99 –6.35 = q Add 16.99 to each side. Simplify. Solving Equations by Adding or Subtracting Decimals Lesson 3-5 Pre-Algebra Additional Examples Alejandro wrote a check for $49.98. His new account balance is $169.45. What was his previous balance? Words previous balance minus check is new balance Let p = previous balance. Equation p – 49.98 = 169.45 p – 49.98 = 169.45 p – 49.98 + 49.98 = 169.45 + 49.98 p = 219.43 Add 49.98 to each side. Simplify. Alejandro had $219.43 in his account before he wrote the check. Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 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 Pre-Algebra Additional Examples Solve –6.4 = 0.8b. –6.4 = 0.8b –6.4 0.8b = 0.8 0.8 –8 = b Check: Divide each side by 0.8. Simplify. –6.4 = 0.8b –6.4 0.8(–8) –6.4 = –6.4 Replace b with –8. Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 Pre-Algebra Additional Examples 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? Words daily milk consumption times number of days is 250 gallons = 250 Let x = number of days. Equation 85.8 • x Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 Pre-Algebra Additional Examples (continued) 85.8x = 250 85.8x 250 = 85.8 85.8 Divide each side by 85.8. x = 2.914 . . . Simplify. x 3 Round to the nearest whole number. The school will take about 3 days to use 250 gallons of milk. Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 Pre-Algebra Additional Examples Solve –37.5 = –37.5 = –37.5(–1.2) = c . –1.2 c –1.2 c (–1.2) –1.2 45 = c Multiply each side by –1.2. Simplify. Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 Pre-Algebra Additional Examples A little league player was at bat 15 times and had a batting average of 0.133 rounded to the nearest thousandth. hits (h) The batting average formula is batting average (a) = . times at bat (n) Use the formula to find the number of hits made. h a= n h 0.133 = 15 Replace a with 0.133 and n with 15. Solving Equations by Multiplying or Dividing Decimals Lesson 3-6 Pre-Algebra Additional Examples (continued) h 0.133(15) = 15 (15) 1.995 = h 2 h Multiply each side by 15. Simplify. Since h (hits) represents an integer, round to the nearest integer. The little league player made 2 hits. Using the Metric System Lesson 3-7 Pre-Algebra Objectives: 1.To identify appropriate metric measures 2. To convert metric units Using the Metric System Lesson 3-7 Additional Examples Pre-Algebra Choose an appropriate metric unit. Explain your choice. a. the width of this textbook Centimeter; the width of a textbook is about two hands, or ten thumb widths, wide. b. the mass of a pair of glasses Gram; glasses have about the same mass as many paperclips, but less than this textbook. c. the capacity of a thimble Milliliter; a thimble will hold only a small amount of water. Using the Metric System Lesson 3-7 Additional Examples Pre-Algebra Choose a reasonable estimate. Explain your choice. a. capacity of a drinking glass: 500 L or 500 mL 500 mL; a drinking glass holds less than a quart of milk. b. length of a hair clip: 5 m or 5 cm 5 cm; the length of a hair clip would be about 5 widths of a thumbnail. 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. Using the Metric System Lesson 3-7 Pre-Algebra Additional Examples Complete each statement. a. 7,603 mL = L 7,603 ÷ 1,000 = 7.603 To convert from milliliters to liters, divide by 1,000. 7,603 mL = 7.603 L b. 4.57 m = cm 4.57 100 = 457 cm 4.57 m = 457 cm To convert meters to centimeters, multiply by 100. Using the Metric System Lesson 3-7 Pre-Algebra Additional Examples A blue whale caught in 1931 was about 2,900 cm long. What was its length in meters? Words length in centimeters ÷ centimeters per meter = length in meters Equation 2,900 ÷ 100 = 29 The whale was about 29 m long. Problem Solving Strategy: Act It Out Lesson 3-8 Pre-Algebra Objectives: 1.To solve complex problems by first solving simpler cases Problem Solving Strategy: Act It Out Lesson 3-8 Pre-Algebra Additional Examples 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? Days after the first Number of pennies Amount 0 1 2 3 4 5 1 2 2•2= 4 4•2= 8 8 • 2 = 16 16 • 2 = 32 $0.01 $0.02 $0.04 $0.08 $0.16 $0.32 Problem Solving Strategy: Act It Out Lesson 3-8 Additional Examples (continued) 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. 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 = 1024 10 twos = 10 days after the first penny is given Marta will give her sister $10.24 in pennies on October 11. Pre-Algebra