2-5 Dividing Integers

Transcription

1 Find each quotient ( 10) ( 3) ( 4) Evaluate each expression if s = 2 and t = s t t (2s) Financial Literacy The following are the changes of a value of a certain stock over the last 5 days: $7, +$3, +$6, $2, $5. Find the mean and interpret the quotient. $1; the value of the stock changed an average of $1 each day Find each quotient ( 2) ( 5) esolutions Manual - Powered by Cognero Page 1

2 , if x = 21 and y = Financial Literacy The last 5 transactions at Mr. Brigham s ATM were $250, $60, $94, $300, and $186. Find the mean and interpret the quotient. $42; The mean amount for the last 5 transactions was $ The table shows the extreme high and low temperatures for different states. The expression, where F represents the temperature in degrees Fahrenheit, can be used to convert temperatures from degrees Fahrenheit to degrees Celsius Evaluate each expression. 25., if n = k, if k = , if a = 24 and b = 4 36 a. Find the extreme high and low temperatures for each state in degrees Celsius. Round to the nearest tenth. b. The difference between the extreme high and low temperatures is called the range. Find the range of the temperatures in degrees Celsius for each state. c. List the states in order from least to greatest ranges. a. Arizona: low: 40 C, high: 53.3 C; Florida: low: 18.9 C, high: 42.8 C; Kentucky: low: 36.7 C, high: 45.6 C; Michigan: low: 46.1 C, high: 44.4 C; New York: low: 49.4 C, high: 42.2 C b. Arizona: 93.3 C; Florida: 61.7 C; Kentucky: 82.3 C; Michigan: 90.5 C; New York: 91.6 C c. Florida, Kentucky, Michigan, New York, Arizona esolutions Manual - Powered by Cognero Page 2

3 31. Financial Literacy A small clothing company s total income was $64,000, while its total expenses were $67,600. Use the expression, where I represents total income and E represents total expenses, to find the average difference between the company s income and expenses each month. Interpret the quotient. $300; Sample answer: Every month, the company spends $300 more than they earn. Replace each _ with <, >, or = to make a true sentence ( 2) _ = 33. _ < Find the value of x that makes each statement true x = Reason Abstractly For Exercises 38 40, write an expression to represent each real-world situation. Then evaluate the expression and interpret the quotient. 38. Jean owes her parents $90, to be paid in 5 equal installments. How much is each installment? $90 5; $18; She will pay her parents $18 each time to repay the debt. 39. The temperature dropped a total of 40 F over an 8 hour period. What was the mean hourly temperature drop? 40 8; 5 F; Each hour the temperature dropped an average of 5 F. 40. In October, the full price of a television is $695. Over the next seven months, the price of the television drops a total of $140. How much did the price of the television drop each month on average? $140 7; $20; The price dropped an average of $20 every month. 41. The table shows the deepest point of each of the Great Lakes = x ( 34) x ( 17) = x = a. What is the mean of the deepest points of the Great Lakes? b. Suppose each of the deepest points were 10 meters higher. Find the mean. Compare the new mean to the original. a m b m; The mean would be 10 meters higher. esolutions Manual - Powered by Cognero Page 3

4 42. Multiple Representations In this problem, you will investigate the relationships between distance and time. Suppose Joseph was tracking a submarine. The submarine descended 480 feet in 20 minutes. a. Numbers How many feet did the submarine descend per minute? b. Symbols Write an expression to determine the change, in feet, of the submarine's elevation after any number of minutes. c. Table Use the expression you wrote in part b to create a table showing the change in the submarine's depth after 5, 10, 15, and 18 minutes. a. 24 ft b. 24m c. Time (min) 24m Change in Depth (ft) 5 24(5) (10) (15) (18) Model with Mathematics Write a division expression with a quotient between 20 and 25. Then describe a real-world situation in which the equation represents the solution. Sample answer: = 22; Jessie's total score in a word game is 110 points after 5 rounds. What is Jessie's mean score per round? 44. Persevere with Problems The mean temperature during 5 days was 10 F. Give a sample set of what the temperatures might have been for the 5 days. Sample answer: 4, 8, 11, 12, Persevere with Problems Addition and multiplication are said to be closed for whole numbers, but subtraction and division are not. That is, when you add or multiply any two whole numbers, the result is a whole number. Which operations are closed for integers? addition, subtraction, and multiplication 47. Building on the Essential Question Explain whether the Associative Property and Commutative Property are true for division of integers. Support your reasoning with an example. Then explain your reasoning to a classmate. Sample answer: The Associative Property is not true for the division of integers because the way the integers are grouped affects the solution. [24 ( 6)] 2 = 2; 24 [( 6 2)] = 8; The Commutative Property is not true for the division of integers because the order of the integers affects the solution = 0.2; 10 ( 2) = Yesterday s low temperature was 24 degrees Fahrenheit. Use the expression, where F represents the temperature in degrees Fahrenheit, to find the approximate low temperature in degrees Celsius. A 9.8 C B 4.4 C C 4.4 C D 9.8 C B 45. Reason Inductively Find the next two numbers in the pattern 1024, 256, 64, 16,.... Explain your reasoning. 4, 1; Divide the previous term by 4 esolutions Manual - Powered by Cognero Page 4

5 49. The temperature dropped 30 F in a 6 hour period. What was the mean hourly temperature change? F 5 F G 6 F H 5 F J 6 F F 50. The depth of a reservoir decreased 84 inches in two weeks. If the water depth changed by the same amount each day, how much did the depth of the water change per day? A 7 in. B 6 in. C 6 in. D 7 in. B 51. Miss Washer recorded the low temperature each day for a week. What is the mean low temperature? F 9.6 F G 1.2 F H 9.6 F J 1.2 F J 52. During low tide, in Wrightsville, North Carolina, the beachfront in some places is about 350 feet from the ocean to the homes. High tide can change the width of a beach at a rate of 17 feet an hour. It takes 6 hours for the ocean to move from low to high tide. a. What is the change in the width of the beachfront from low to high tide? b. What is the distance from the ocean to the homes at high tide? a. 102 ft b. 248 ft Find each product ( 4) ( 11) ( 5)( 3) (4)( 9) ( 2)( 2) 24 Find each difference esolutions Manual - Powered by Cognero Page 5

6 C 69. E (2, 7) (5, 4) ( 7) ( 10) ( 12) Financial Literacy The starting balance in a checking account was $50. What was the balance after checks were written for $25 and for $32? $7 Refer to the coordinate plane shown. Write the ordered pair that names each point. 66. A 67. G (0, 3) (5, 1) esolutions Manual - Powered by Cognero Page 6