2-1 Integers and Absolute Value

Transcription

1 Write an integer for each situation. Identify its opposite and describe its meaning. 1. a bank withdrawal of $ ; +500 or 500; a deposit of $ a gain of 4 pounds +4 or 4; 4; a loss of 4 pounds Write two inequalities using the number pairs. Use the symbols or and 5 2 5; and 8 4 8; and 1 1 1; 1 1 Replace each _ with,, or = to make a true sentence _ _ _ 0 9. Order the state temperatures from least to greatest. 80, 48, 45, 39, 34, 27, 23, 2, 12 Evaluate each expression Evaluate each expression if x = 7 and y = Write an integer for each situation. Identify its opposite and describe its meaning strokes above par +5 or 5; 5; 5 strokes below par feet below sea level 200; +200 or 200; 200 feet above sea level 18. an elevator descent of 18 floors 18; +18 or 18; an elevator rise of 18 floors esolutions Manual - Powered by Cognero Page 1

2 19. no gain on fourth down 0 Write two inequalities using the number pairs. Use the symbols or and ; and ; and 1 1 6; and 4 0 4; and ; 25. and _ _ _ _ _ = 33. _ = 34. In a recent year, Jimmy Johnson was the point leader in NASCAR s Chase to the Cup. Other drivers standings are shown. ; Replace each _ with,, or = to make a true sentence _ _ 17 a. Write an integer to describe each driver s standing with respect to the leader. b. Order the integers from least to greatest. a. K. Busch: 40; K. Harvick: 50; J. Gordon: 20; T. Stewart: 30 b. 50, 40, 30, 20 esolutions Manual - Powered by Cognero Page 2

3 35. The top fourth round scores of a recent PGA Championship were +4, 2, +6, +1, 4, 3, +5, 1, +2, and +3. Order the scores from least to greatest. 4, 3, 2, 1, +1, +2, +3, +4, +5, +6 Evaluate each expression Evaluate each expression if x = 3, y = 4, and z = Justify Conclusions Movies are ranked based on ticket sales. The top movies for one week are listed in the table showing the change in position from the previous week. Which movie had the greatest absolute change? Explain. Movie F; the absolute value of 8 is 8, and 8 is greater than the absolute value of any other change in the table esolutions Manual - Powered by Cognero Page 3

4 The table below shows the freezing point of various elements. 59. { 28, 62, 35, 20, 59} 62, 20, 28, 35, { 42, 1, 6, 74, 0, 11} 74, 1, 0, 6, 11, Write two inequalities using the freezing point of neon and helium ; Order the temperatures from least to greatest using a number line. 272, 249, 201, 157, Is the absolute value of the freezing point of chlorine greater than or less than the absolute value of the freezing point of nitrogen? less than 55. The average temperature of Saturn is 218 F while the average temperature of Jupiter is 162 F. Which planet has the lower average temperature? Explain. Saturn; Order the integers in each set from greatest to least. 56. {4, 2, 10, 3} 4, 3, 2, { 13, 5, 0, 5} 5, 0, 5, {7, 26, 15, 32, 19} 32, 7, 15, 19, {88, 72, 83, 232, 165, 94} 232, 88, 72, 83, 94, Model with Mathematics Write a real-world situation in which you compare two negative integers. Sample answer: A temperature of 2 F is greater than a temperature of 5 F. Persevere with Problems Determine whether each statement is always, sometimes, or never true. Explain your reasoning Always; the absolute value of a number and its opposite are equal. Sometimes; the expressions are equal when x = 0. Sometimes; the expressions are equal when x = Reason Abstractly Write a vocabulary term that completes the analogy: The symbol = is related to an equation in the same way as is related to a(n)?. Inequality esolutions Manual - Powered by Cognero Page 4

5 67. Identify Structure What is the least integer value of n such that n 0? Building on the Essential Question Order the integers 12, 5, 15, 10, 3 from least to greatest without using a number line. Explain your method. 15, 12, 10, 5, 3; Sample answer: Order the integers from greatest to least according to their absolute values. Replacing these absolute values with their original integers orders the original set of integers from least to greatest. 69. Which of the following statements is false if a = 3 and b = 3? A b = a B b 0 C b = a D b 0 D 70. If x = 1, what is the value of x? F 1 G 1 H 1 and 0 J 1 and 1 J 71. Short Response Order,, 4, 0,, and 7 from least to greatest. Explain how you determined the order. 10, 9, 4, 0, 5, 7; Sample answer: Graph each integer on a number line. Then write the numbers as they appear from left to right. The integers 10, 9, 4, 0, 5, and 7 are in order from least to greatest. 72. The table shows the number of points selected players have at the end of a game. Which list shows the order of the players from greatest to least points? A D, C, A, E, B B B, E, A, C, D C D, C, A, B, E D B, C, A, D, E A Name the property shown by each statement = Commutative (+) = 16 Identity (+) 75. (19 15) 2 = 19 (15 2) Associative ( ) = 0 Multiplicative Property of Zero 77. (7 + 9) + 6 = 7 + (9 + 6) Associative (+) = 1 Multiplicative Identity esolutions Manual - Powered by Cognero Page 5

6 Translate each phrase into an algebraic expression. 79. nine less than twice the number of boys 2b the distance Darren ran plus four more miles d three times the difference of the number of video games sold and two 3 (g 2) 82. Multiple Representations A roll of wrapping paper costs $3. a. Symbols Write an equation that can be used to find the cost y of buying x number of rolls of wrapping paper. b. Table Make a function table to find the cost of 3, 4, 5, and 6 rolls. c. Graph Graph the ordered pairs. a. y = 3x b. c. 83. Find each quotient R38 esolutions Manual - Powered by Cognero Page 6

7 , 328 R R14 Find the area of each figure cm in ft 2 esolutions Manual - Powered by Cognero Page 7