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See pages 29-30 for: ¯ Getting Started ¯ Vocabulary Start-Up ¯ Notes ~ I:saen~:ia! ~ Quest:ion What happens when you add, subtract, multiply, and divide integers? ~o~ Common Core o~; ~taLe ~tandards Content Standards Preparation for 7,NS,1. 7.NS.la What Vou’ll Learn ¯ Corn pare ano order integers. ¯ Find the absolute value of an expression. Geocaehing is an outcloor treasure huntin~ game. Some ~reasures. or geocaches, are located hundreds of feet above sea level. O~e~ are hidden in lakes and can only be reached by snorkeling or scuba diving. A negative number is a number less than zero A positive number is a number greater than zero. Negative numbers and positive numbers are members of the set of integers. An integer is any number from the set {,.., -3. -2, -1,0, 1, 2, 3, ...}, where ,.. means continues indefinitely. Mathematical Practices 1,2,3.4,7 ’:~/Vocabulary negative number oositive number integer opposites coordinate inequality absolute value Math Symbols < is less than > is greater than Integers such as 4-3 and -3 are called opposites, because they are the same distan~ from zero on the number line. Write an integer fl~r each situation. Then identify its opposite and describe it means. a, 23°F below zero Because it is belowzero, the integer is --23. Its opposite is 4-23 or 23, which me~ 23°F above zero. b. 11 inches more than normal Because it is more thegn norma~ the integer is + 11 or 11 Its opposite is -means 11 inches less tl~an normal ~ ~? Do these problems to find out. la, ~ loss of 8 yards lb. a deposit of $1S To graph an integer, locate the point named by the integer on a number line. The coordinate is the number that corresponds to the point on a number line. --6--5--4--32--10123456 an expression. Any mathematical sentence containing < or > is called an inequality. An inequality compares numbers or quantities, When two numbers are graphed on a number line, the number to the left is always less than the number to the right. outdoor treasure or geocaches, are level. Others are ~each~d by snorkeling Use the integers graphed on the number line be~oWo than zero. A positive number is a number s and positive numbers are members of the set from the set {..., -3, -2, -I, 0, I, 2, 3, .. The inequality symbol always points to the lesser number. ao Write two inequalities involving I and -2. Since I is to the right of -2, I is greater than -2. So, I > -2. Since -2 is to the left of I, -2 is less than I. So, -2 < I. b. Replace the ~:: with <, >, or -- in -4 ~: -6 to make a true sentence. Since -4 is to the right of -6, -4 is greater. So, -4 > -6. GO~ I~ Do these problems to find out. 2a. Write two inequalities involving -7 and -3. 2b. Replace the ~ with <, >, or = in -I ~ 2 to make a true sentence. , are the same distance Bethany and her friends played a question-and-answer video game. Their scores at the end of the game were 1, -5, O, - 1, 2, and 4. Order the scores from ~east to greatest. Graph each integer on a number line. --7--65--4--3--2--101234567 is --I Write the numbers as they appear from left to right.The scores 5,-I, 0, 1,2, and 4 are in order from least to greatest. 60~ I~2 Do this problem to find out. The recorded highs in degrees Celsius at Niagara Falls from February 21 to 28 of a recent year are 4, 2, 3, -6, -5, -I, 0, and I. Order the temperatures from greatest to least. ~=esson2-1 IntegersandAbsoluteValue 47 Words The absolute value of a number is the distance the number is from zero on the number line.The absolute value of a number is always greater than or equal to zero. Example 161 and 1-61 6 units 6 units --6--5--4--3--2--I 0 1 2 3 4 5 i~ Notice on the number line that -6 and 6 are each 6 units from O, even though they are on opposite sides of O. The absolute value of a number is the distance the number is from zero on a number line. So, -6 and 6 have the same absolute value. Evaluate each expression. When you evaluate an expression, you find the numerical value of the expression. --5--4 --3--2 --I 0 I 2 3 4 5 =3 (~0~ ~ Do these problems to find out. 4a. 1-31 4b. 1-41-131 You can use absolute value notation with algebraic expressions since variables represent numbers. Evaluate 6 + Ixl ifx: -2. 6e~ ~? Do this problem to find out. 5. Evaluate lY] + 8 ify = --7. ~,8 (~hap~er20perationswith Integers Write an integer for each situation. Identify its opposite and describe its meaning. I. a bank withdrawal of $500 2. a gain of 4 pounds Write two inequalities using the number pairs. Use the symbols < or >. 4. -4 and -8 5. -I and I 3. 2and-5 Replace each @ with <, >, or = to make a true sentence, 7. --7@7 6. -9@-16 8. --6@0 9. Order the state temperatures from least to greatest. (E,~,ample i State AL[ AK ’ CA ’l FL H ME ~ Temperature -27 -80 ~ -45 i -2 J N ~ OH ~ TX ~ 12 ~ -48 -34 ~39 -23 Evaluate ea~ e~tess~oB. 12. 1181-1-51 11, ~-~41+131 10. 1-12! Evaluate each expression ifx = 7 and ~ = --6, (~;,o~m~e ~) 13. 15-]yI 14. lYl+X 15. 31YI Go Write an integer for each situation. ~denti{y its opposite and describe its meaning. (;~m~pk ~) 16. 5 strokes above par 17. 200 feet below sea level 18. an elevator descent of 18 floors 19. no gain on fourth down Write two inequalities using the number pairs. Use the symbols < or >. ( ,,~m ~=[ ~) 20. 5 and -11 21. -8 and 14 23.0and-4 22. -6 and -1 25° I 271andl-301 24. 1551and1501 Replace each <~ with <, >, or = to make a true sentence. ( 7,m/i>i~ 2) 26.--110--9 30. 21 <~0 27. --14 ~) --17 31. 0~’--35 28. 15 --6 32. 1131#~;I--131 34. In a recent year, Jimmy Johnson was the point leader in NASCAR’s Chase to the Cup. Other drivers’ standings are shown in the table. /I;< ~mk Write an integer to describe each driver’s standing with respect to the leader. b. Order the integers from least to greatest. 29. --2~:~16 ~. 1--271~I--271 Number 0f P0ints Behind the leader Driver K. B~lsch K. Ha,rick J. Gordon 20 ~The top fourth-round scores of a recent PGA Championship ~ T Stewa t ! were +4, -2, +6, +I, -4, -3, +5, -I, +2, and +3. Order IT the scores from least to greatest. (Ex, m!~le~) 30 Lesson2-1 IntegersandAbsoluteValue ~9 Evaluate each expression. 39. 37.1-171 40. 101÷-141 42.112!-1-21 43. 1-321- !-61 36.]81 Evaluate each expression if x = --3, y = 4, and z = 2. 45. lO--Ixl 46. 2y- Ixl 48. 3y+3z+lxl 38. 1-211 ~-1-71+ 1121 44. 118-41-19-41 47. Izl+ 19 49. 14yzl-31xl 50. 2(z+y)--Ixl 51. ~£,g~ ~lu~L[fy ¢o~c[e~h)nn 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 in position? Explain. ~ The table at the right shows the freezing point of various elements. Element [ Freezing .......... Point (oc) 52. Write two inequalities using the freezing point of neon and helium. chlorine 53. Order the temperatures from least to greatest. 54. Is the absolute value of the freezing point of chlorine greater than or less than the absolute value of the freezing point of nitrogen? 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. heli0m [ --272 krypton [ -157 neon 59. {-28,62,--35,20,-59} 60. {-42,1,--6,74,0,--11} 61. {88,-72,-83,232,--165,-94} 62. ~, ~ode[ ~[Lh [~n~he~n~[c~ Write a real-world situation in which you compare two negative integers. ~ ~: ~e~ev~e ~h Pr~b[~ Determine whether each statement ~s ~lw~ys, sometimes, or never true. Explain your reasoning. 63. Ixl=l-xl 64. Ixl=-Ixl 65. I-xl=-Ix[ 66. ~-~; [~eanon gb~:~nc~cSy Write a vocabulary term that completes the analogy:The symbol = is related to an equation in the same way as > is related to n(n) .~. What is the least integer value of n such that n > O? 68. ~ l~ui~dingon~heEssen~iaIQuee~on Order the integers -12, -5, -15, -l O, 3 from least to greatest without using a number line. Explain your method. Chapter 2 Operations with Integers --249 nitrogen [ --201 Order the integers in each set from greatest to least. 57. {--13,5,0,--5} 56. (4,--2,-10,3} 58. {7,-26,--15,32,--19} --101 ldardized Test Practise Which of the following statements is false if -- 3and b = -37 72. The table shows the number of points selected players have at the end of a game. Player Points A -10 B -50 C -5 D 0 E -15 If txl -- 1, what is the value of x? H -1 and0 J land-1 F land2 G land0 Order the integers I-5 I, -I 9 I, -4, O, -I 10 I, 7 from least to greatest. Explain how you determined the order. Which list shows the finishing order of the players from first to fifth? A D,C, A, E, B B B, E, A,C, D C D, C, A, B, E D B, C, A, D, E Colm~on Core Review property shown byeach statement. 7.EEl1 74. 16+0=16 73. 42+36=36+42 75. (19,15),2=19,{15-2) 76. 33 ¯ 0 = 0 78. 25-I=25 (7+9)+6=7+(9+6) Translate each phrase into an algebraic expression. &EE.2a 79. nine less than twice the number of boys BO. the distance Darren ran plus four more miles the number of video games sold minus two 82. ~ ~t~p~e ~p~esentat~ons A roll of wrapping paper costs $3. 7,EE,4 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 table to find the cost of 3, 4, 5, and 6 rolls. ¢. Graph Graph the ordered pairs. Find each quotient. 6,NS.2 83. 14)2730 84. 54~4736 85. 63119,278 86. 45 2~,250 87. 8~122,628 88. 103)21,129 of each figure. 6,G,1 90. 7cm 91. 2.Sft 24 cm 5ft