Learn o Multiply integers. Simplify algebraic expressions.

Transcription

1 Guide Link Learn o Multiply integers. Simplify algebraic expressions. ~ Reag-Wor~d Line Hot air balloon races grab the attention of people from miles around. During a balloon race, pilots must fly over a target on the ground and drop a marker as close to the target as possible. During a recen~ race, the winning oalloon descended at a rate of about 8 meters per secona. Core EE.3 Multiolication is reoeated addition. So. 3(-40) means that -40 is used as an addend 3 times. 3(-40] = -40) + -40) + (-40) = By the Commutative Property of Multiplication, 3/-40/= -40(3). This and other similar examples demonstrate the rule for multiplying integers with different signs. Words The product of two integers with different signs is negative. Examples 2(--6) = (6) = --12 Find each product, a (12) b. 4(-7) 4(-7) GO~ t~ ~ Do these problems to find out. lb Multiplying Integers

2 s The product of two integers with the same sign is positive. Exampl~... e~s 4-6 = ) = /) The oroduct of two positive integers is positive. What is the sign of the product of two negative integers? Look at the pattern below. Factor Rule: Times-5 Product 2-5(2) (01 _1-5( ( Find each product. a. -5(-7) -5(--7) = (--14) -8(--14)=112 6#{ ~{? Do these problems to find out. 2a. --5(--11) 2b. -13(-4) An airplane descends at a rate of 175 feet per minute. What is the airplane s change in altitude after 5 minutes? Write a multiplication expression. Then find and interpret the product. The word descends means downward, so the rate per minute is represented by a negative integer. Words 5 minutes times descent rate of!75 feet per minute Expression 5 x (-175) So, the airplane descends 875 feet after 5 minutes. 6e{ ~? Do this problem to find out. A scuba diver descends from the surface at a rate of 7 feet per minute. What was the scuba diver s depth after 15 minutes? Write a multiplication expression. Then find and interpret the product. Chapter 2 Operations with Integers

3 Use the Commutative and Associative Properties of Multiplication to multiply more than two integers. Find -4(12)(-5). Look for products that are multiples often to make the multiplication (~[~~--~.~ Use the Associative Property --4(12)(--5) = [-4(12)](--5) = --48(--5) = 240 Use the Commutative Property -4(12)(-5) = -4(-5)(12) = 20(12) = 240 ~0# I~ Do these problems to find out. 4a. --7(9)(--6) 4b. -3(-4)(-5) You can use the rules for multiplying integers to simplify and evaluate algebraic expressions. Simplify --Ta(4b). -7a(4b) = (-7)(a)(4)(6) = (-7.4)(a- b) : -28ab ~0# I~ Do these problems to find out. 5;b. - 9x(3y) Evaluate 3xy ifx = 2 and y = --6. = [3(2)](--6) < ~0~ /~ Do these problems to find out. 6a. Evaluate 2rs if r = 5 and s = b. Evaluate 4ab if a = -8 and b = -4. Lesson 2-4 Multiplying Integers

4 3. 8(-3)(-5) Mr. Heppner bought lunch with his debit card every day for 5 days. Each day he spent $8. If these were his only transactions, what was the change in his account balance? Write a multiplication expression.then find and interpret the product. /~x~m!~! ~:~) Simplify each expression. 0x,, rq~i~ m (7b) 8. -6e(-4f) 9. 8j, ifj= cd, if c = -3 and d Solutions Find each product. ~3(--9) 12. 8(--9) (--8) (-7) 16. 2(-11)(5) (--7)(--6) (-20)(5) 19, 20. ~ T~" ~ ~ ~I The temperature dropped 2 F every hour for the last 6 hours. What is the total change n temperature?write a multiplication expression.then find and interpret the product, ii~, ~ ~ ~i An elevator takes passengers from the ground floor down to an underground parking garage. Where will the elevator be in relation to the ground floor after 5 seconds if it travels at a rate of 3 feet per second? Write a multiplication expression. Then find and interpret the product. Simplify each expression. ( ~i:~, } 21. 5(-6m) s 25. 4~(b)(-9) (-j)(-3k) Et, alue~e each expression. 2g. --9m(--9n) 27. 3e(--2f)(gg) Ia(7c) 28. 3r(7s)(5t) n, ifn = --I m, if m = , 4xyifx= -6 andy = st, ifs = 4and t = g~,~ ~dej ~[t~ ~a~ rsat[es Diego borrowed $780 from his father to buy a new saddle for his horse. He earns $65 each weekend cleaning stables and uses his earnings to pay off his debt. Write an expression Diego can use to determine how much he owes each week.then make a table to show how much he owes after 2, 4, 6, and 8 weeks. Based on the pattern in the table, predict how long it will take Diego to repay his father. The table shows the number of Calories burned per minute for a 120-pound person during different activities, What is the change in the number of Calories in a 120-pound person s body if he runs for 20 minutes and swims for 25 minutes? Interpret the product. Activity Calories per ~Jnute ballet dancin~ 6 bicycling 12 ~unning 18 swimming 8 Operations with integers

5 (-5) card every day for, what was the 0n,Then find and (-8) (-20)(5) Replace each with <, >, or = to make a true sentence. 3S. --4(6) ~, 3(8) 36. 3(--2) ;, 4(--I) 37. (--I I)(--3)(6)(--2) --24(18) :38. (--5)(--2)(9)(4)(10)(--9) ~ ~t,$~ ~eaeon Ab~t~ae~:l~ Two teams of students played a trivia game. Each team earned 5 points for every correct answer, lost Team Correct Incorrect ]Passed 8 points for every incorrect answer, and lost 2 points for every I 12 3 passed question. For each team, write an expression to determine the number of points they earned Which team won?,,~:: The price of stock fell $2 each day for 14 consecutive days. The original price of the stock was $41. Write an expression that you could use to find the price of the stock on any day. 41. ~gg~ ~u[t[p[e l~ep~e~e~at[o~8 In this problem, you will investigate the relationship between time and altitude. A hot air balloon is at an altitude of 600 feet It begins descending at a constant rate of 15 feet per minute. a. Table Complete the table below that shows the altitude every S minutes. Altitude (feet) 600 parking if it Words What does 0 minutes represent? c. Graph Graph the ordered pairs. d. Symbols Determine the time it will take for the balloon to reach the ground. Explain how you solved. 1 u(7c) 42. ~ ~demt~fy ~ract~e Name two integers that have a product between -10 and , ~J~ ~en~:~fy g~et~e Name all of the values ofx if 71 x I = ~ ~ef~eve~e ~t~e I~ob~e~n~ Positive integersa and CsatisfyA(A - C) = 23. What is the value of C? 45. ~ ~demtify 9t~oet~e Calculate (-10)(5)(18)[7 ( 7)] mentally. Justify your answer. g~ &~ Ose a ~3o~terexa~e Determine whether each of ~he following is true or false. If false, give a ounterexampleo 46. The product of three negative integers is positive. 47. The product of four negative integers is positive. 48. ~ 8~Idi~ o~ l:~e E~e~a~ ~e~ie~ When multiplying more than two integers, how can you determine the sign of the product? Lesso. 2-4 Multiplying integers

6 50. A submarine descends at a constant rate of 300 feet per minute, Which of the following equations could be used to find the altitude of the submarine after 5 minutes? 5(--300) = (300) = (300) = (--300) = 1500 Which of the following equations is modeled by the number line below? 51. Simplify - 14(-2)(-12). A-336 C 168 B -168 D 288, The distance from the water line to the bottom of a cargo ship changes based on the weight of the cargo. weight0f Dept,0fShip! j ~rgo (t~s! i (feet) i !2 18 F -2(-6)=--12 H 2{6)= (6)=-12 J 2(--6)=--12 If the pattern in the table continues, find the depth of the ship if the ship is carrying 100 tons of cargo. +::~ The highest point in California is Mount Whitney, with an elevation of 14,494 feet. The lowest point is Death Valley, with an elevation of -282 feet. How much greater is the elevation of Mount Whitney than Death Valley? 7.NS.ld (-9)+9 56, {-10) (-13) (--12) 58. The table shows the lowest recorded temperatures for certain states. 6.NS.7b State Station Date Temperature ( F) Alaska Prospect Creek Camp Jan. 23, Montana Rogers Pass Jan. 20, I Wisconsin Danbury Jan. 24, ao Compare the lowest temperature in Montana and the lowest temperature in Wisconsin using an inequality. Write the temperatures in order from greatest to least. Find each difference 7,NS.lc Challenger Deep is 10,924 meters below sea level. Write an integer to represent this depth of Challenger Deep.Then identify its opposite and describe the meaning. 6.Ns.s