Pre-Algebra & Pre-Algebra Enriched Unit 1 Introductory Topics & Operations with Integers Name Period ____i)Unit 1: Introductory Lesson 1 — Variables and Expressions Objective: Vocabulary: Definition Examples Variable = |', used to represent a Numerical Bs | Eapneceion | Contains only and Variable A . May contain : Expression | and one or more Example 1: Identify each expression as a numerical expression or a variable expression. For a variable expression, name the variable. a)5-5 b)e-5 )8rx+9 d) 100 +6 Example 2: List possible clue words that would tell you to complete each of the following: ‘Addition ‘Subtraction | Multiplication Division Parentheses Example 3: Select the BEST way to write each expression a) The product of a and 5 b) ‘The quotient of 3 and x O axs O 3+x O as 3 0 5xa | OD 5a OD xs3 o wisUnit 1: Introductory Lesson 1 — Variables and Expressions Example 4: Complete the table below. ‘Word Phrase Variable Expression Nine more than a number y yto \4 Tess than a number n Anumber z fimes three Anumber a divided by 12 5 limes the quantily 4 plus a number c Example 5: Write a variable expression for each word phrase. a) 16 more than m b) the product of e and 3 c) btimes 8 d) xless than 2 e) 4 more than the quotient of g and 6 £) 10 less than the quotient of a number cand 13 g) less than 18 times a number x h) 6 times the sum of a number q and 9 {)_ one fifth of the sum of 10 and a number q j) 12 times the quotient of a number g and 43 19 6 less than the product of tand 7 Example 6: Write a variable expression to represent the situation. a) number of hours in m minutes ) cost of p pens priced at $0.29 eachrai i Name Period Express each phrase as an algebraic expression. @ @) @) @ () (6) @” (8) (9) (10) Gy (2) G3) (14) Gs) (46) G7) Gs) 6 less than a number k multiplied by 25 12 times the sum of a number v and 41 4 more than the difference of 12 and a number j less than the product of 3o and a number r half the quotient of 4 and a number y 8 plus 43 less than a number w 3 less than the difference of 15 and a number u the difference of 36 and a number h sum of 23 and a number x 4 more than the quotient of 24 and a number m 5 plus the product of 39 and a number e 8 times the sum of a number z and 3 7 plus a number d less than 37 11 times the sum of a number z and 3 3 less than the product of a number g and 49 11 times the product of 19 and a number g a fifth of the sum of number a and 34 9 more than the quotient of 14 anda number nAlgebraic Expressions Self-Assessment Name Period Express each phrase as an algebraic expression. Q@ Keep track of the @ - problems answered incorrectly when we 3) —__________ ——— discuss the correct responses. Place an “X” CG) ——— on the line when you respond incorrectl CG) eee = : a a —— @m - go as Cy — (10) Q@y ee ll ——— — G3) —___________ — Ga) Gs) (6) - — oe — Gay —s (9) ——= (20) Gy eee ——_ te = My Score: (23) a (ea) — ——__/ 25 (25)Algebraic Expressions Worksheet 2 Name Period Express each phrase as an algebraic expression. @ @) @) @ () (6) o” (8) @) (10) ay G2) (43) (14) Gs) (16) a7) (48) Go) (20) 8 less than 25 multiplied by a number q 7 more than the quotient of 26 and a number d 3g more than the difference of 20 and a number m Anumber x plus 45 A fifth of the product of a number x and 8 9 more than a number w 4 times the sum of 41 anda number k 5 less than the quotient of a number u and 15 7 less than the difference of 22 and a number e 5 times the sum of a number u and 15, 3 plus the product of 35 and y 3 plus 27 less than a number q 7 times the product of a number c and 7 6 more than the quotient of a number d and 12 8 plus a number y increased by 38 4 more the quotient of a number d and 12 Add a number j to 33 11less than the difference of 19 and a number k 8 times the product of 28 and a number g 11 less than 43 times a number r(21) (22) (23) (24) @s) (26) @” (28) (9) (30) Go (32) (33) (34) (35) (36) Difference of a number n and 17 3 plus the product of 37 and a number p 11 Jess than the sum of a number v and 23 Half the product of a number t and 48 1 more than the difference of a number fand 18 2 more than the quotient of a number b and 6 a fourth of the difference of 10 and a number a 4 less than the sum of 29 and a number u 10 plus § times the number x 3 times the quotient of 39 and a number n 10 less than a number j multiplied by 44 2 plus 40 more than a number x 13 times a number p anless than the product of 47 and a number e 4 times the sum of a number fand 46 ‘The product of 4 and a number gressions Worksh: Name Period Express each phrase as an algebraic expression. (1) 5 less than the difference of a number f and 35 (2) 6 less than the quotient of 2 and a number f (8) The quotient of a number p and 38 (4) 4 more than the difference of a number x and 10 (5) 9 plus the product of 47 and a number ¢ (6) The product of 44 and a number y (7) 40 divided by a number ¢ (8) 10 plus 21 increased by a number k (9) 11 times the product of 31 and a number p (10) 3 more than the sum of 32 and a number d (11) 1 less than 5 times a number g (12) 5 less than the quotient of a number e and 33 (13) 10 plus the product of 48 and a number x (14) Subtract a number m from 45 (15) 9 less than the sum of a number u and 20 (16) One-third of the product of 13 and a number n (17) 10 more than the difference of a number h and 27 (18) 7 times the difference of 17 and a number bAlgebraic Ex, sions Worksheet 3 Answer Key @) (f-35)-5 2 @ 76 ‘There is more than «@) z ‘one correct way to write some of these i is 4 +4 answers. ASK if you 5) 9+47¢ (6) 44y @ © (8) 10+ (21+%) (9) 1131p) Go) (32+) +3 Qt) 59-11 G2) 5-5 (13) 10 + 48x (a4) 45-—m G5) (u+20)-9 (6) (13) G7) (h-27)+10 G8) 7(17-)Unit 1: Introductory Lesson 2 ~ The Order of Operations Objective: Key Ideas Order of Operations An agreed upon set of rules so th answer to a given problem. Example 1: Show and name the different types of grouping symbols. Example 2: What is the difference between 6? and 6.2? Example 3: Simplify using the order of operations. a) 448+246-3 bd) 6-(3+2)s15 ce) 14416-2°-8 +2? aUnit 1: Introductory Lesson 2 e) 2[(12-3) ge) 3+4[13-2(6-3)] h) ‘The Order of Operations Example 4: Some urban planners specialize in planning entire new towns. These towns are designed for livability, with plenty of open space. The sketch below shows the dimensions for a new town called Panorama. Find Panorama’s area. 3km 4k 2km 6kmSimplify the expression. @ > 9423-5 (2) @) 7-1445-2 © @ 14+@%-7) (8) Go) 8-3(2-(@+1)?+8-2) Gn) (3) 3:5-(8?+2)+72+8 (44) (6) 6(5+3)+4(6-3) a7) Name Period 43-3022 2? + 6(3 + 10) 20 = (4-(10-8)) 3745(2+9) 8-3-(24-4) +2 10+2°[18+ (5+) @) (6) (9) (a2) (5) (as) 9445+9-8 87+ (8-4) ros10 73 P-8-346 11+3(19 +2) (6-2)-0+8Order of Operations Worksheet 2 Simplify the expression. @ 15+(2+2- (3) (16-8) -4+16 (5) (2410) + (6-4) (7-444) 44 (9) (4244+6)+3 (1) (G42+3)+5]-9 (a3) (20-4+3)+247 Name Period (2) (8+4)+(24=8) (4) (G+9)+745 (6) (21+ (40-3)+3] (8) [49-4)-2]+6 Go) [(27-6)+3]-7 (2) (67-4) +9] -6 (14) 4-(45+5)+6-17 Continue to next page >Gs) G7) G9) (2) (23) (25) 64+ (749-8) -3 8+7-(27=3-4) (74+8-3-3)=2 ((21-4)-3]-7°5 42 -{8-[(7 +8) +5]} 7+ 2244203? -2264+12=4) (16) 8) (20) (22) (24) 7-(5+3)+(9-5) (28 + 2-6): (5 +2) 12-3-[14+(3+4)] 60 + [(9-6) 5] +7 {((18- 9) -4] +7}-0OUnit 1: Introductory Lesson 3 —- Writing and Evaluating Expressions Objective: © When substituting, ALWAYS use ! Example 1: Evaluate each expression when a = 3 and b = 5. a) Ja—ab+b b) — 10a+ (2h) ©) 4ab-6b + Sa Example 2: Evaluate each expression when a = 2 and b = 6. a) 3b+(2a-1)+b b) 9b+a* +8 2 apt 3(b-2) ) (a +8)+a rN) ier) Example 3: Evaluate the expression when a = 6, b = 10, and ¢ = 2. a(b+2-2c)—a Ib\v nit 1: Introductory Lesson 3 — Writing and Evaluating Expressions Example 4: Evaluate the expression when a = 9 and b = 3. a) (2a—30)+4 °) xe +(2a+6) 4d) 8(4b—a)-(a*-b')ing Expressions Worksheet Name Period Evaluate the expression using the values given. Q@ (3) ® a 9) a? —bwhena = Bandb=7 a+ab when a = Sand b =2 10-a+b+2whena = 3andb = 14 a(b — 1)? when a = 8andb = 4 3(x? — 4y + x) when x = 6 andy =7 @) (4) (6) (8) (ao) 3(x —y) when x = 4andy =1 x+y whenx =2andy=3 12 - (x? + y*) when x = Landy =2 $- 3b +5 when a = 24 and b =2 = + 2awhena = 6andb =8a) 3) (a4) Gs) ab? — b when a = 2andb = 4 (12) 4 when x =3andy=4 3(Ba — 5b) — 2(a + b) when a = 3 and b = 2 xyz +x? — y? when x = 3 andy =4andz=5 ySimplify each expression. GQ) 37+5-10 (3) 4477-9 () 207-5) +3-4 (17412-1044 (9) 5@G+2)+5 (1) (4?7-6)-8-5 G3) 89-6) +4 (a5) 18(9- 37) +11 (7) 5(19- 11) - 4(7-2) Name Period (2) +9)+5-2 (4) 10+2-6+3 (6) 5:7-4+2 () 4-329 Go) 23-3(11-7) (2) 5?-3? +4? (14) (42-77) +15 (6) (9-4)+(6-5) (98) 12+3(7-5)20 G9) (21) (23) Evaluate each expression when a = 3, b = (25) (27) (29) (3) (33) 18410 2-5 (443) 127 Ba—b (a-b+4)+5 4(7 + ac) +4 (2 +3) +2 ce +b—b2 (20) FS (22) (24) (26) (28) b?-c+5 (30) a?-bte (32) 105 +3c—b (34)arbre (36) (38) c?-3b+4a Write an expression to represent the situation. Do NOT solve! (g9) Seven of the algebra classes at a school have 23 students each. ‘The eighth class has 25 students. What is the total number of students? (40) During a paper drive, four teams each collected 5 tons of paper the first week. Altogether, the teams collected 2 tons each week for the next six weeks. How many tons of paper did each team collect if they each collected equal amounts? AlaaObjective: Unit 1: Section 1.2 — Adding Integers Example 1: Use the number line to find the sum. a) -2+(-2) b) 3 +(2) 4 > 4 > 54321012345 S43241012345 547 $5 -4-3-2-10123 45 Key Ideas Add the Use the common sign. Adding Integers with the Same Sign _ of the integers, Examples: Adding Integers with Different Signs Subtract the absolute value from the absolute value. Use the sign of the integer with the absolute value. Examples: Additive Inverse Property The sum of a number and its opposite ( iis Examples: Example 2: Simplify. a) 12+(-5) bd) -11+6 -1S+¢4) a3Unit 1: Section 1.2 — Adding Integers Example 3: Two integers have different signs. Their sum is ~5. What are three sets of possible values for the two integers? Option 1: Option 2: Option 3: When you have more than two integers, you can follow these steps: 1. the positive integers. 2 the negative integers. 3. Follow the process for adding integers with Example a: Simplify. a)2+(-7)+(-3) b) -5 + (-2) + (4) + 7) c)-1 +9 + (-6) Example 5: At 2:00 p.m., the water pressure on a submarine is 325 pounds per square inch. From 2:00 p.m. to 2:30 p.m.,, the water pressure increases 83 pounds per square inch. From 2:30 p.m. to 3:00 p.m., the water pressure decreases 37 pounds per square inch, What is the water pressure at 3:00 p.m.? Example 6: Simplify. a)—12 + (6) +15 + (3) +104 (-12) b) 5+ (-1) 42+ C10) + 12+ (-25) anAdding Integers Worksheet 1 1. 2. 3. 10. 1. 12, 13. 4. 15. 16. i. 18. 19. 20. 6+(-4) = -2+5= 4495 -8+(-6) = -9+8= T+45 0+(-2)= -3415 5+ (-5)= -44+8= 9+2= 6+5= —8+C-9)= “7435 2+ (-1= -446= 1495 -1+(-2)= 10+ (-4) = 8+(-7)= Name Period QL. -34+(-4)= 22. 5+1= 23, -6+2= 24. 8+ (-3) = 25. —5+(-1) 26. -9+5= 27, 2475 35. 36. 37. 38. 39. 40. 1B +2= 44(-3) = 14465 -3+(-4) = -3 + (-12) = -84+7= 41, 42, 43. 44, 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 24(-2= -S4+7= -2+(-4) = 44 (-3)= 5495 —440= 24 (-6) = —84+5= 9475 0+ (-2)= —44+8= -6 + (-9) -7+15 2+4= -3+(-6) = 7+3= -8 + (-5) = -5+(-6)= -14+(-9 = 12+ (-11) =ao Adding Integers Worksheet 2 10. uu. 12. 13. 14. 15. 16. 17. 18. 19. 20. . 449+ (6) . 6+ (-4) + (3) = . 245455 -8+(-6)+8= . 948+ (-5) = TH 44 (9) = 2 OF (-2)4+2= . —34+143= . 5+ (-5) + (-7) = -44+842= 94+2+(-8)= 6+54+4= -B+(-9) + (-9 -74347= 2+ (-7) + (-13) = 446445 14+9+(-14) = -1+(-2)+(-3)= 10 + (~4) + (-3) = 8+ (-7) + (-8) = Name Period ai 22. 23. 24, 25. 26. 27. 28, 29. 30. 31. 32, 33. 34, 35. 36. 37. 38. 39. 40. 10 + (-3) + (-9) = -S+(-4)+6= 3411+(-8)= 94+24(-1) = (-1) +(-5) #11 = -B+147= 1+0+(-10) = 7+ (-10) + (-8) = -8+(-7) +125 24+10+9= 6+3+(-1)= -7+(-9) + (-6) = 945405 5 + (-8) + (-4) = -34+745= -8+(-6)+2= 4+(-9)+3= -7+(-8)+(-9) = -64+12411= 4+(-6)+9=Date Find the sum. 1.842 2. -S+(-3) 3. -9+(-3) 4, 6+(-6) 5. 4+ (-4) 6. 9+(-6) 7. 5+(-2) 8. 7+(-13) 9. -18+1 10. -12+(-5) 11. 0+(-7) 12, 12+ (15) 43. Your bank account has a balance of -$21. You deposit $50. What is your 14, 17. 20. 23. 26. 29. 12 new balance? 745+(2) 18, -13+7+(-3) 16. 17+ (5) #1) 44+8+(-8) 418. -12+(-4)+9 19. -10+10+(-3) (in +s+ C12) 24. 7+15+(-7) 22. “12 +(-5) +10) (1) +5+(-12) 24, 74+15+(-7) 25. -12+(-5)+(-10) 8+(-9) +3415) 27, 3417+ (-7)+(-3) 28. -9 + (-10) + (8) + (2) In golf, a golfer must have a score of 0 in order to be at par. A golfer scores 2 above par on the first hole, 1 below par on the second hole, and 2 below par on the third hole. Which expression can be used to decide whether the golfer is at par after the first three holes? (Cys? 2+ (C1)+2 (2+) +] Big Ideas Math: Modeling Real Life Grade 7 Copyright © Big Ideas Learning, LLC Ot Resources by Chapter Al ights reservedName. Puzzle Time Date _ Why Did The Golfer Wear Two Pairs Of Pants? Write the letter of each answer in the box containing the exercise number ancwers Find the sum. 8. 18 N, -18 4.1245 2. 7+(-7) 0: 12 c.-8 3. -10+2 4. 9+ (-6) L. -17 H. -25 8. -15 +27 6. 23 + (-23) ae au T. 7 a3 7. -17+12 8. 13+(-15) A. -2 9. -9+(-9) 10. -14+(-11) 41. 12 +(-10) + 16 42. 15+(-15)+12 13. -22 + 30 + (-26) 14, -8 +(-8) + (-9) 15. 37+ (-21) + (-16) 16. -42+8+17 17. -30+34+(-9) 18. 14+ (-21)+7 49, -25+17+6 20. -4 + (-8) + (-6) 24. A roller coaster climbs 84 feet on the first hill then drops 60 feet down. On the second hill the roller coaster climbs another 32 feet then drops 44 feet. What is the height at the end of the second hill? 7]ePo7 2] * |] sp] | ep] 4 ]2] 1 fa] ep 0] 2] 16] 2 w/e 3 [a0] 6 16 Big Ideas Math: Modeling Real Life Grade 7 Resources by Chapter Copyright © Big Ideas Learning, LLC All rights reserved.Unit 1: Section 1.4 ~ Subtracting Integers Objective: Example 1: Use the number line to find the sum. a) 4-1 b) @) ete 5-43-2-10123 45 a5 <4 -31-2\-1) 08 f 293 4 5 Key Ideas Subtracting Integers Subtracting integers is equivalent to the Then, follow the rules of, integers. Examples: Example 2: Simplify the expression. a)-7-8 b) 4-17 ce) 5-3) Example 3: Simplify the expression. a)-1—(-6)-3 b) 5-3-(-19) o)7 (-2)- 10 d) 32-(-3)- (C1) e) 40 — 16 + 8) - (2) f) 14-6 -(-11) +2) aUnit 1: Section 1.4 — Subtracting Integers Example 4: Which continent has the greater range of elevations? South America, al Highest " | Elevation 6960 m 5642 m Lowest [Blevation | “9™ |“ Example 5: The temperature decreases from 52°F at 11:00 p.m. to 47°F at 12:00 a.m. The temperature changes by the same amount each hour until 5:00 a.m. Find the total change in temperature from 11:00 p.m. to §:00 a.m. Example 6: Simplify the expression. 2 = (5) + (1) ~ (16) 12 + 25 ~(-10)- 14 +3Subtracting Integers Worksheet 1 a 4. 16. 17. 18. 19. 20. 6-(-4)= -2-5= . 2-(-1)= 24. 22, 23. 24, 25. 26. 27. 28, 29, 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. Name _ Period (-4)= 5-1= -6-2= 8-(-3)= -$-(-1)= -9-S= 2-7= 3-(-7)= -7-(Ca= 2-8= —§-(-5) = 4-(-2)= 41. 42, 43. 44, 45. 46, 2-(-2)= -5-7= 2-H 4-(-3)= 5-9= 54. 55. 56. 57. 58. 59. 60. 2-4= -3-(-6)= 7-3= -8-(-5)= -5-(-6)= -14-(-9) = 12-(-1)= 3|3a Subtracting Integers Worksheet 2 1. 6-(-4) —(-3)= 2-2 3. 4-9-(-6)= 4, -8-(-6)-8= 5. -9-8-(-5)= 6. 7-4-(-9= 7. 0-(-2)-25 8, -3-1-3= 9. 5-(-5)-(-7) = 10, -4-8 11, 9-2-(-8)= 12, 6-5-4= 13. —8 —(-9) -(-9) = U4, -7-3 15, 2~(-7) = (-13) = 16. -4-6-45 11. 1-9-(-14) = 18, -1-(-2)-(-3)= 19. 10 ~ (~4) ~ (-3) = 20. 8-(-7)-(-8)= Name Pernod 21. 22, 23. 24. 25. 26. 27. 28, 29. 30. 31. 32. 33. 34, 36. 37. 38. 39. 40. 10 ~ (-3) -(-9) = -5-(-4)-6= 3-11-(-8) = 9-2-(-7)= (-1)-(-8)-11= 8-1 1-0-(-10) = 7 = (-10) - (-8) = -8-(-7)-12= 2-10-9 6-3-(-1)= 7-9) - (6) = 9-5-0= 5-(-8)-(-4)= . -3-7-5= -8-(-6)-2= 4-(-9)-3= -7-(-8)-(-9) = -6-12-11= 4-(-6)-9=Date Find the difference. 1,3-8 2. 4-(-5) 3-6-4 4, -9-(-6) 5. 10-(-9) 6 12-4 7. -15-7 8. ~6-(-14) 3) 10. 15-(-7) 14, 20-(-10) 12, 31-14 13. You are scuba diving at —8 feet. You dive 5 feet deeper. What is your position in the water? 14. 8-12-(-8) 15. 3-(-8)-3 16. 0-(-4)-4 47. 9-(-4)+(-9) 18, 7-12-(-12) 19. -11-(-8)- (3) 20. Your friend finds the difference. Is your friend correct? Explain your reasoning. 21. The table shows the highest and lowest elevations for City elevation (feet) two cities. Long Beach, CA 360 a. Find the range of elevations New Orleans, LA 25 for Long Beach. 8 b. Find the range of elevations for New Orleans. Copyright © Big ideas Leaming, LLC 24 _ Big Ideas Math: Modeling Real Life Grade 7 Allrights reserved Resources by Chapter3D Name Date - Puzzle Time What Did The Sea Say To The Sand? Write the letter of each answer in the box containing the exercise number Find the difference. Answers 4.3-11 2. -5-12 J04 ow Ww. G. 40 3. :14-(-10) 4. oO, 3 E. -7 5. 25-(-8) 6. -13-(-13) Bt S. 25 N. -17 Evaluate the expression. v3 A-23 7. -6+15~(-4) 8. 11-22-(-8) UL 13 4 9. -14-7-(-25) 40. 17+8~-(-15) 41, -9-(-4)-2 42, -16+5-12 43. The high temperature for a day in January was 7 degrees Fahrenheit, The low temperature that day was —5 degrees Fahrenheit. What is the difference in temperatures? 44, The top of a sailboat mast is 22 feet above the water surface, The bottom of the sailboat is 3 feet below the water surface. What is the difference in the elevations? 2]5)9]3]e]2]) Jsl]s a]7]4] 9 1]2]a]"]4 28 Big Ideas Math: Modeling Real Life Grade 7 Copyright © Big Ideas Learning, LLC Resources by Chapter Al ights reservedMixed Operations Worksheet 1. 6-(-4) + (-3)- (4) = 2 -2-5+5-1= ~ . 4-94 (-6)-2= s . 8 (-6) +8 - (-3) = * . —9-84+(-5)-(-1) = = 7-44(-9)-5S= a 0-(-2)42-7= » -3-14+3-(-7)= 9. 5-(-5) + (-7)-(-3) = 10, -4-8+2-85 11, 9-2+(-8)-(-5) = 12. 6-54+4-(-2)= 18. -8- (9) +(-9)-3= 14, -7-34+7-S5= 15. 2-(-7)+(-13)-2= 16. -4-6+4-(-3)= 17. 1-9+(-14)-6= 18. -1-(-2) +(-3)-(-4)= 19. 10 -(—4) + (-3) - (-12) = 20. 8-(-7)+(-8)-7= Name Period ___ 21, 22, 23. 24, 25. 26. 27. 28, 29. 30. 31. 32. 33. 34, 35. 36. 37. 38. 39. 40. 10 — (3) + (-9) -5= -5-(-4)+6-8= 3-114 (-8)-(-4) = 9-24+(-I)-7= (-1) -(-5) +11-6= —B-147-9= 1-0 + (-10) -(-3) = 7 — (-10) + (-8) - (-5) = -8-(-7)+12-10= 2-10+9-2= 6-3+(-1)-(-4) = -7-(-9) + (-6)-11= 9-54+0-3= 5 -(-8)+(-4)-(-D= -3-7+5-2= -8-(-6)+2-(-9) = 4-(-9)+3-(-12) = -7 ~ (-8) + (-9) ~ (-10) = -6-124+11-14= 4-(-6)+9-(-10) =Unit 1: Section 2.1 — Multiplying Integers Unit 1: Section 2.2 ~ Dividing Integers Objective: Key Ideas Multiplying/Dividing Integers with the Same Sign The product/quotient of two nonzero integers with the same sign is Examples: + Multiplying/Dividing Integers with Different Signs The product/quotient of two nonzero integers with the different signs is i Examples: + Zero with Multiplication and Division ‘The product of any integer and 0 is Examples: Zero divided by any integer is Examples Division by zero is Examples: General Rule: + When the number of negative signs is even (only when multiplying or dividing), then the answer is . When the number of negative signs is odd, (only when multiplying or dividing), then the answer is ; Example 1: Simplify the expression. a) AYDAVYOO|-) » AAQ)A\A\)2) 3tExample 2: Simplify the expression a) 2-6) 3) da 45-11) +2 Unit 1: Section 2.1 — Multiplying Integers Section 2.2 — Dividing Integers 2437-6 oo) -8-3)(-2)-1) -H-14)(-13)(-15}(0) a) 455411 -3)+2-4 Example 3: A roller coaster starts at a height of 45 meters. From the starting position, the roller coaster descends 3 meters per second for 5 seconds. How high is the roller coaster 5 seconds after the ride begins? Write an expression to represent the problem. Do not solve! Example 4 (Texthook Page 52, Problem 17): Players in a racing game earn 3 points for each coin they collect. Each player loses 5 points for each second that he or she finishes after the first-place finisher. The table shows the results of a race. List the players in order from greatest to least. (iPyer [Coins | “Time 1 31 | 0:02:03 [2 | 4. 0:01:55, 3 24 0:01:58 | 4 27 0:02:01 Example 5: Find the mean of the integers: 3, —8, 1, -.Date Find the product. 4.493) 2. 695 3. -8(-2) 4.9°6 5. 0+(-7) 6. -12(-3) 7 Ue7 8. 5(-5) 9, -13+7 10. -1+9 14, 2(-12) 12. ~9 + (-9) 13. A water tank leaks 5 gallons of water each day. What integer represents the change in the number of gallons of water in the tank after 7 days? Evaluate the expression. 14, 2+(-3) 95 15, -5(-4)(-1) 16. 7+2+(-3) 17, 0+ (-8)+6 18, -6+4+(-2) 19. 5(-4)(-5) 20. (-3 21. -37 22. (-2)° 23, -S* 24, -3 + (-4)? 25, (-7)2+2 26. (-2)* + (-6) 27. -5(-2)-3(-4) 28. 2+ (37S? 42 Big ideas Math: Modeling Real Life Grade 7 ‘Copyright © Bg Ideas Learning, LLC Resources by Chapter Al rights reserve. AName __ Date Puzzle Time When Do Kangaroos Celebrate Their Birthdays? eleee on |Poe| scrips ejulfila «]etu]w Complete each exercise. Find the answer in the answer column. Write the letter under the answer in the box containing the exercise letter. 36 Multiply. . = AL 5 +(-12 B. -14¢3 4 12 ae coe ~25 ° ™ =105 ~48 E cc. -10(-11) D. 8+(-7) 7 25 ~64 P A 50 E. -9+(-5) F. 6(-2)(-3) 80 ce L =60 =50 D G. -4+5+(-4) H. (-7)(-3)-5) u 72 100 s 8 5 sy? 64 1-15 00 d5) i (12) ) fe =25 =56 1 kK. -P 37+ 8 . =a2 =110 uv J 9 5 66 P M. (-4) 8 =36 54 H R 52 N. You are making a necklace that is 9 inches long. “72 w ‘You use 6 beads for each inch. What integer is E 110 the change in your supply of beads after making oo R the necklace? K Q 46 _ Big Ideas Math: Modeling Real Life Grade 7 Copyright © Big Ideas Leaning, LLC Resources by Chapter Allrghts reservedName eee 22 Reteach (continued) Remember to use the order of operations when evaluating expressions. EXAMPLE Evaluating an Expression Find the value of when x=~12 and y= ~2, Substitute -12 for x and -2 for y. ‘Write (-12) as repeated multiplication. sign, the product is positive. Date__ Multiply -12 and ~12. Because the integers have the same 14 Multiply 3 and ~2. Because the integers have different signs, “6 the product is negative the quotient is negative. D> The value of the expression is ~24. Find the quotient, if possible. 1, 99+9 2. :121+(-11) 3. (-125)+5 5. 0+(-3) 6 (-3)+0 7 2 -n -60 3 10. = Ww Evaluate the expression. 13. (-2)(-25) + (-10) +3 14, -10-+ 10(-12) +6 15, (-4)(10) = (C1) +5 Divide 144 by ~6, Because the integers have different signs, 4, (-56)=(-1) 3 ae 12, = 16, 5+2(-4)+3 17, -20+(-2)+3 18. 6°-2+4 Evaluate the expression when x = 30, y= -3, and z= ~2. 19, x=2y 20, 812)" 21. Syzttx 22, x+(y+z) 23, 24, 2 2. 26. y a = 50 Big Ideas Math: Modeling Real Life Grade 7 Resources by Chapter Al Copyright © Big ideas Learning, LLC Allrights reserve.Ha Integer Rules with Order of Operations 1 Simplify each expression using the order of operations. Show your steps! 1) 24+ (-84 +-6-16)--9 2) 49+-7-6-(-2) 3) -15+36+6--3 4) 224-11 19-(-5) 5) -23 +-80+-8--4 6) 1-(244+-29-(.27)) +4 7) -3+-4+12-(-20) 8) 28 -(-6) + 39+-3 9) 18-(-40+-36) +-4 10) -5-49+-7-2u) 13) 15) 17) 19) 33+ (-22)+2--4 17-(22"-1) +-2 36 +-12-3-(-5) -12-28+-7--3-12 14+-14+-7+-32-(-8) 12) 14) 16) 18) 20) 23--5+5°-3 24+ (-84+-6)-9 T+Q+-3)+(6) 7-5 ~(-33)411 -255 +5 --2-(-3) ABInteger Rules with Order of Operations 2 Name __ Period Simplify each expression using the order of operations. Show your steps! 5 2) -91+-7-(-3)-(-8) v ~ (-96 +-6 ~27) 4) 77 +-11-(-3)-C5P 3) -15+72+(4 5) 23 + (-108) + (-12)--2 6) -1-(23+13-6F +2 7D 9-4 = (12) - 20) - C7? 8) -32+(-4)-39+-13 9) 18-(-40+-36) + 19-1 10) -13 + (21 +7) - (32) + (C8)REVIEW: Operations with Integers Simplify each expression. 1) -1-29-17+-35 3) 13 +33-(4)-18 +43 5) ” 9) 1) 13) 15) 34 +27 +-31-21-(-9) 494-741 23 -(-5)+5-7 48 + (40) +38 - (1) - 48 14+-21-30+-18 Name Period 2) 30+-6-28 4) -3--4--10 6) -5--3°-2--1 8) §:-3+-2-1 10) 18-9-38 12) 244-18 +1436 14) 16) -25+-21 2) 3) 4) 5) 6) D 8) 9 10) 11) 12) 13) 14) 15) 16) 4517) 19) 21) 23) 25) 27) 29) 31) 33) 18 — 43 ~(-33) - (34) + 13 1-3+39 29-(-1) +45 144+ 12+-12 -12+-8 GAC) -29 31 -(-44) +41 -31+35-(49) 35 ~ 29 +-28 -(-39) 18) 20) 22) 24) 26) 28) 30) 32) 34) -2+-2-(-30) (AETIB) Q-DEDEDED 20+-2 16-5+-15 1-3+39 17) ___ 18) 19) 20) 25) 26) 27) 28) 17-28 +27 - (-32) +34 Q)C1I)-DE-2) 29) 30) 31) 32) 33) 34)Units Review Name Period Simplify the expression by adding and/or subtracting. 1) -25-10-12~(-13) 2) 10-3) + (-4)- (12) 3) -19- 30) + 9) -(-11) 4) ~42+(-13) + (12) = 15 5) 20+-11 +(-12)- (12) 6) 6+ 15-16~-17-(16) 7) 10-(-5) +30+€-6)-2 8) 35-25 -(-25) - (35) Simplify the expression. 9) -3--14--2 10) 4834-4 » = 3(-4412) . -3(9+-24) rs 13) 3-3-(-18)+6 _ 15) 81+-9--2-(-8) 16) 4--3+-1248-(-2) 47) (-10)(-4)=(-2) 18) -3-4-6-7 19) (-1)(-1)(-2)(-3)(-4) 20) 6+8-(-8)-10+11-8 448 Evaluate the expression. 21) a(b— 1)? ifa=—2andb=4 22) $-4b+2ifa=—6andb = 23) 3(x2+4y—x) ifx= Sandy = vifr=3, w= I, and 1=5 25) x(r-+w) 2,r=3,we 1w=4,and7=5 Express each phrase as an algebraic expression. 26) 4 times the quotient of a number g and 6 27) 7 more than the product of a number ¢ and 7 28) 2 more than the quotient of a number b and 6 29) 11 less than the sum of a number v and 23 30) Find the mean: 12,—7,6,3,—4,—5,2,1O