Exercises: Integers (1.3)
Exercises: Multiply Integers
Instructions: For questions 1-8, multiply.
1. [latex]-4\cdot 8[/latex]
Solution
[latex]-32[/latex]
2. [latex]-3\cdot 9[/latex]
3. [latex]9(-7)[/latex]
Solution
[latex]-63[/latex]
4. [latex]13(-5)[/latex]
5. [latex]-1\cdot 6[/latex]
Solution
[latex]-6[/latex]
6. [latex]-1\cdot 3[/latex]
7. [latex]-1(-14)[/latex]
Solution
[latex]14[/latex]
8. [latex]-1(-19)[/latex]
Exercises: Divide Integers
Instructions: For questions 9-14, divide.
9. [latex]-24\div6[/latex]
Solution
[latex]-4[/latex]
10. [latex]35\div(-7)[/latex]
11. [latex]-52\div(-4)[/latex]
Solution
[latex]13[/latex]
12. [latex]-84\div(-6)[/latex]
13. [latex]-180\div15[/latex]
Solution
[latex]-12[/latex]
14. [latex]-192\div12[/latex]
Exercises: Simplify Expressions with Integers
Instructions: For questions 15-32, simplify each expression.
15. [latex]5(-6)+7(-2)-3[/latex]
Solution
[latex]-47[/latex]
16. [latex]8(-4)+5(-4)-6[/latex]
17. [latex](-2)^6[/latex]
Solution
[latex]64[/latex]
18. [latex](-3)^5[/latex]
19. [latex]-4^2[/latex]
Solution
[latex]-16[/latex]
20. [latex]-6^2[/latex]
21. [latex]-3(-5)(6)[/latex]
Solution
[latex]90[/latex]
22. [latex]-4(-6)(3)[/latex]
23. [latex](8-11)(9-12)[/latex]
Solution
[latex]9[/latex]
24. [latex](6-11)(8-13)[/latex]
25. [latex]26-3(2-7)[/latex]
Solution
[latex]41[/latex]
26. [latex]23-2(4-6)[/latex]
27. [latex]65\div(-5)+(-28)\div(-7)[/latex]
Solution
[latex]-9[/latex]
28. [latex]52\div(-4)+(-32)\div(-8)[/latex]
29. [latex]9-2\left[3-8(-2)\right][/latex]
Solution
[latex]-29[/latex]
30. [latex]11-3\left[7-4(-2)\right][/latex]
31. [latex](-3)^2-24\div(8-2)[/latex]
Solution
[latex]5[/latex]
32. [latex](-4)^2-32\div(12-4)[/latex]
Exercises: Evaluate Variable Expressions with Integers
Instructions: For questions 33-50, evaluate each expression.
33. [latex]y+(-14)[/latex] when
a. [latex]y=-33[/latex]
b. [latex]y=30[/latex]
Solution
a.[latex]-47[/latex]
b. [latex]16[/latex]
34. [latex]x+(-21)[/latex] when
a. [latex]x=-27[/latex]
b. [latex]x=44[/latex]
35.
a. [latex]a+3[/latex] when [latex]a=-7[/latex]
b. [latex]-a+3[/latex] when [latex]a=-7[/latex]
Solution
a.[latex]-4[/latex]
b. [latex]10[/latex]
36.
a. [latex]d+(-9)[/latex] when [latex]d=-8[/latex]
b. [latex]-d+(-9)[/latex] when [latex]d=-8[/latex]
37. [latex]m+n[/latex] when
[latex]m=-15,n=7[/latex]
Solution
[latex]-8[/latex]
38. [latex]p+q[/latex] when
[latex]p=-9,q=17[/latex]
39. [latex]r+s[/latex] when
[latex]r=-9,s=-7[/latex]
Solution
[latex]-16[/latex]
40. [latex]t+u[/latex] when
[latex]t=-6,u=-5[/latex]
41. [latex]{\left(x+y\right)}^{2}[/latex] when
[latex]x=-3,y=14[/latex]
Solution
[latex]121[/latex]
42. [latex](y+z)^2[/latex] when
[latex]y=-3,z=15[/latex]
43. [latex]-2x+17[/latex] when
a. [latex]x=8[/latex]
b. [latex]x=-8[/latex]
Solution
a. [latex]1[/latex]
b. [latex]33[/latex]
44. [latex]-5y+14[/latex] when
a. [latex]y=9[/latex]
b. [latex]y=-9[/latex]
45. [latex]10-3m[/latex] when
a. [latex]m=5[/latex]
b. [latex]m=-5[/latex]
Solution
a.[latex]-5[/latex]
b. [latex]25[/latex]
46. [latex]18-4n[/latex] when
a. [latex]n=3[/latex]
b. [latex]n=-3[/latex]
47. [latex]2w^2-3w+7[/latex] when [latex]w=-2[/latex]
Solution
[latex]21[/latex]
48. [latex]3u^2-4u+5[/latex] when [latex]u=-3[/latex]
49. [latex]9a-2b-8[/latex] when
[latex]a=-6,b=-3[/latex]
Solution
[latex]-56[/latex]
50. [latex]7m-4n-2[/latex] when
[latex]m=-4,n=-9[/latex]
Exercises: Translate English Phrases to Algebraic Expressions
Instructions: For questions 51-64, translate to an algebraic expression and simplify if possible.
51. the sum of [latex]3[/latex] and [latex]-15[/latex], increased by [latex]7[/latex]
Solution
[latex](3+(-15))+7[/latex]
[latex](3+(-15))+7=-5[/latex]
52. the sum of [latex]-8[/latex] and [latex]-9[/latex], increased by [latex]23[/latex]
53. the difference of [latex]10[/latex] and [latex]-18[/latex]
Solution
[latex]10-(-18)[/latex]
[latex]10-(-18)=28[/latex]
54. subtract [latex]11[/latex] from [latex]-25[/latex]
55. the difference of [latex]-5[/latex] and [latex]-30[/latex]
Solution
[latex]-5-(-30)[/latex]
[latex]-5-(-30)=25[/latex]
56. subtract [latex]-6[/latex] from [latex]-13[/latex]
57. the product of [latex]−3[/latex] and [latex]15[/latex]
Solution
[latex]-3\cdot 15[/latex]
[latex]-3\cdot 15=-45[/latex]
58. the product of [latex]−4[/latex] and [latex]16[/latex]
59. the quotient of [latex]-60[/latex] and [latex]-20[/latex]
Solution
[latex]-60\div(-20)[/latex]
[latex]-60\div(-20)=3[/latex]
60. the quotient of [latex]-40[/latex] and [latex]-20[/latex]
61. the quotient of [latex]-6[/latex] and the sum of [latex]a[/latex] and [latex]b[/latex]
Solution
[latex]\frac{-6}{a+b}[/latex]
62. the quotient of [latex]-7[/latex] and the sum of [latex]m[/latex] and [latex]n[/latex]
63. the product of [latex]-10[/latex] and the difference of [latex]p[/latex] and [latex]q[/latex]
Solution
[latex]-10(p-q)[/latex]
64. the product of [latex]-13[/latex] and the difference of [latex]c[/latex] and [latex]d[/latex]
Exercises: Use Integers in Applications
Instructions: For questions 65-72, solve the given word problems.
65. Temperature. On January [latex]15[/latex], the high temperature in Anaheim, California, was [latex]84^\circ[/latex]. That same day, the high temperature in Embarrass, Minnesota was [latex]-12^\circ[/latex]. What was the difference between the temperature in Anaheim and the temperature in Embarrass?
Solution
[latex]96^\circ[/latex]
66. Temperature. On January [latex]21[/latex], the high temperature in Palm Springs, California, was [latex]89^\circ[/latex], and the high temperature in Whitefield, New Hampshire was [latex]-31^\circ[/latex]. What was the difference between the temperature in Palm Springs and the temperature in Whitefield?
67. Football. At the first down, the Chargers had the ball on their [latex]25[/latex] yard line. On the next three downs, they lost [latex]6[/latex] yards, gained [latex]10[/latex] yards, and lost [latex]8[/latex] yards. What was the yard line at the end of the fourth down?
Solution
[latex]21[/latex]
68. Football. At the first down, the Steelers had the ball on their [latex]30[/latex] yard line. On the next three downs, they gained [latex]9[/latex] yards, lost [latex]14[/latex] yards, and lost [latex]2[/latex] yards. What was the yard line at the end of the fourth down?
69. Checking Account. Mayra has [latex]$124[/latex] in her checking account. She writes a check for [latex]$152[/latex]. What is the new balance in her checking account?
Solution
[latex]-$28[/latex]
70. Checking Account. Selina has [latex]$165[/latex] in her checking account. She writes a check for [latex]$207[/latex]. What is the new balance in her checking account?
71. Checking Account. Diontre has a balance of [latex]-$38[/latex] in his checking account. He deposits [latex]$225[/latex] to the account. What is the new balance?
Solution
[latex]$187[/latex]
72. Checking Account. Reymonte has a balance of [latex]-$49[/latex] in his checking account. He deposits [latex]$281[/latex] to the account. What is the new balance?
Exercises: Everyday Math
Instructions: For questions 73-74, solve the given everyday math word problems.
73. Stock market. Javier owns [latex]300[/latex] shares of stock in one company. On Tuesday, the stock price dropped [latex]$12[/latex] per share. What was the total effect on Javier’s portfolio?
Solution
[latex]-$3600[/latex]
74. Weight loss. In the first week of a diet program, eight women lost an average of [latex]3[/latex] pounds each. What was the total weight change for the eight women?
Exercises: Writing Exercises
Instructions: For questions 75-78, answer the given writing exercises.
75. In your own words, state the rules for multiplying integers.
Solution
Answers may vary
76. In your own words, state the rules for dividing integers.
77. Why is [latex]-2^4\ne (-2)^4[/latex]?
Solution
Answers may vary
78. Why is [latex]-4^3=(-4)^3[/latex]?
