33) The length of a rectangle is [latex]7[/latex] less than the width. Let [latex]w[/latex] represent the width of the rectangle. Write an expression for the length of the rectangle.

34) The width of a rectangle is [latex]6[/latex] less than the length. Let [latex]l[/latex] represent the length of the rectangle. Write an expression for the width of the rectangle.

Instructions: For questions 1-14, translate from algebra to English.

1)  [latex]16-9[/latex]

2)  [latex]3\cdot9[/latex]

3)  [latex]28\div4[/latex]

4)  [latex]x+11[/latex]

5)  [latex](2)(7)[/latex]

6)  [latex](4)(8)[/latex]

7)  [latex]14<21[/latex]

8)  [latex]17<35[/latex]

9)  [latex]36\ge 19[/latex]

10)  [latex]6n=36[/latex]

11)  [latex]y-1>6[/latex]

12)  [latex]y-4>8[/latex]

13)  [latex]2\le 18\div6[/latex]

14)  [latex]a\ne 1\cdot12[/latex]

Odd Answers

1)  [latex]16[/latex] minus [latex]9[/latex], the difference of sixteen and nine

3)  [latex]28[/latex] divided by [latex]4[/latex], the quotient of twenty-eight and four

5)  [latex]2[/latex] times [latex]7[/latex], the product of two and seven

7)  fourteen is less than twenty-one

9)  thirty-six is greater than or equal to nineteen

11)  [latex]y[/latex] minus [latex]1[/latex] is greater than [latex]6[/latex], the difference of [latex]y[/latex] and one is greater than six

13)  [latex]2[/latex] is less than or equal to [latex]18[/latex] divided by [latex]6[/latex]; two is less than or equal to the quotient of eighteen and six

Instructions: For questions 15-20, determine if each is an expression or an equation.

15)  [latex]9\cdot6=54[/latex]

16)  [latex]7\cdot 9=63[/latex]

17)  [latex]5\cdot 4+3[/latex]

18)  [latex]x+7[/latex]

19)  [latex]x+9[/latex]

20)  [latex]y-5=25[/latex]

Odd Answers

15)  equation

17)  expression

19)  expression

Instructions: For questions 21-24, simplify each expression.

21)  [latex]5^3[/latex]

22)  [latex]8^3[/latex]

23)  [latex]2^8[/latex]

24)  [latex]10^5[/latex]

Odd Answers

21)  [latex]125[/latex]

23)  [latex]256[/latex]

Instructions: For questions 25-46, simplify using the order of operations.

25)  [latex]3+8\cdot5[/latex]

26)  [latex]2+6\cdot3[/latex]

27)  [latex](3+8)\cdot5[/latex]

28)  [latex](2+6)\cdot3[/latex]

29)  [latex]2^3-12\div(9-5)[/latex]

30)  [latex]3^2-18\div(11-5)[/latex]

31)  [latex]3\cdot8+5\cdot2[/latex]

32)  [latex]4\cdot7+3\cdot5[/latex]

33)  [latex]2+8(6+1)[/latex]

34)  [latex]4+6(3+6)[/latex]

35)  [latex]4\cdot12/8[/latex]

36)  [latex]2\cdot36/6[/latex]

37)  [latex](6+10)\div(2+2)[/latex]

38)  [latex](9+12)\div(3+4)[/latex]

39)  [latex]20\div4+6\cdot5[/latex]

40)  [latex]33\div3+8\cdot2[/latex]

41)  [latex]3^2+7^2[/latex]

42)  [latex](3+7)^2[/latex]

43)  [latex]3(1+9\cdot6)-4^2[/latex]

44)  [latex]5(2+8\cdot4)-7^2[/latex]

45)  [latex]2\left[1+3(10-2)\right][/latex]

46)  [latex]5\left[2+4(3-2)\right][/latex]

Odd Answers

25)  [latex]43[/latex]

27)  [latex]55[/latex]

29)  [latex]5[/latex]

31)  [latex]34[/latex]

33)  [latex]58[/latex]

35)  [latex]6[/latex]

37)  [latex]4[/latex]

39)  [latex]35[/latex]

41)  [latex]58[/latex]

43)  [latex]149[/latex]

45)  [latex]50[/latex]

Instructions: For questions 47-60, evaluate the expressions.

47 )  [latex]7x+8[/latex] when [latex]x=2[/latex]

48)  [latex]8x-6[/latex] when [latex]x=7[/latex]

49)  [latex]x^2[/latex] when [latex]x=12[/latex]

50)  [latex]x^3[/latex] when [latex]x=5[/latex]

51)  [latex]x^5[/latex] when [latex]x=2[/latex]

52)  [latex]4^x[/latex] when [latex]x=2[/latex]

53)  [latex]x^2+3x-7[/latex] when [latex]x=4[/latex]

54 ) [latex]6x+3y-9[/latex] when [latex]x=6,y=9[/latex]

55)  [latex](x-y)^2[/latex] when [latex]x=10,y=7[/latex]

56)  [latex](x+y)^2[/latex] when [latex]x=6,y=9[/latex]

57)  [latex]a^2+b^2[/latex] when [latex]a=3,b=8[/latex]

58)  [latex]r^2-s^2[/latex] when [latex]r=12,s=5[/latex]

59)  [latex]2l+2w[/latex] when [latex]l=15,w=12[/latex]

60) [latex]2l+2w[/latex] when [latex]l=18,w=14[/latex]

Odd Answers

47)  [latex]22[/latex]

49)  [latex]144[/latex]

51)  [latex]32[/latex]

53)  [latex]21[/latex]

55)  [latex]9[/latex]

57)  [latex]73[/latex]

59)  [latex]54[/latex]

Instructions: For questions 61-64, identify the coefficient of each term.

61)  [latex]8a[/latex]

62)  [latex]13m[/latex]

63)  [latex]5r^2[/latex]

64)  [latex]6x^3[/latex]

Odd Answers

61)  [latex]8[/latex]

63)  [latex]5[/latex] 

Instructions: For questions 65-68, identify the like terms.

65)  [latex]x^3,8x,14,8y,5,8x^3[/latex]

66)  [latex]6z,3w^2,1,6z^2,4z,w^2[/latex]

67)  [latex]9a,a^2,16,16b^2,4,9b^2[/latex]

68)  [latex]3,25r^2,10s,10r,4r^2,3s[/latex]

Odd Answers

65)  [latex]x^3\text{ and }8x^3,14\text{ and }5[/latex]

67)  [latex]16\text{ and }4,16b^2\text{ and }9b^2[/latex]

Instructions: For questions 69-72, identify the terms in each expression

69)  [latex]15x^2+6x+2[/latex]

70)  [latex]11x^2+8x+5[/latex]

71)  [latex]10y^3+y+2[/latex]

72)  [latex]9y^3+y+5[/latex]

Odd Answers

69)  [latex]15x^2,6x,2[/latex]

71)  [latex]10y^3,y,2[/latex]

Instructions: For questions 73-82, simplify the expressions by combining like terms.

73)  [latex]10x+3x[/latex]

74)  [latex]15x+4x[/latex]

75)  [latex]4c+2c+c[/latex]

76)  [latex]6y+4y+y[/latex]

77)  [latex]7u+2+3u+1[/latex]

78)  [latex]8d+6+2d+5[/latex]

79)  [latex]10a+7+5a-2+7a-4[/latex]

80)  [latex]7c+4+6c-3+9c-1[/latex]

81)  [latex]3x^2+12x+11+14x^2+8x+5[/latex]

82)  [latex]5b^2+9b+10+2b^2+3b-4[/latex]

Odd Answers

73)  [latex]13x[/latex]

75)  [latex]7c[/latex]

77)  [latex]10u+3[/latex]

79)  [latex]22a+1[/latex]

81)  [latex]17x^2+20x+16[/latex]

Instructions: For questions 83-94, translate the phrases into algebraic expressions.

83)  the difference of [latex]14[/latex] and [latex]9[/latex]

84)  the difference of [latex]19[/latex] and [latex]8[/latex]

85)  the product of [latex]9[/latex] and [latex]7[/latex]

86)  the product of [latex]8[/latex] and [latex]7[/latex]

87)  the quotient of [latex]36[/latex] and [latex]9[/latex]

88)  the quotient of [latex]42[/latex] and [latex]7[/latex]

89)  the sum of [latex]8x[/latex] and [latex]3x[/latex]

90) the sum of [latex]13x[/latex] and [latex]3x[/latex]

91)  the quotient of [latex]y[/latex] and [latex]3[/latex]

92)  the quotient of [latex]y[/latex] and [latex]8[/latex]

93)  eight times the difference of [latex]y[/latex] and nine

94)  seven times the difference of [latex]y[/latex] and one

Odd Answers

83)  [latex]14-9[/latex]

85)  [latex]9\cdot7[/latex]

87)  [latex]36\div9[/latex]

89) [latex]8x+3x[/latex]

91)  [latex]\frac{y}{3}[/latex]

93)  [latex]8(y-9)[/latex]

Instructions: For questions 95-98, write an expression for the given word problems.

95)  Eric has rock and classical CDs in his car. The number of rock CDs is 3 more than the number of classical CDs. Let [latex]c[/latex] represent the number of classical CDs. Write an expression for the number of rock CDs.

96)  The number of girls in a second-grade class is 4 less than the number of boys. Let [latex]b[/latex] represent the number of boys. Write an expression for the number of girls.

97)  Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let [latex]n[/latex] represent the number of nickels. Write an expression for the number of pennies.

98)  Jeannette has [latex]$5[/latex] and [latex]$10[/latex] bills in her wallet. The number of fives is three more than six times the number of tens. Let [latex]t[/latex] represent the number of tens. Write an expression for the number of fives.

Odd Answers

95) [latex]c+3[/latex]

97)  [latex]2n-7[/latex]

Instructions: For questions 99-100, answer the given everyday math word problems.

99)  Car insurance: Justin’s car insurance has a [latex]$750[/latex] deductible per incident. This means that he pays [latex]$750[/latex] and his insurance company will pay all costs beyond [latex]$750[/latex] . If Justin files a claim for [latex]$2,100[/latex]: 

a)  how much will he pay?
b) how much will his insurance company pay?

100)  Home insurance: Armando’s home insurance has a [latex]$2,500[/latex] deductible per incident. This means that he pays [latex]$2,500[/latex] and the insurance company will pay all costs beyond [latex]$2,500[/latex]. If Armando files a claim for [latex]$19,400[/latex]:

a)  how much will he pay?
b) how much will the insurance company pay?

Odd Answers

99a)  [latex]$750[/latex]
99b) [latex]$1,350[/latex]

Instructions: For questions 101-104, answer the given writing exercises.

101)  Explain the difference between an expression and an equation.

102)  Why is it important to use the order of operations to simplify an expression?

103)  Explain how you identify the like terms in the expression [latex]8a^2+4a+9-a^2-1[/latex].

104)  Explain the difference between the phrases “4 times the sum of [latex]x[/latex] and [latex]y[/latex]” and “the sum of 4 times [latex]x[/latex] and [latex]y[/latex].”

Odd Answers

101)  Answers may vary

103)  Answers may vary