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Exercises: Introduction To the Language of Algebra (1.2)

Exercises: Use Variables and Algebraic Symbols

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

1. 169

Solution

16 minus 9, the difference of sixteen and nine


2. 39


3. 28÷4

Solution

28 divided by 4, the quotient of twenty-eight and four


4. x+11


5. (2)(7)

Solution

2 times 7, the product of two and seven


6. (4)(8)


7. 14<21

Solution

fourteen is less than twenty-one


8. 17<35


9. 3619

Solution

thirty-six is greater than or equal to nineteen


10. 6n=36


11. y1>6

Solution

y minus 1 is greater than 6, the difference of y and one is greater than six


12. y4>8


13. 218÷6

Solution

2 is less than or equal to 18 divided by 6; two is less than or equal to the quotient of eighteen and six


14. a112


Exercises: Expression or Equation

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

15. 96=54

Solution

equation


16. 79=63


17. 54+3

Solution

expression


18. x+7


19. x+9

Solution

expression


20. y5=25


Exercises: Simplify Expressions Using the Order of Operations

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

21. 53

Solution

125


22. 83


23. 28

Solution

256


24. 105


Exercises: Simplify Using Order of Operations

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

25. 3+85

Solution

43


26. 2+63


27. (3+8)5

Solution

55


28. (2+6)3


29. 2312÷(95)

Solution

5


30. 3218÷(115)


31. 38+52

Solution

34


32. 47+35


33. 2+8(6+1)

Solution

58


34. 4+6(3+6)


35. 412/8

Solution

6


36. 236/6


37. (6+10)÷(2+2)

Solution

4


38. (9+12)÷(3+4)


39. 20÷4+65

Solution

35


40. 33÷3+82


41. 32+72

Solution

58


42. (3+7)2


43. 3(1+96)42

Solution

149


44. 5(2+84)72


45. 2[1+3(102)]

Solution

50


46. 5[2+4(32)]


Exercises: Evaluate an Expression

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

47. 7x+8 when x=2

Solution

22


48. 8x6 when x=7


49. x2 when x=12

Solution

144


50. x3 when x=5


51. x5 when x=2

Solution

32


52. 4x when x=2


53. x2+3x7 when x=4

Solution

21


54. 6x+3y9 when
x=6,y=9


55. (xy)2 when
x=10,y=7

Solution

9


56. (x+y)2 when
x=6,y=9


57. a2+b2 when
a=3,b=8

Solution

73


58. r2s2 when
r=12,s=5


59. 2l+2w when
l=15,w=12

Solution

54


60. 2l+2w when
l=18,w=14


Exercises: Simplify Expressions by Combining Like Terms

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

61. 8a

Solution

8


62. 13m


63. 5r2

Solution

5


64. 6x3


Exercises: Identify Like Terms

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

65. x3,8x,14,8y,5,8x3

Solution

x3 and 8x3,14 and 5


66. 6z,3w2,1,6z2,4z,w2


67. 9a,a2,16,16b2,4,9b2

Solution

16 and 4,16b2 and 9b2


68. 3,25r2,10s,10r,4r2,3s


Exercises: Identify Terms in an Expression

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

69. 15x2+6x+2

Solution

15x2,6x,2


70. 11x2+8x+5


71. 10y3+y+2

Solution

10y3,y,2


72. 9y3+y+5


Exercises: Simplify by Combining Like Terms

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

73. 10x+3x

Solution

13x


74. 15x+4x


75. 4c+2c+c

Solution

7c


76. 6y+4y+y


77. 7u+2+3u+1

Solution

10u+3


78. 8d+6+2d+5


79. 10a+7+5a2+7a4

Solution

22a+1


80. 7c+4+6c3+9c1


81. 3x2+12x+11+14x2+8x+5

Solution

17x2+20x+16


82. 5b2+9b+10+2b2+3b4


Exercises: Translate an English Phrase to an Algebraic Expression

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

83. the difference of 14 and 9

Solution

149


84. the difference of 19 and 8


85. the product of 9 and 7

Solution

97


86. the product of 8 and 7


87. the quotient of 36 and 9

Solution

36÷9


88. the quotient of 42 and 7


89. the sum of 8x and 3x

Solution

8x+3x


90. the sum of 13x and 3x


91. the quotient of y and 3

Solution

y3


92. the quotient of y and 8


93. eight times the difference of y and nine

Solution

8(y9)


94. seven times the difference of y and one


Exercises: Word Problems

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 c represent the number of classical CDs. Write an expression for the number of rock CDs.

Solution

c+3


96. The number of girls in a second-grade class is 4 less than the number of boys. Let b 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 n represent the number of nickels. Write an expression for the number of pennies.

Solution

2n7


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


Exercises: Everyday Math

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

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

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

Solution

a. $750
b. $1,350


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

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


Exercises: Writing Exercises

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

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

Solution

Answers may vary


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 8a2+4a+9a21.

Solution

Answers may vary


104. Explain the difference between the phrases “4 times the sum of x and y” and “the sum of 4 times x and y.”

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Fanshawe Pre-Health Sciences Mathematics 1 Copyright © 2022 by Domenic Spilotro, MSc is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.