1.3E: Exercises
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- Aug 24, 2020
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Practice Makes Perfect
Use Variables and Algebraic Symbols
In the following exercises, translate from algebra to English.
Exercise 1.3E.55
16−9
- Answer
-
16 minus 9, the difference of sixteen and nine
Exercise 1.3E.56
3⋅9
Exercise 1.3E.57
28÷4
- Answer
-
28 divided by 4, the quotient of twenty-eight and four
Exercise 1.3E.58
x+11
Exercise 1.3E.59
(2)(7)
- Answer
-
2 times 7, the product of two and seven
Exercise 1.3E.60
(4)(8)
Exercise 1.3E.61
14<21
- Answer
-
fourteen is less than twenty-one
Exercise 1.3E.62
17<35
Exercise 1.3E.63
36≥19
- Answer
-
thirty-six is greater than or equal to nineteen
Exercise 1.3E.64
6n=36
Exercise 1.3E.65
y−1>6
- Answer
-
y minus 1 is greater than 6, the difference of y and one is greater than six
Exercise 1.3E.66
y−4>8
Exercise 1.3E.67
2≤18÷6
- Answer
-
2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six
Exercise 1.3E.68
a≠1⋅12
In the following exercises, determine if each is an expression or an equation.
Exercise 1.3E.69
9⋅6=54
- Answer
-
equation
Exercise 1.3E.70
7⋅9=63
Exercise 1.3E.71
5⋅4+3
- Answer
-
expression
Exercise 1.3E.72
x+7
Exercise 1.3E.73
x+9
- Answer
-
expression
Exercise 1.3E.74
y−5=25
Simplify Expressions Using the Order of Operations
In the following exercises, simplify each expression.
Exercise 1.3E.75
53
- Answer
-
125
Exercise 1.3E.76
83
Exercise 1.3E.77
28
- Answer
-
256
Exercise 1.3E.78
105
In the following exercises, simplify using the order of operations.
Exercise 1.3E.79
- 3+8⋅5
- (3+8)⋅5
- Answer
-
- 43
- 55
Exercise 1.3E.80
- 2+6⋅3
- (2+6)⋅3
Exercise 1.3E.81
23−12÷(9−5)
- Answer
-
5
Exercise 1.3E.82
32−18÷(11−5)
Exercise 1.3E.83
3⋅8+5⋅2
- Answer
-
34
Exercise 1.3E.84
4⋅7+3⋅5
Exercise 1.3E.85
2+8(6+1)
- Answer
-
58
Exercise 1.3E.86
4+6(3+6)
Exercise 1.3E.87
4⋅12/8
- Answer
-
6
Exercise 1.3E.88
2⋅36/6
Exercise 1.3E.89
(6+10)÷(2+2)
- Answer
-
4
Exercise 1.3E.90
(9+12)÷(3+4)
Exercise 1.3E.91
20÷4+6⋅5
- Answer
-
35
Exercise 1.3E.92
33÷3+8⋅2
Exercise 1.3E.93
32+72
- Answer
-
58
Exercise 1.3E.94
(3+7)2
Exercise 1.3E.95
3(1+9⋅6)−42
- Answer
-
149
Exercise 1.3E.96
5(2+8⋅4)−72
Exercise 1.3E.97
2[1+3(10−2)]
- Answer
-
50
Exercise 1.3E.98
5[2+4(3−2)]
Evaluate an Expression
In the following exercises, evaluate the following expressions.
Exercise 1.3E.99
7x+8 when x=2
- Answer
-
22
Exercise 1.3E.100
8x−6 when x=7
Exercise 1.3E.101
x2 when x=12
- Answer
-
144
Exercise 1.3E.102
x3 when x=5
Exercise 1.3E.103
x5 when x=2
- Answer
-
32
Exercise 1.3E.104
4x when x=2
Exercise 1.3E.105
x2+3x−7 when x=4
- Answer
-
21
Exercise 1.3E.106
6x+3y−9 when x=10,y=7
- Answer
-
9
Exercise 1.3E.107
(x+y)2 when x=6,y=9
Exercise 1.3E.108
a2+b2 when a=3,b=8
- Answer
-
73
Exercise 1.3E.109
r2−s2 when r=12,s=5
Exercise 1.3E.110
2l+2w when l=15,w=12
- Answer
-
54
Exercise 1.3E.111
2l+2w when l=18,w=14
Simplify Expressions by Combining Like Terms
In the following exercises, identify the coefficient of each term.
Exercise 1.3E.112
8a
- Answer
-
8
Exercise 1.3E.113
13m
Exercise 1.3E.114
5r2
- Answer
-
5
Exercise 1.3E.115
6x3
In the following exercises, identify the like terms.
Exercise 1.3E.116
x3,8x,14,8y,5,8x3
- Answer
-
x3 and 8x3, 14 and 5
Exercise 1.3E.117
6z,3w2,1,6z2,4z,w2
Exercise 1.3E.118
9a,a2,16,16b2,4,9b2
- Answer
-
16 and 4, 16b2 and 9b2
Exercise 1.3E.119
3,25r2,10s,10r,4r2,3s
In the following exercises, identify the terms in each expression.
Exercise 1.3E.120
15x2+6x+2
- Answer
-
15x2,6x,2
Exercise 1.3E.121
11x2+8x+5
Exercise 1.3E.122
10y3+y+2
- Answer
-
10y3,y,2
Exercise 1.3E.123
9y3+y+5
In the following exercises, simplify the following expressions by combining like terms.
Exercise 1.3E.124
10x+3x
- Answer
-
13x
Exercise 1.3E.125
15x+4x
Exercise 1.3E.126
4c+2c+c
- Answer
-
7c
Exercise 1.3E.127
6y+4y+y
Exercise 1.3E.128
7u+2+3u+1
- Answer
-
10u+3
Exercise 1.3E.129
8d+6+2d+5
Exercise 1.3E.130
10a+7+5a−2+7a−4
- Answer
-
22a+1
Exercise 1.3E.131
7c+4+6c−3+9c−1
Exercise 1.3E.132
3x2+12x+11+14x2+8x+5
- Answer
-
17x2+20x+16
Exercise 1.3E.133
5b2+9b+10+2b2+3b−4
Translate an English Phrase to an Algebraic Expression
In the following exercises, translate the phrases into algebraic expressions.
Exercise 1.3E.134
the difference of 14 and 9
- Answer
-
14−9
Exercise 1.3E.135
the difference of 19 and 8
Exercise 1.3E.136
the product of 9 and 7
- Answer
-
9⋅7
Exercise 1.3E.137
the product of 8 and 7
Exercise 1.3E.138
the quotient of 36 and 9
- Answer
-
36÷9
Exercise 1.3E.139
the quotient of 42 and 7
Exercise 1.3E.140
the sum of 8x and 3x
- Answer
-
8x+3x
Exercise 1.3E.141
the sum of 13x and 3x
Exercise 1.3E.142
the quotient of y and 3
- Answer
-
y3
Exercise 1.3E.143
the quotient of y and 8
Exercise 1.3E.144
eight times the difference of y and nine
- Answer
-
8(y−9)
Exercise 1.3E.145
seven times the difference of y and one
Exercise 1.3E.146
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.
- Answer
-
c+3
Exercise 1.3E.147
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.
Exercise 1.3E.148
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.
- Answer
-
2n−7
Exercise 1.3E.149
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.
Everyday Math
Exercise 1.3E.150
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.
- how much will he pay?
- how much will his insurance company pay?
- Answer
-
- $750
- $1,350
Exercise 1.3E.151
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.
- how much will he pay?
- how much will the insurance company pay?
Writing Exercises
Exercise 1.3E.152
Explain the difference between an expression and an equation.
- Answer
-
Answers may vary
Exercise 1.3E.153
Why is it important to use the order of operations to simplify an expression?
Exercise 1.3E.154
Explain how you identify the like terms in the expression 8a2+4a+9−a2−1
- Answer
-
Answers may vary
Exercise 1.3E.155
Explain the difference between the phrases “4 times the sum of x and y” and “the sum of 4 times x and y.”
Self Check
ⓐ Use this checklist to evaluate your mastery of the objectives of this section.
ⓑ After reviewing this checklist, what will you do to become confident for all objectives?