Perform the indicated operations.
117)
4· (–26) + 22 · (–21)
117)
A)
–566
B)
1722
C)
–1722
D)
–336
State the phrase as a mathematical expression. Use x to represent the variable.
118)
Two times a number
118)
A)
2x
B)
2+ x
C)
2
x
D)
2– x
Use the commutative or the associative property to complete the statement. State which property is used.
119)
11 · (3·8) = (11 ·) ·8
119)
A)
3; commutative property
B)
–3; commutative property
C)
3; associative property
D)
–3; associative property
Decide whether the problem is an equation or an expression.
120)
4(9x + 7) =6(8x – 4)
120)
A)
Expression
B)
Equation
21
A
Provide an appropriate response.
121)
The table shows the number of pupils per teacher in selected counties in a certain state.
County Pupils per Teacher
Addison 16.7
Branson 14.7
Cumberland 20.5
Dixson 12.5
Hendricks 12.3
Kendall 17.8
Putnum 13.9
Which counties have a figure greater than 12.5?
121)
A)
Addison, Branson, Cumberland, Dixson, Kendall, Putnum
B)
Hendricks
C)
Dixson, Hendricks
D)
Addison, Branson, Cumberland, Kendall, Putnum
Write the word statement in symbols.
122)
Nine is greater than two plus six.
122)
A)
9+ 2 >6
B)
9<2+ 6
C)
9>2+ 6
D)
2+ 6 >9
Find the quotient.
123)
4.948
4
123)
A)
1.237
B)
–0.31
C)
–1.237
D)
0.31
Provide an appropriate response.
124)
Which one of the following is an example of a pair of like terms?
124)
A)
4xw, 8wx
B)
–8s2x, 6sx2
C)
9t2, 4t3
D)
8t, 9w
22
Use the distributive property to rewrite the expression. Simplify if possible.
125)
7(5x +7y +8)
125)
A)
35x +7y +8
B)
35x +49y +56
C)
35x +49y +8
D)
35x +7y +56
Change the word statement to an equation. Use x as the variable.
126)
A number minus 5 equals 5.
126)
A)
x =5– 5
B)
5– x =5
C)
x – 5 =5
Decide whether the problem is an equation or an expression.
127)
7x – 9
x + 9 –x
3+ 5
127)
A)
Equation
B)
Expression
128)
3(4 – x) +3x + 8
9
128)
A)
Equation
B)
Expression
Provide an appropriate response.
129)
What property is used to clear parentheses and write 7(x +4) as 7x +28?
129)
A)
Distributive property
B)
Identity property
C)
Associative property
D)
Commutative property
23
B
List the numbers from the set that are of the type indicated.
130)
{0, 6, –9, 2
3, –11
2, 4.5, 3}
Integers
130)
A)
12
B)
12, 6
C)
0, –9, 3
D)
12, –9
Use the properties of real numbers to simplify the expression.
131)
–3
5+7
8+9
8+3
5
131)
A)
0
B)
4
C)
8
D)
2
Evaluate the expression, given x = – 2, y = 3, and a = – 4.
132)
9x + 8y – 2a
132)
A)
–8
B)
–56
C)
14
D)
19
Find the sum.
133)
4.2 + [(–4.1) + (–3.6)]
133)
A)
4.7
B)
11.9
C)
3.7
D)
–3.5
Perform the indicated operations.
134)
5–6+2–14
134)
A)
18
B)
42
C)
–42
D)
–18
24
Find the value of the expression.
135)
5
7+4
7·7
12
135)
A)
21
4
B)
4
21
C)
3
4
D)
8
13
Solve the problem.
136)
A bike road race starts at an elevation of 840 feet and passes through 5 stages where the elevation
changes by –691 feet, 371 feet, –558 feet, –12 feet, and 59 feet. At what elevation does the race end?
136)
A)
–2531 ft
B)
1207 ft
C)
2531 ft
D)
9 ft
Provide an appropriate response.
137)
If a, b, and c are real numbers, is this statement true or false? –(a + b) = – a – b
137)
A)
True
B)
False
Write the phrase as a mathematical expression. Use x to represent the number. Combine like terms if possible.
138)
6 times a number added to –8, added to 6 times the sum of 9 times the number and 7
138)
A)
6(–8+ x) + 6(9x + 7); 60x – 41
B)
6x – 8 + 6(9 + 7x); 48x + 60
C)
6(–8+ x) + 6(9 + 7x); 13x + 6
D)
6(9x + 7) + [6x + (–8)]; 60x + 34
Use the distributive property to rewrite the expression. Simplify if possible.
139)
2(2r +6+6s)
139)
A)
4r +12 +6s
B)
4r +6+6s
C)
4r +12 +12s
D)
4r +6+12s
25
C
Find the sum.
140)
3
4+ – 11
20
140)
A)
1
5
B)
1
2
C)
1
D)
1
20
Answer the question.
141)
What value for x makes the expression 28 – x equal to 10?
141)
A)
18
B)
19
C)
38
D)
28
Solve the problem.
142)
Company A showed a profit of $80,830 last year, while Company B had a loss of $83,870. Find the
difference between these amounts.
142)
A)
–$3040
B)
$164,700
C)
–$164,700
D)
$3040
143)
The windchill temperature was –4° F, and the actual temperature was 13° F. Find the difference
between the actual temperature and the windchill temperature.
143)
A)
34°F
B)
19°F
C)
9°F
D)
17°F
Simplify by finding the absolute value.
144)
––6
144)
A)
6
B)
–6
C)
0
D)
12
Identify the group of terms as like or unlike.
145)
y, z
145)
A)
Like
B)
Unlike
State the phrase as a mathematical expression. Use x to represent the variable.
146)
A number increased by seven
146)
A)
7x
B)
x – 7
C)
x + 7
D)
7
Determine whether the statement is true or false.
147)
17 <16 – 9
147)
A)
True
B)
False
Decide whether the problem is an equation or an expression.
148)
x + y – 8
148)
A)
Equation
B)
Expression
Find the quotient.
149)
0
–97
149)
A)
0
B)
97
C)
1
D)
Undefined
Find the sum.
150)
[–19 + (–17)] + [(–16) + (–14)]
150)
A)
–28
B)
6
C)
–66
D)
4
27
B
Find the numerical value of the expression for a) x = 4 and b) x = 18.
151)
3x2+ 8x
151)
A)
a) 80 b) 1116
B)
a) 56 b) 252
C)
a) 16 b) 828
D)
a) 44 b) 198
Find the quotient.
152)
–480
96
152)
A)
–15
B)
–5
C)
–1
5
D)
5
Use order of operations to simplify the expression.
153)
–6–6+ (–4) + (–6)
153)
A)
10
B)
–10
C)
6
D)
–6
Simplify.
154)
11 ·6+10 ·19
154)
A)
1444
B)
256
C)
3344
D)
2156
Find the sum.
155)
734 +846 + (–34) + (–46)
155)
A)
1592
B)
1580
C)
1568
D)
1500
28
156)
1736 + 1314 + (–36) + (–14)
156)
A)
3072
B)
3028
C)
3000
D)
3100
Decide whether the statement is an example of the commutative, associative, identity, inverse, or distributive property.
157)
4· 1 =4
157)
A)
Inverse
B)
Distributive
C)
Identity
D)
Commutative
Provide an appropriate response.
158)
The table shows the number of pupils per teacher in selected counties in a certain state.
County Pupils per Teacher
Addison 16.7
Branson 14.7
Cumberland 20.5
Dixson 12.5
Hendricks 12.3
Kendall 17.8
Putnum 13.9
Which counties have a figure that is at most 14.7?
158)
A)
Addison, Cumberland, Kendall
B)
Addison, Branson, Cumberland, Kendall
C)
Dixson, Hendricks, Putnum
D)
Branson, Dixson, Hendricks, Putnum
C
Refer to the table to answer the question.
Production
Category
Change
’98–‘99
Change
’99–’00
Public Relations 3.5 4.2
Training 1.7 2.8
Sales –4.3 1.6
Catalog 2.3 –1.1
159)
Which category and year shows the smallest absolute change?
159)
A)
Sales, ’99–’00
B)
Catalog ‘99–’00
C)
Catalog, ’98–’99
D)
Training ’98–’99
Evaluate the expression for the given values. If necessary, round to the nearest tenth.
160)
4x + 15y
2 x =10, y =8
160)
A)
80
B)
91
C)
40
D)
160
Find the sum.
161)
–11
16 +3
4
161)
A)
1
4
B)
2
3
C)
1
16
D)
1
64
Write the phrase as a mathematical expression. Use x to represent the number. Combine like terms if possible.
162)
Eight times a number added to –7, subtracted from twice the sum of eight times the number and –6
162)
A)
8(x – 7) –(2 + 8)(x – 6); 4– 2x
B)
(2 + 8)(x + – 6) –8(x – 7); –4+ 2x
C)
(–7+ 8x) –2(8x – 6); 5– 8x
D)
2(8x – 6) – (–7+ 8x); –5+ 8x
B
List the numbers from the set that are of the type indicated.
163)
{ 7, –13, 0, 3
7, –21
3, 7.2, 5}
Natural numbers
163)
A)
–13, 0
B)
0, 5
C)
5
D)
0
Select the smaller of the two given numbers.
164)
–5
18 , –5
8
164)
A)
–5
18
B)
–5
8
Write a numerical expression for the phrase and simplify it.
165)
Seven–ninths of the difference between –9 and –27.
165)
A)
7
9+ [(–9) – (–27)]; 42
B)
7
9 [(–9) – (–27)]; 14
C)
7(9) [(–9) – (–27)]; 14
D)
7(9) [(–9) – (–27)]; 1134
Rewrite the statement so the inequality symbol points in the opposite direction.
166)
8.43 6.93
166)
A)
8.43 <6.93
B)
8.43 6.93
C)
6.93 8.43
D)
6.93 8.43
Write a numerical expression for the phrase and simplify it.
167)
Three–eighths of the sum of –4 and –12.
167)
A)
3
8+ [(–4) + (–12)]; 1
B)
(3 + 8)(–4) + (–12); –56
C)
3
8 [(–4) + (–12)]; –6
D)
3
8 [(–4) + (–12)]; –12
Decide if the given number is a solution to the given equation.
168)
p + 8 =21; 13
168)
A)
Yes
B)
No
Determine whether the statement is true or false.
169)
7[4 + (4– 3)] <29
169)
A)
False
B)
True
Use an integer or rational number to express the number representing change.
170)
Sales in Jeff’s Toys Shop decline 5.7% from last month to this month.
170)
A)
–5.7
B)
5.7
Find the product.
171)
–5 · 4 ·67 · (–5)
171)
A)
–6700
B)
–335
C)
6700
D)
670
Simplify by combining like terms.
172)
6x + 2x – 2x + x + 10x
172)
A)
17x
B)
16x
C)
18
D)
–18
32
C
Find the sum.
173)
–4.2 + [(–1.9) + (–1.7)]
173)
A)
4
B)
0.6
C)
–7.8
D)
4.4
Write a numerical expression for the phrase and simplify it.
174)
The product of –8 and 1, subtracted from –9
174)
A)
–9– (–8)(1); –1
B)
(–9)(–8)(1); 72
C)
[–9– (–8)](1); –1
D)
–9+ (–8)(1); –17
Find the difference.
175)
–3
4–5
8
175)
A)
–1
4
B)
–11
8
C)
11
8
D)
–1
State the phrase as a mathematical expression. Use x to represent the variable.
176)
173 divided by a number
176)
A)
173
x
B)
173 + x
C)
173 – x
D)
173x
Find the product.
177)
–6(76)
177)
A)
432
B)
556
C)
–456
D)
–426
C
Evaluate the expression, given x = – 2, y = 3, and a = – 4.
178)
(3 + x)(–9+ y)(–8– a)
178)
A)
72
B)
24
C)
–24
D)
360
Answer the question.
179)
There is a distributive property for multiplication with respect to addition: a(b + c) = ab + ac. Is
there a distributive property for division with respect to addition? If so, state the property.
179)
A)
Yes. a/(b + c) = a/b + a/c
B)
No.
Solve the problem.
180)
The ocean surface is at 0 ft elevation. A diver is underwater at an elevation of –150 ft near a rock
formation. In this area, the ocean floor has an elevation of –136 ft. The rock formation rises to a
peak 107 ft above the ocean floor. How many feet below the top of the rock formation is the diver?
180)
A)
–14 ft
B)
29 ft
C)
43 ft
D)
121 ft
Write the expression without parentheses.
181)
–(4x +2y)
181)
A)
–4x +2y
B)
–4x –2y
C)
4x +2y
D)
4x –2y
Find the product.
182)
–11(–11)
182)
A)
–131
B)
131
C)
121
D)
–121
B
Rewrite the statement so the inequality symbol points in the opposite direction.
183)
42 >12
183)
A)
12 >42
B)
12 <42
C)
42 12
D)
42 <12
Write a numerical expression for the phrase and simplify it.
184)
The product of 1
2 and –4
7, divided by 3
4.
184)
A)
1
2–4
7
3
4
; –3
14
B)
3
4
1
2–4
7
; –21
8
C)
1
2
–4
7
3
4
; –7
6
D)
1
2–4
7
3
4
; –8
21
Evaluate the expression, given x = – 2, y = 3, and a = – 4.
185)
1
4x –4
3y–1
6a
185)
A)
– 3
B)
–7
3
C)
– 18
D)
41
18
Evaluate the expression using the given values.
186)
3x –9y2; x = 3, y = – 4.
186)
A)
–63
B)
–27
C)
153
D)
–135
Answer the question or complete the sentence to make a true statement.
187)
According to the rules for the order of operations, what should be the first step when simplifying
the expression [9 + (–3+ 3)] + (–6)?
187)
A)
Find the sum of 9 and –6
B)
Find the sum of 3 and –6
C)
Find the sum of –3 and 3
D)
Find the sum of 9 and –3
Evaluate the expression, given x = – 2, y = 3, and a = – 4.
188)
9y –6a2
188)
A)
–69
B)
–21
C)
3
D)
123
Provide an appropriate response.
189)
The table shows the number of pupils per teacher in selected counties in a certain state.
County Pupils per Teacher
Alaska 16.7
Branson 14.7
Cumberland 20.5
Dixson 12.5
Hendricks 12.3
Kendall 17.8
Putnum 13.9
Which counties have a figure greater than 14.7?
189)
A)
Addison, Cumberland, Dixson, Kendall
B)
Addison, Branson, Cumberland, Kendall
C)
Addison, Branson, Cumberland
D)
Addison, Cumberland, Kendall
Select the smaller of the two given numbers.
190)
–20, –24
190)
A)
–20
B)
–24
Find the difference.
191)
–10.7 – 13.8
191)
A)
3.1
B)
–3.1
C)
24.5
D)
–24.5
Determine whether the statement is true or false.
192)
6· (7+ 8) + 6 ·2
6· (6– 1)<10
192)
A)
True
B)
False
Use the distributive property to rewrite the expression. Simplify if possible.
193)
9(6x) + 9(–3y)
193)
A)
9x(6– 3) =27x
B)
54x – 27y
C)
18(6x – 3y)
D)
9(6x – 3y)
Decide if the given number is a solution to the given equation.
194)
7x2+ 5 =47; 3
194)
A)
Yes
B)
No
Use order of operations to simplify the expression.
195)
14 – (7– 8)
195)
A)
15
B)
13
C)
29
D)
–1
D
Provide an appropriate response.
196)
The table shows the number of pupils per teacher in selected counties in a certain state.
County Pupils per Teacher
Addison 16.7
Branson 14.7
Cumberland 20.5
Dixson 12.5
Hendricks 12.3
Kendall 17.8
Putnum 13.9
For which counties are the values not less than 12.5?
196)
A)
Dixson, Hendricks
B)
Addison, Branson, Cumberland, Kendall, Putnum
C)
Hendricks
D)
Addison, Branson, Cumberland, Dixson, Kendall, Putnum
Decide if the statement is true or false.
197)
–(–7) > – 21
197)
A)
False
B)
True
198)
– – 12 – – 20
198)
A)
True
B)
False
Answer the question or complete the sentence to make a true statement.
199)
The sum of three negative numbers will always be a number.
199)
A)
Negative
B)
Positive
Answer the question.
200)
Assume a is positive, b is negative, and c is positive for the expression
a · b3· c
Tell whether the value of the given expression is positive, negative or cannot be determined.
200)
A)
Cannot be determined
B)
Negative
C)
Positive
Find the numerical value of the expression for a) x = 4 and b) x = 18.
201)
3x – 3
6x
201)
A)
a) 5
36 b) 19
36
B)
a) 3
8 b) 17
36
C)
a) 1
12 b) 17
36
D)
a) 17
36 b) 3
8
Evaluate the expression, given x = – 2, y = 3, and a = – 4.
202)
–8a + 5y + 4x
202)
A)
39
B)
34
C)
–55
D)
8
Decide whether the statement is an example of the commutative, associative, identity, inverse, or distributive property.
203)
5·4=4·5
203)
A)
Identity
B)
Distributive
C)
Commutative
D)
Associative
Give the numerical coefficient of the term.
204)
–w
204)
A)
–1
B)
–w
C)
1
D)
0