Deck 1: Real Numbers and Algebraic Expressions

Question 1

Place $$\text { EOr } \notin \text { in }$$ the space provided to make the statement true.
$\sqrt { 2 }$ ـــــــــــــــــ $\{ x \mid x$ is a rational number \}

A) $\notin$
B) $\in$

Answer 1

A

Question 2

List all the elements of B that belong to the given set.
B = $\left\{ 11 , \sqrt { 5 } , - 16,0 , \frac { 0 } { 4 } , \sqrt { 25 } , 0.24 \right\}$
Rational numbers

A) $\sqrt { 5 } , \frac { 0 } { 4 } , 0.24$
B) $\sqrt { 5 } , \sqrt { 25 }$
C) 11,0, $\sqrt { 25 }$
D) $11 , - 16,0 , \frac { 0 } { 4 } , \sqrt { 25 } , 0.24$

Answer 2

D

Question 3

Place $$\text { EOr } \notin \text { in }$$ the space provided to make the statement true.
0 {4,8,12, ... }

A) $\in$
B) $\notin$

Answer 3

B

Question 4

List all the elements of B that belong to the given set.
B= $\left\{ 4 , \sqrt { 6 } , - 15,0 , \frac { 1 } { 2 } , - 2,5.5 , \sqrt { 4 } \right\}$
Whole numbers

A) 4,0 , $\sqrt { 4 }$
B) 4,0
C) 4,-15,0 , $\sqrt { 4 }$
D) 4,-15,0

Question 5

List the elements in the set.
$\{ x \mid x$ is a whole number less than 26 }

A) {0,1,2, ... , 23,24,25}
B) {... , 24,25,26}
C) {0,1,2, ... , 24,25,26}
D) {1,2,3, ... , 23,24,25}

Question 6

Which of these is the most important general tip for success in a mathematics course?

A) Don't be afraid to ask questions
B) Organize your class materials
C) Do your homework
D) Check your work

Question 7

List the elements in the set.
$\{ x \mid x$ is an even natural number}

A) {0,2,4,6,8, ...}
B) {2,4,6,8}
C) {2,4,6,8, ....}
D) {...-8,-6,-4,-2,2,4,6,8, ...}

Question 8

Which of these is NOT listed as a tip to help you succeed in this course?

A) Hand in assignments on time.
B) Read your textbook after you attend class.
C) Exchange names and phone numbers with at least one other person in class.
D) Know how to get help if you need it.

Question 9

Place $$\text { EOr } \notin \text { in }$$ the space provided to make the statement true.
25 {xx is an integer }

A) $\notin$
B) $\in$

Question 10

Which of these is NOT an end-of-chapter component designed to help you understand the concepts of the chapter?

A) Chapter test
B) Calculator exercises
C) Vocabulary checks
D) Highlights

Question 11

List the elements in the set.
$\{ x \mid x$ is a natural number less than 28 }

A) { ..., 26,27,28}
B) {1,2,3, ... , 26,27,28}
C) {0,1,2, ... , 25,26,27}
D) {1,2,3, ... , 25,26,27}

Question 12

List the elements in the set.
$| x | x$ is an integer greater than 0}

A) {-1,-2,-3, ...}
B) {-1,-2,-3}
C) {1,2,3, ...}
D) {1,2,3,4}

Question 13

Which of these is listed as one of several steps in preparing for an exam?

A) Practice exercises by working the chapter review.
B) Skip over the chapter Highlights.
C) Leave for the exam as late as possible to increase your amount of study time.
D) Use your notes, previous assignments, and text the entire time you are studying.

Question 14

List all the elements of B that belong to the given set.
B= $\left\{ 4 , \sqrt { 8 } , - 4,0 , \frac { 0 } { 4 } , \sqrt { 9 } , 0.5 \right\}$
Irrational numbers

A) $\sqrt { 8 } , \sqrt { 9 }$
B) $\sqrt { 8 } , \sqrt { 9 } , 0.5$
C) $\sqrt { 8 }$
D) $\sqrt { 8 } , 0.5$

Question 15

List all the elements of B that belong to the given set.
B= $\left\{ 3 , \sqrt { 5 } , - 24,0 , \frac { 2 } { 3 } , - \frac { 3 } { 2 } , 6.1 , \sqrt { 9 } \right\}$
Integers

A) 3,0
B) 3,0, $\sqrt { 9 }$
C) 3,-24,0
D) 3,-24,0 , $\sqrt { 9 }$

Question 16

List the elements in the set.
$\{ x \mid x$ is an integer between 4 and 8 }

A) {5,6,7,8}
B) {4,5,6,7}
C) {4,5,6,7,8}
D) {5,6,7}

Question 17

Place $$\text { EOr } \notin \text { in }$$ the space provided to make the statement true.
$\frac { 7 } { 4 } ـــــــــــ \{ x \mid x$ is a rational number}

A) $E$
B) $\notin$

Question 18

List all the elements of B that belong to the given set.
B= $\left\{ 19 , \sqrt { 7 } , - 18,0 , \frac { 0 } { 9 } , \sqrt { 4 } \right\}$
Real numbers

A) 19,-18,0 , $\frac { 0 } { 9 }$
B) $19 , \sqrt { 7 } , - 18,0 , \frac { 0 } { 9 } , \sqrt { 4 }$
C) $19 , - 18,0 , \frac { 0 } { 0 } , \sqrt { 4 }$
D) 19,-18,0 , $\sqrt { 4 }$

Question 19

List the elements in the set.
$\{ x \mid x$ is a natural number less than -3}

A) $\phi$
B) {-2,-1,0, ...}
C) {....,-6,-5,-4}
D) {-4,-5,-6, ...}

Question 20

List all the elements of B that belong to the given set.
B= $\left\{ 11 , \sqrt { 7 } , - 23,0 , \frac { 3 } { 4 } , - \frac { 4 } { 3 } , 7.3 , \sqrt { 25 } \right\}$
Natural numbers

A) -23,0,11
B) 11,0, $\sqrt { 25 }$
C) 11,0
D) 11, $\sqrt { 25 }$

Question 21

Tell whether the statement is true or false.
Some real numbers are integers.

A) True
B) False

Question 22

Write the phrase as a variable expression. Use x to represent "a number."
The quotient of 49 and a number

A) x-49
B) 49-x
C) $\frac { x } { 49 }$
D) $\frac { 49 } { x }$

Question 23

Tell whether the statement is true or false.
Every irrational number is a rational number.

A) True
B) False

Question 24

Write the phrase as a variable expression. Use x to represent "a number."
35 subtracted from a number

A) 35
B) 35 x
C) x-35
D) 35- x

Question 25

Write the phrase as a variable expression. Use x to represent "a number."
3 more than 6 times a number

A) 3x+6
B) 6(3+x)
C) 6x+3
D) 9x

Question 26

Tell whether the statement is true or false.
- $\frac { 5 } { 3 }$ is a real number.

A) True
B) False

Question 27

Write the sentence as an equation.
The difference of twice x and 7 is the same as 15 .

A) 2 x+7=15
B) 2 x-7=15
C) x- $2 \cdot 7$ =15
D) 7-2 x=15

Question 28

Write the phrase as a variable expression. Use x to represent "a number."
The quotient of ten and the sum of a number and two

A) $\frac { 10 } { x + 2 }$
B) $\frac { x + 2 } { 10 }$
C) $\frac { x - 2 } { 10 }$
D) $\frac { 10 } { x - 2 }$

Question 29

Write the phrase as a variable expression. Use x to represent "a number."
2 times a number

A) 2-x
B) 2x
C) 2 + x
D) $\frac { 2 } { x }$

Question 30

Tell whether the statement is true or false.
Every irrational number is a natural number.

A) True
B) False

Question 31

Write the phrase as a variable expression. Use x to represent "a number."
The sum of a number and 97

A) 97
B) x+97
C) 97-x
D) 97x

Question 32

Write the sentence as an equation.
The sum of x and 8 is -17 .

A) x -8=-17
B) x +8=-17
C) x +8=-17 .
D) 8x=-17

Question 33

Write the phrase as a variable expression. Use x to represent "a number."
The difference of eight and a number

A) x-8
B) x+8
C) 16-x
D) 8-x

Question 34

Write the phrase as a variable expression. Use x to represent "a number."
A number divided by 60

A) x-60
B) $\frac { 60 } { x }$
C) $\frac { x } { 60 }$
D) 60x

Question 35

Write the phrase as a variable expression. Use x to represent "a number."
A number less than five and nine-tenths

A) $x - 5 \frac { 9 } { 10 }$
B) $5 \frac { 9 } { 10 } - x$
C) $5 \frac { 9 } { 10 } x$
D) $x + 5 \frac { 9 } { 10 }$

Question 36

Write the phrase as a variable expression. Use x to represent "a number."
seven less than four times a number

A) x-28
B) 4x-7
C) 7-4x
D) 28- x

Question 37

Write the phrase as a variable expression. Use x to represent "a number."
111 less a number

A) 111x
B) 111
C) 111-x
D) x+111

Question 38

Write the phrase as a variable expression. Use x to represent "a number."
Twice the difference of a number and eight

A) 2 x-8
B) 2(x-8)
C) 2(x+8)
D) 2 x+8

Question 39

Write the phrase as a variable expression. Use x to represent "a number."
5 less than 9 times a number

A) 5-9x
B) 5x-9
C) 9-5x
D) 9x-5

Question 40

Write the phrase as a variable expression. Use x to represent "a number."
The product of 4 and a number

A) 4x
B) 4+x
C) 4-x
D) $\frac { 4 } { x }$

Question 41

Write the sentence as an equation.
Twice x plus 2 is -17 .

A) 2x(2)=-17
B) 2x+2=-17
C) 2x-2=-17
D) 2 x $\div$ 2=-17

Question 42

Insert $$< , > \text {, or } =$$ to in the space provided to form a true statement.
-95 / 85

A) $- 95 > 85$
B) -95<85
C) -95=85

Question 43

Insert $$< , > \text {, or } =$$ to in the space provided to form a true statement.
2.7-5.8

A) 2.7>-5.8
B) 2.7=-5.8
C) 2.7<-5.8

Question 44

Write the sentence as an equation.
The quotient of 99 and x amounts to 11 .

A) 99x=11
B) $\frac { x } { 99 }$ =11
C) 99-x=11
D) $\frac { 99 } { x }$ =11

Question 45

Write the sentence as an equation.
When 5 times x is subtracted from 7 times x , the result is 20 .

A) 5(x-7)=20 x
B) 5 x+10 x=20
C) 7 x-5 x=20
D) 5 x(7-x)=20

Question 46

Write the sentence as an equation.
Five more than four times x is the same as x increased by 35 .

A) 4x -5=x+35
B) 4(x+5)=x+35
C) 4x +5=35x
D) 4x +5=x+35

Question 47

Write the sentence as an equation.
The sum of x and 4 is 15 .

A) x-4=15
B) 4 x=15
C) x $\frac{4}{4}$ 4=15
D) x+4=15

Question 48

Write the sentence as an equation.
The quotient of 48 and x is 4 .

A) $\frac { 48 } { x }$ =4
B) $\frac { 48 } { 4 }$ =x
C) 48-x=4
D) $\frac { x } { 48 }$ =4

Question 49

Write the sentence as an equation.
If 5 times x is added to -4 , the result is equal to 9 times x .

A) 14 x-9 x=4
B) 5 x+(-4)=9 x
C) 4 x+(-4)=9 x
D) 9(5 x-4)=-4

Question 50

Write the sentence as an equation.
The sum of -15 and x amounts to -17 .

A) x-17=-15
B) x=-15+17
C) -15+x=-17
D) -15-17=x

Question 51

Write the sentence as an equation.
Four times x amounts to 28 .

A) $\frac { 4 } { x }$ =28
B) 4+x=28
C) $x ^ { 4 }$ =28
D) 4x=28

Question 52

Write the sentence as an equation.
The product of three-fourths and x is 42 .

A) $\frac { 3 } { 4 }$ =42x
B) $\frac { 3 } { 4 }$ +x=42
C) $\frac { 3 } { 4 }$ -x=42
D) $\frac { 3 } { 4 }$ x=42

Question 53

Write the sentence as an equation.
Five times x divided by 17 is 45 .

A) $\frac { 5 } { 17 x }$ =45
B) $\frac { 17 x } { 5 }$ =45
C) $\frac { 5 x } { 17 }$ =45
D) $\frac { 17 } { 5 x }$ =45

Question 54

Write the sentence as an equation.
Seven subtracted from x is equal to 5 .

A) 7-x=5
B) 5-7=x
C) 7+x=5
D) x-7=5

Question 55

Insert $$< , > \text {, or } =$$ to in the space provided to form a true statement.
-6 / -5

A) -6=-5
B) -6>-5
C) -6<-5

Question 56

Write the sentence as an equation.
Eight subtracted from three times x amounts to 16 .

A) 8-3 x=16
B) 3(x-8)=16
C) 8(3-x)=16
D) 3 x-8=16

Question 57

Insert $$< , > \text {, or } =$$ to in the space provided to form a true statement.
-44 & -39

A) $- 44 = - 39$
B) -44<-39
C) -44>-39

Question 58

Write the sentence as an equation.
Thirty-nine increased by x equals 55 .

A) 39 x=55
B) 39-x=55
C) 39+x=55
D) 39+55=x

Question 59

Write the sentence as an equation.
Eight times x is 12 more than three times x .

A) 8x +12=3x
B) 8 + x=3 x+12
C) 8x=3 x+12
D) 8x=3(x+12)

Question 60

Write the sentence as an equation.
Four times x added to 9 times x is the same as 52 .

A) 4(x+9)=52 x
B) 4 x-9 x=52
C) 4 x(9+x)=52
D) 4 x+9 x=52

Question 61

Write the reciprocal (or multiplicative inverse) of the number if it exists.
$\frac { 5 } { 7 }$

A) 1
B) $\frac { 7 } { 5 }$
C) $- \frac { 5 } { 7 }$
D) $- \frac { 7 } { 5 }$

Question 62

Determine if the statement is true or false.
2>4

A) True
B) False

Question 63

Find the opposite (or additive inverse) of the number.
$\frac { 6 } { 7 }$

A) $- \frac { 6 } { 7 }$
B) $\frac { 6 } { 7 }$
C) $\frac { 7 } { 6 }$
D) 0

Question 64

Determine if the statement is true or false.
25>14

A) True
B) False

Question 65

Find the opposite (or additive inverse) of the number.
-26

A) 26
B) -26
C) $- \frac { 1 } { 26 }$
D) 0

Question 66

Insert $$< , > \text {, or } =$$ to in the space provided to form a true statement.
8.055 \ 8.5

A)
B) 8.055=8.5
C) 8.055>8.5

Question 67

Write the reciprocal (or multiplicative inverse) of the number if it exists.
$\frac { 0 } { 3 }$

A) Undefined
B) 3
C)
D) 0

Question 68

Write the reciprocal (or multiplicative inverse) of the number if it exists.
$- \frac { 4 } { 9 }$

A) $- \frac { 9 } { 4 }$
B) $\frac { 4 } { 9 }$
C) 1
D) $\frac { 9 } { 4 }$

Question 69

Determine if the statement is true or false.
-45<0

A) True
B) False

Question 70

Find the opposite (or additive inverse) of the number.
15

A) -15
B) $\frac { 1 } { 15 }$
C) 0
D) 15

Question 71

Find the opposite (or additive inverse) of the number.
14

A) $\frac { 1 } { 14 }$
B) 0
C) 14
D) -14

Question 72

Write the reciprocal (or multiplicative inverse) of the number if it exists.
14

A) 1
B) $\frac { 1 } { 14 }$
C) -14
D) - $\frac { 1 } { 14 }$

Question 73

Find the opposite (or additive inverse) of the number.
-2.2

A) 0
B) 2.2
C) -2.2
D) $\frac { 1 } { - 2.2 }$ .

Question 74

Write the reciprocal (or multiplicative inverse) of the number if it exists.
0

A) 1
B) Undefined
C) $\frac { 1 } { 0 }$
D) 0

Question 75

Determine if the statement is true or false.
16 $\geq$ 9

A) True
B) False

Question 76

Determine if the statement is true or false.
18 $\leq$ 6

A) True
B) False

Question 77

Insert $$< , > \text {, or } =$$ to in the space provided to form a true statement.
$\frac { 2 } { 8 } ــــ \frac { 1 } { 4 }$

A) $\frac { 2 } { 8 } > \frac { 1 } { 4 }$
B) $\frac { 2 } { 8 } < \frac { 1 } { 4 }$
C) $\frac { 2 } { 8 } = \frac { 1 } { 4 }$

Question 78

Determine if the statement is true or false.
-5 $\geq$ 21

A) True
B) False

Question 79

Determine if the statement is true or false.
18<-2

A) True
B) False

Question 80

Determine if the statement is true or false.
-3 14

A) True
B) False