Deck 1: Fundamentals of Algebra

Question 1

Evaluate $| - 11.5 |$ .

A) 0.5
B) 1.5
C) 0
D) -11.5
E) 11.5

Answer 1

11.5

Question 2

Choose the correct expression.

A) $\left| - \frac { 1 } { 7 } \right| < - \left| \frac { 2 } { 5 } \right|$
B) $\left| - \frac { 1 } { 7 } \right| > - \left| \frac { 2 } { 5 } \right|$
C) $\left| - \frac { 1 } { 7 } \right| = - \left| \frac { 2 } { 5 } \right|$

Answer 2

$\left| - \frac { 1 } { 7 } \right| > - \left| \frac { 2 } { 5 } \right|$

Question 3

Determine which of the numbers in the set below are rational. $\left\{ - 11,33 , \frac { 1 } { 11 } , 5.5 , - 4.25 \right\}$

A) $\left\{ \frac { 1 } { 11 } \right\}$
B) $\{ 5.5 , - 4.25 \}$
C) $\{ - 11,33 \}$
D) $\left\{ - 11,33 , \frac { 1 } { 11 } , 5.5 , - 4.25 \right\}$
E)none are rational

Answer 3

$\left\{ - 11,33 , \frac { 1 } { 11 } , 5.5 , - 4.25 \right\}$

Question 4

Choose the correct expression.

A) $| - 9 | = | 9 |$
B) $| - 9 | < | 9 |$
C) $| - 9 | > | 9 |$

Question 5

Find the distance between $3$ and 0 on the real number line.

A)0
B)1
C) 1.5
D) -3
E) 3

Question 6

List all even integers between $- 6 \cdot 4$ and $6.2$ .

A) $- 4 , - 2,0,2,4$
B) $- 6 , - 4 , - 2,2,4,6$
C) $- 4 , - 2,2,4$
D) $- 6 , - 4 , - 2,0,2,4,6$
E) $2,4,6$

Question 7

Find the opposite of the real number $\frac{5}{9}$ .

A) $\frac{9}{5}$
B) - $\frac{9}{5}$
C) $\frac{5}{9}$
D) - $\frac{5}{9}$
E) -4

Question 8

Find the distance between and 0 on the real number line.

A)1
B)
C)
D)
E)0

Question 9

Evaluate $- | 3.75 |$ .

A) -0.75
B) 0.75
C) 3.75
D)0
E) -3.75

Question 10

Find the distance between and .

A)
B)
C)
D)
E)

Question 11

Determine which of the numbers in the set below are integers. $\left\{ - 8,13 , \frac { 2 } { 5 } , 10.5 , - 2.25 \right\}$

A) $\{ - 8,13,10.5 , - 2.25 \}$
B) $\left\{ - 8,13 , \frac { 2 } { 5 } , 10.5 , - 2.25 \right\}$
C) $\{ 13 \}$
D) $\left\{ \frac { 2 } { 5 } , 10.5 , - 2.25 \right\}$
E) $\{ - 8,13 \}$

Question 12

Find a true inequality that involves the real number $- \frac { 10 } { 7 }$ .

A) $- \frac { 10 } { 7 } > \frac { 3 } { 7 }$
B) $- \frac { 10 } { 7 } < - \frac { 17 } { 7 }$
C) $- \frac { 10 } { 7 } < - \frac { 4 } { 3 }$
D) $\frac { 10 } { 7 } > - \frac { 7 } { 6 }$
E) $- \frac { 10 } { 7 } > - \frac { 3 } { 7 }$

Question 13

Evaluate $- | - 9.25 |$ .

A) 0.25
B) -9.25
C)0
D) - 0.25
E) 9.25

Question 14

Evaluate |2| .

A) $- \frac { 1 } { 2 }$
B) $\frac { 1 } { 2 }$
C) 2
D) -2
E)0

Question 15

Plot the number on the real number line.

A)
B)
C)
D)
E)

Question 16

Evaluate .

A)0
B)
C)1
D)
E)

Question 17

Approximate the two numbers and list them in ascending order.

A) $- 4.5,2$
B) $- 2, - 4.5$
C) $- 4.5 , - 2$
D) $4.5,2$
E) $4.5 , - 2$

Question 18

Find a true inequality that involves the real number $\frac { 11 } { 6 }$ .

A) $\frac { 11 } { 6 } < \frac { 5 } { 6 }$
B) $\frac { 11 } { 6 } > \frac { 11 } { 8 }$
C) $\frac { 11 } { 6 } > \frac { 17 } { 6 }$
D) $\frac { 11 } { 6 } < \frac { 11 } { 9 }$
E) $\frac { 11 } { 6 } < - \frac { 17 } { 6 }$

Question 19

Find the opposite of the real number 5 .

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

Question 20

Use an overbar symbol to rewrite the decimal $5.438438438 \ldots$ using the smallest number of digits possible.

A) $5 . \overline { 438 }$
B) $\bar{5}.4384$
C) $\overline{5.438}$
D) $5 . \overline { 4384 }$
E) $\overline { 5 } \cdot 438$

Question 21

Find the difference $9 - ( - 4 )$ .

A)6
B)13
C)-5
D)5
E)-13

Question 22

Find the difference $- 84 - 117$ .

A)-33
B)33
C)-201
D)201
E)-211

Question 23

Evaluate $4.6 + 1.764 - 8.63$ and round the answer to two decimal places.

A)13.61
B)-5.72
C)-2.27
D)-20.87
E)-5.79

Question 24

Find the difference $- 7 - ( - 7 )$ .

A)-14
B)-7
C) 0
D)14
E)7

Question 25

Find the difference .

A)30
B)40
C)35
D)50
E)39

Question 26

Evaluate the expression $- 4 + 7 - ( - 2 ) + 10$ .

A)1
B)-5
C)23
D)15
E)11

Question 27

Determine the distance from each point to zero.

A)distance from 0 to a : 5 distance from 0 to b : 5
B)distance from 0 to a : 3 distance from 0 to b : 3
C)distance from 0 to a : 4 distance from 0 to b : 4
D)distance from 0 to a : $9$ distance from 0 to b : $8$
E)distance from 0 to a : $8$ distance from 0 to b : $4$

Question 28

Find the sum .

A)2
B)-18
C)80
D)18
E)-2

Question 29

Find the sum $26 + ( - 19 )$ .

A)-8
B)-9
C)9
D)8
E)7

Question 30

Write an inequality to describe the following statement: The tire pressure p is at least 27 pounds per square inch and no more than 34 pounds per square inch.

A) $27 \leq p \leq 34$
B) $27 \leq p \geq 34$
C) $27 = p$
D) $27 < p < 34$
E) $27 > p \geq 34$

Question 31

Find the sum $41 + ( - 24 ) + ( - 23 )$ .

A)-6
B)-88
C)40
D)42
E)88

Question 32

Find the difference .

A)-276
B)286
C)-266
D)276
E)-286

Question 33

Find the difference $30 - ( - 11 )$ .

A)20
B)-41
C)19
D)41
E)-19

Question 34

Find the difference $18 - ( - 35 )$ .

A)43
B)-7
C)53
D)-17
E)-53

Question 35

Find the difference $- 128 - ( - 33 )$ .

A)95
B)-161
C)-105
D)161
E)-95

Question 36

Find the difference .

A)30
B)-40
C)40
D)-30
E)-35

Question 37

Evaluate the expression $25 - 5 + 14$ .

A)16
B)-6
C)6
D)44
E)34

Question 38

Plot and its opposite on the real number line.

A)
B)
C)
D)
E)

Question 39

Evaluate the expression $- ( - 3 ) + 6 - 10 + 12$ .

A)25
B)-31
C)7
D)-13
E)11

Question 40

Find the sum .

A)51
B)50
C)52
D)53
E)49

Question 41

Find the product .

A)-13
B)13
C)-40
D)40
E)3

Question 42

Multiply the fractions $\left( \frac { 4 } { 9 } \right) \left( - \frac { 5 } { 2 } \right)$ and write the result in simplest form.

A) $- \frac { 37 } { 18 }$
B) $\frac { 1 } { 7 }$
C) - $\frac { 1 } { 7 }$
D) $- \frac { 10 } { 9 }$
E) $\frac { 10 } { 9 }$

Question 43

Add the fractions $\frac { 2 } { 12 } + \frac { 9 } { 12 }$ and write the result in simplest form.

A) $\frac { 1 } { 8 }$
B) $\frac { 11 } { 24 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 11 } { 12 }$
E) $\frac { 3 } { 2 }$

Question 44

Find the reciprocal of 7.

A) -7
B) $- \frac { 1 } { 7 }$
C) 7
D)0
E) $\frac { 1 } { 7 }$

Question 45

Multiply $8 \left( \frac { 4 } { 7 } \right)$ and write the result in simplest form.

A) $\frac { 4 } { 15 }$
B) $\frac { 60 } { 7 }$
C) $\frac { 12 } { 7 }$
D) $\frac { 32 } { 7 }$
E) - $\frac { 32 } { 7 }$

Question 46

Write $4 \left( \frac { 4 } { 12 } \right)$ as repeated addition.

A) $16 + 16 + 16 + 16$
B) $\frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 }$
C) $\frac { 16 } { 12 } + \frac { 16 } { 12 } + \frac { 16 } { 12 } + \frac { 16 } { 12 }$
D) $\frac { 4 } { 12 } + \frac { 4 } { 12 } + 4$
E) $\frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 }$

Question 47

Perform the division $26 \div ( - 26 )$ , if possible.

A)-1
B)0
C)1
D)-26
E)not possible

Question 48

Write $( - 0.4 ) ^ { 6 }$ as a repeated multiplication problem.

A) $( 0.4 ) ( 0.4 ) ( 0.4 ) ( 0.4 ) ( 0.4 ) ( 0.4 )$
B) $6 ( - 0.4 )$
C) $( - 0.4 ) ( - 0.4 ) ( - 0.4 ) ( - 0.4 ) ( - 0.4 ) ( - 0.4 )$
D) $( - 0.4 ) ( - 0.4 ) ( - 0.4 ) ( - 0.4 ) ( - 0.4 ) ( - 0.4 ) ( - 0.4 )$
E) $( - 2.4 ) ( - 2.4 ) ( - 2.4 ) ( - 2.4 ) ( - 2.4 ) ( - 2.4 )$

Question 49

Subtract $5 - \frac { 7 } { 4 }$ and write the result in simplest form.

A) $\frac { 1 } { 2 }$
B) $\frac { 13 } { 4 }$
C) $- \frac { 1 } { 2 }$
D) $- \frac { 13 } { 4 }$
E) $\frac { 15 } { 4 }$

Question 50

Rewrite the expression in exponential form. $( - 3.6 ) ( - 3.6 ) \cdot ( - 3.6 )$

A)-11
B) $3 \times ( - 3.6 )$
C) $3 ^ { - 3.6 }$
D) $3 ^ { 3.6 }$
E) $( - 3.6 ) ^ { 3 }$

Question 51

Rewrite the expression in exponential form. $9.9 .9$

A) $3 ^ { 9 }$
B)27
C)729
D) $9 ^ { 3 }$
E) $3 \times 9$

Question 52

Evaluate the expression $- 1 \frac { 4 } { 5 } - 4 \frac { 2 } { 3 }$ and write the result in simplest form.

A) $\frac { 4 } { 15 }$
B) $- \frac { 97 } { 15 }$
C) $\frac { 28 } { 15 }$
D) $- \frac { 28 } { 15 }$
E) $\frac { 67 } { 15 }$

Question 53

Find the product $( - 4 ) ( - 4 ) ( - 5 )$ .

A)80
B)-320
C)-13
D)320
E)-80

Question 54

Add the fractions $\frac { 3 } { 6 } + \frac { 2 } { 8 }$ and write the result in simplest form.

A) $\frac { 5 } { 14 }$
B) $\frac { 5 } { 6 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 1 } { 8 }$
E) $\frac { 5 } { 48 }$

Question 55

Multiply $2 \frac { 4 } { 3 } \div 3 \frac { 2 } { 3 }$ and write the result in simplest form.

A) $\frac { 10 } { 11 }$
B) $\frac { 11 } { 10 }$
C) $\frac { 17 } { 2 }$
D) $\frac { 110 } { 9 }$
E) $\frac { 4 } { 3 }$

Question 56

Find the product .

A)2
B)1
C)-1
D)-2
E)3

Question 57

Divide the fractions $\left( - \frac { 10 } { 9 } \right) \div \left( - \frac { 8 } { 7 } \right)$ and write the result in simplest form.

A) $\frac { 35 } { 36 }$
B) 1
C) -1
D) - $\frac { 35 } { 36 }$
E) $- \frac { 143 } { 72 }$

Question 58

Multiply the fractions $\left( \frac { 10 } { 3 } \right) \left( - \frac { 3 } { 10 } \right)$ and write the result in simplest form.

A)30
B)-30
C)0
D) -1
E)1

Question 59

Write $\left( - \frac { 2 } { 7 } \right) + \left( - \frac { 2 } { 7 } \right) + \left( - \frac { 2 } { 7 } \right) + \left( - \frac { 2 } { 7 } \right)$ as a multiplication problem.

A) $4 \left( \frac { 2 } { 7 } \right)$
B) $2 \left( \frac { 2 } { 7 } \right)$
C) $4 \left( \frac { 2 } { 14 } \right)$
D) $- 4 \left( \frac { 2 } { 7 } \right)$
E) - $4 \left( \frac { 2 } { 14 } \right)$

Question 60

Subtract the fractions $\frac { 2 } { 16 } - \frac { 11 } { 16 }$ and write the result in simplest form.

A) $- \frac { 9 } { 16 }$
B) $\frac { 9 } { 0 }$
C) $\frac { 13 } { 32 }$
D) $- \frac { 13 } { 16 }$
E) $\frac { 9 } { 16 }$

Question 61

What is the multiplicative inverse of $- 6 z , z \neq 0$ ?

A) $- \frac { 1 } { 6 }$
B) 6z
C) -6z
D) $- \frac { 1 } { 6 z }$
E) $\frac { 1 } { 6 z }$

Question 62

Identify the property of real numbers illustrated by $6 ( y + 3 ) = 6 \cdot y - 6 \cdot 3$ .

A)Distributive Property
B)Additive Inverse Property
C)Associative Property of Addition
D)Additive Identity Property
E)Commutative Property of Addition

Question 63

You save $48 per month for 10 years. How much money has been saved during 10 years?

A)$480
B)$576
C)$14,400
D)$5,760
E)$17,280

Question 64

Evaluate $80 - 7 \left( 3 ^ { 2 } \div 9 \right)$ .

A)17
B)7
C)79
D)73
E)87

Question 65

Evaluate the expression $( 20 - 8 ) \div ( 11 - 5 )$ , if possible.

A) $- \frac { 1 } { 3 }$
B)4
C) $\frac { 157 } { 11 }$
D)2
E)not possible

Question 66

Evaluate the expression $2 ^ { 5 }$ .

A)64
B)10
C)200,000
D)32
E)25

Question 67

Rewrite $6 ( 2 \cdot 5 )$ using the Associative Property of Multiplication.

A) $( 6 \cdot 2 ) \frac { 1 } { 5 }$
B) $( 6 \cdot 2 )$
C) $( - 6 \cdot 2 ) 5$
D) $( 6 \cdot 2 ) 5$
E) $\left( 6 \cdot \frac { 1 } { 2 } \right) 5$

Question 68

Evaluate $\frac { 530 } { 1.055 ^ { 14 } }$ . Round your answer to two decimal places.

A)237.40
B)250.46
C)35.88
D)502.37
E)264.24

Question 69

Find the additive inverse and the multiplicative inverse of 26 .

A)additive inverse: $- \frac { 1 } { 26 }$ multiplicative inverse: $\frac { 1 } { 26 }$
B)additive inverse: 26 multiplicative inverse: $\frac { 1 } { 26 }$
C)additive inverse: -26 multiplicative inverse: $\frac { 1 } { 26 }$
D)additive inverse: $- 26$ multiplicative inverse: $- \frac { 1 } { 26 }$
E)additive inverse: $26$ multiplicative inverse: $- \frac { 1 } { 26 }$

Question 70

You save $53 per month for 21 years in a savings account earning 2% interest compounded monthly. The total amount in the account after 21 years will be $$53 \left[ \left( 1 + \frac { 0.02 } { 12 } \right) ^ { 252 } - 1 \right] \left( 1 + \frac { 12 } { 0.02 } \right)$$ . How much money is in the account after 21 years? Round your answer to two decimal places.

A)$48,462.10
B)$13,641.56
C)$16,609.10
D)$14,867.44
E)$34,698.81

Question 71

Identify the property of real numbers illustrated by $17 - 17 = 0$ .

A)Distributive Property
B)Additive Inverse Property
C)Commutative Property of Addition
D)Associative Property of Addition
E)Additive Identity Property

Question 72

Evaluate the expression $163 - \left( 6 \cdot 3 ^ { 2 } \right)$ .

A)109
B)-161
C)487
D)21,025
E)217

Question 73

Find the additive inverse and the multiplicative inverse of $- 14 y$ .

A)additive inverse: $- 14 y$ multiplicative inverse: $- \frac { 1 } { 14 } y$
B)additive inverse: $- 14 y$ multiplicative inverse: $\frac { 1 } { 14 } y$
C)additive inverse: $- \frac { 14 } { y }$ multiplicative inverse: 14y
D)additive inverse: $14 y$ multiplicative inverse: $\frac { 1 } { 14 } y$
E)additive inverse: $14 y$ multiplicative inverse: $- \frac { 1 } { 14 y }$

Question 74

If you save $75 every month, how much money will you have after 7 years?

A)$525
B)$6300
C)$984
D)$82
E)$5,250

Question 75

Identify the property of real numbers illustrated by $( 12 - 5 ) 19 = 12 \cdot 19 - 5 \cdot 19$ .

A)Commutative Property of Addition
B)Distributive Property
C)Additive Inverse Property
D)Associative Property of Addition
E)Additive Identity Property

Question 76

Identify the property of real numbers illustrated by the statement $( 5 + 9 ) + 7 = 5 + ( 9 + 7 )$ .

A)Commutative Property of Multiplication
B)Commutative Property of Addition
C)Distributive Property
D)Associative Property of Multiplication
E)Associative Property of Addition

Question 77

Identify the property of real numbers illustrated by the statement $( 10 ) ( - 6 ) = ( - 6 ) ( 10 )$ .

A)Distributive Property
B)Associative Property of Multiplication
C)Commutative Property of Addition
D)Associative Property of Addition
E)Commutative Property of Multiplication

Question 78

What is the additive inverse of ?

A)
B)
C)
D)
E)

Question 79

Evaluate the expression $- 6 ^ { 2 }$ .

A)-64
B)64
C)-12
D)36
E)-36

Question 80

The area of triangle is given by $\text { Area } = \frac { 1 } { 2 } \cdot \text { base } \cdot \text { height }$ Find the area of the triangle in square inches. $$a = 8$$

A)4 square inches
B)10 square inches
C)20 square inches
D)40 square inches
E)13 square inches