Deck 2: Operations With Real Numbers

Question 1

Evaluate: -12 - 11

A) 23
B) 1
C) -23
D) -1
E) 132

Answer 1

-23

Question 2

Your assistant brings four bills for $10 each. Find the change in net worth for your business.

A) -$40
B) $40
C) -$30
D) -$60
E) $60

Answer 2

-$40

Question 3

Evaluate: $$8 + ( - 8 )$$

A) 16
B) -24
C) 0
D) -16
E) 12

Answer 3

0

Question 4

Evaluate: $$2 + ( - 22 )$$

A) 24
B) -46
C) -20
D) 20
E) 23

Question 5

Write in words the expression $- | x |$ .

A) The opposite of the absolute value of x.
B) The opposite of the opposite of x.
C) The opposite value of x.
D) The absolute value of the opposite of x.
E) The opposite of the opposite of the absolute value of x.

Question 6

Evaluate: $$- 8 + ( - 20 )$$

A) -12
B) -28
C) 12
D) 28
E) 18

Question 7

Calculate the expression. $$- ( - 2 )$$

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

Question 8

What is $- | - x |$ , if $x = 5$ ?

A) -5
B) 5
C) -6
D) 6
E) 7

Question 9

Find the difference in elevation between the given highest and lowest points. South America: Mt. Aconcagua, 6,960 meters, and Valdes Peninsula, -40 meters.

A) 7,000 meters
B) 6,990 meters
C) 6,980 meters
D) 7,030 meters
E) 7,040 meters

Question 10

Evaluate: 13 - (-19)

A) 32
B) -6
C) -32
D) 6
E) 247

Question 11

Multiply: $\frac { 1 } { 3 } \cdot \left( - \frac { 4 } { 5 } \right)$

A) $- \frac { 5 } { 12 }$
B) $- \frac { 1 } { 5 }$
C) $- \frac { 4 } { 15 }$
D) $- \frac { 7 } { 15 }$
E) $- \frac { 20 } { 3 }$

Question 12

Evaluate: 4 - 12

A) 16
B) -8
C) -16
D) 8
E) -48

Question 13

Give the opposite of the number. $$- \frac { 1 } { 3 }$$

A) $- \frac { 1 } { 3 }$
B) $\frac { 1 } { 3 }$
C) -3
D) 3
E) 0

Question 14

Evaluate: -19 - (-20)

A) -39
B) 39
C) -1
D) 1
E) -380

Question 15

Calculate the expression. $$- | - 4 |$$

A) 4
B) $- 4$
C) $- \frac { 1 } { 4 }$
D) $\frac { 1 } { 4 }$
E) 5

Question 16

What is $- ( - x )$ , if $x = - 8$ ?

A) -8
B) 8
C) -7
D) 7
E) 10

Question 17

Your assistant brings three bills for $80 each. Find the change in net worth for your business.

A) $240
B) -$240
C) -$250
D) -$220
E) $220

Question 18

Multiply: $$- \frac { 3 } { 10 } \cdot \frac { 4 } { 9 }$$

A) $- \frac { 2 } { 15 }$
B) $- \frac { 27 } { 40 }$
C) $\frac { 1 } { 90 }$
D) $\frac { 13 } { 90 }$
E) $- \frac { 6 } { 5 }$

Question 19

Calculate the expression. $$| 1 - 3 |$$

A) -2
B) 3
C) 2
D) -3
E) 4

Question 20

Evaluate: $$- 7 + 14$$

A) 21
B) 7
C) -21
D) -7
E) 14

Question 21

Evaluate: $$- 16 + ( - 9 ) + 10$$

A) -35
B) 35
C) 17
D) -15
E) -13

Question 22

Add: $$\frac { 7 } { 20 } + \frac { 1 } { 18 }$$

A) $1 \frac { 73 } { 180 }$
B) $\frac { 73 } { 180 }$
C) $\frac { 73 } { 360 }$
D) $2 \frac { 73 } { 360 }$
E) $1 \frac { 73 } { 360 }$

Question 23

Find the product of $- \frac { 4 } { 15 }$ and $\frac { 5 } { 8 }$ .

A) $\frac { 43 } { 120 }$
B) $\frac { 1 } { 120 }$
C) $- \frac { 1 } { 6 }$
D) $- \frac { 3 } { 40 }$
E) $- \frac { 1 } { 7 }$

Question 24

Evaluate: 19 - (-5) -4

A) 14
B) 18
C) 20
D) 15
E) 40

Question 25

Find the quotient of the rational numbers given below. $$- \frac { 5 } { 8 } \text { and } - \frac { 13 } { 2 }$$

A) $\frac { 65 } { 16 }$
B) $- \frac { 3 } { 104 }$
C) $\frac { 3 } { 5 }$
D) $\frac { 5 } { 52 }$
E) $- \frac { 57 } { 8 }$

Question 26

Divide: $$\left( - \frac { 5 } { 2 } \right) \div \left( - \frac { 6 } { 11 } \right)$$

A) $- \frac { 3 } { 2 }$
B) $\frac { 13 } { 3 }$
C) $- \frac { 1 } { 9 }$
D) $\frac { 55 } { 12 }$
E) $\frac { 11 } { 9 }$

Question 27

Write the reciprocal of the expression below. Assume the variables do not equal zero. $$\frac { x } { y }$$

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

Question 28

Add: $$\frac { 2 } { 11 } + \frac { 5 } { 22 } + \frac { 29 } { 44 }$$

A) $2 \frac { 3 } { 44 }$
B) $1 \frac { 3 } { 22 }$
C) $1 \frac { 3 } { 44 }$
D) $\frac { 3 } { 44 }$
E) $\frac { 3 } { 22 }$

Question 29

Divide: $$- \frac { 1 } { 4 } \div \frac { 13 } { 2 }$$

A) $- \frac { 1 } { 26 }$
B) $- \frac { 13 } { 8 }$
C) $- \frac { 3 } { 2 }$
D) $- \frac { 2 } { 9 }$
E) $\frac { 1 } { 9 }$

Question 30

Write the reciprocal of the number below. $$\frac { 1 } { 2 }$$

A) $\frac { 1 } { 2 }$
B) 2
C) -2
D) - $\frac { 1 } { 2 }$
E) 6

Question 31

Evaluate: -8 - (-28) - 3 - 15

A) 2
B) 54
C) -20
D) 5
E) -40

Question 32

Add: 34.405 + 2.2032 + 425.04

A) 461.6482
B) 451.6482
C) 461.5382
D) 471.7483
E) 561.6583

Question 33

What is $\frac { 3 } { 8 }$ added to $\frac { 3 } { 5 }$ ?

A) $\frac { 39 } { 40 }$
B) $1 \frac { 39 } { 40 }$
C) $\frac { 39 } { 80 }$
D) $2 \frac { 6 } { 13 }$
E) $\frac { 6 } { 13 }$

Question 34

What is $\frac { 3 } { 8 }$ divided by $- \frac { 11 } { 2 }$ ?

A) $- \frac { 41 } { 8 }$
B) $- \frac { 5 } { 3 }$
C) $- \frac { 3 } { 44 }$
D) $\frac { 5 } { 88 }$
E) $- \frac { 33 } { 16 }$

Question 35

Evaluate: $$- 18 + ( - 15 ) + 13 + ( - 9 )$$

A) 32
B) 37
C) -29
D) 39
E) 29

Question 36

Add: 77.05 + 2.66826 + 46.7

A) 125.31826
B) 114.41826
C) 126.31806
D) 136.42926
E) 126.41826

Question 37

Multiply: $$\left( - \frac { 5 } { 6 } \right) \cdot \left( - \frac { 4 } { 13 } \right)$$

A) $- \frac { 3 } { 26 }$
B) $\frac { 9 } { 7 }$
C) $- \frac { 89 } { 78 }$
D) $\frac { 10 } { 39 }$
E) $- \frac { 41 } { 39 }$

Question 38

Divide: $$\frac { 5 } { 4 } \div \left( - \frac { 11 } { 4 } \right)$$

A) $- \frac { 55 } { 16 }$
B) $- \frac { 3 } { 8 }$
C) $- \frac { 5 } { 11 }$
D) $- \frac { 1 } { 7 }$
E) $- \frac { 20 } { 7 }$

Question 39

Add: $\frac { 3 } { 8 } + \frac { 13 } { 16 }$

A) $1 \frac { 1 } { 8 }$
B) $\frac { 11 } { 8 }$
C) $\frac { 3 } { 16 }$
D) $1 \frac { 3 } { 16 }$
E) $2 \frac { 3 } { 16 }$

Question 40

Write the reciprocal of the number below. $$3 \frac { 2 } { 3 }$$

A) $- \frac { 3 } { 11 }$
B) $\frac { 3 } { 11 }$
C) $\frac { 2 } { 3 }$
D) $- \frac { 2 } { 3 }$
E) $\frac { 3 } { 2 }$

Question 41

Evaluate: (-5 )⁴

A) 625
B) -625
C) -1024
D) 1024
E) $\frac { 4 } { 5 }$

Question 42

How many terms are in the expression? $$x ^ { 4 } + 4 x ^ { 3 } + 4 x + 1$$

A) 5
B) 4
C) 7
D) 6
E) 2

Question 43

Identify the numerical coefficient in the term. $$- 4 x ^ { 2 }$$

A) 4
B) $- 4 x$
C) $- x$
D) $x$
E) $- 4$

Question 44

Evaluate: 4³

A) $\frac { 3 } { 4 }$
B) 64
C) 4
D) 3
E) 12

Question 45

Simplify: $$2 ( 11 c - 4 )$$

A) $20 c + 8$
B) $13 c - 8$
C) $20 c - 2$
D) $13 c - 2$
E) $22 c - 8$

Question 46

Simplify: $$4 ( x + 5 )$$

A) $5 x + 5$
B) $20 x + 20$
C) $4 x + 5$
D) $20 x + 9$
E) $4 x + 20$

Question 47

Simplify: $$- 3 ( y - 10 )$$

A) $- 3 y + 30$
B) $3 y + 30$
C) $- 30 y - 13$
D) $3 y - 13$
E) $- 30 y - 30$

Question 48

Simplify: $$( y - 8 ) 3$$

A) $3 y - 5$
B) $- 3 y - 24$
C) $3 y - 24$
D) $- 3 y + 24$
E) $- 5 y - 5$

Question 49

Simplify: $$2 ( 7 x + 12 )$$

A) $14 x + 14$
B) $9 x + 24$
C) $14 x + 24$
D) $26 x + 14$
E) $26 x - 10$

Question 50

Simplify: $$6 x + 8 ( x + 3 )$$

A) $48 x + 24$
B) $14 x + 24$
C) $14 x + 5$
D) $48 x + 11$
E) $17 x + 11$

Question 51

How many factors are in the expression? $( a + b ) ( c + d )$

A) 2
B) 4
C) 3
D) 1
E) 6

Question 52

Simplify the following expression. $$- 4 ( 4 a - 4 )$$

A) $- 4 a + 16$
B) $- 16 a - 4$
C) $- 16 a + 16$
D) $- 16 a - 16$
E) $16 a + 16$

Question 53

Simplify the following expression. $$7 ( x - 6 )$$

A) $7 x + 42$
B) $7 x - 6$
C) $7 x + 6$
D) $7 x - 42$
E) $- 7 x + 42$

Question 54

Simplify: $$8 y - 2 ( y + 12 )$$

A) $16 y + 14$
B) $16 y - 24$
C) $6 y + 14$
D) $6 y - 24$
E) $18 y + 12$

Question 55

Identify the base for the exponent. $$t m ^ { 2 }$$

A) $t m$
B) $t$
C) $m$
D) 3
E) $t m ^ { 2 }$

Question 56

Simplify: $$- 2 y + 12 ( y - 5 )$$

A) $14 y - 60$
B) $10 y - 60$
C) $10 y + 7$
D) $14 y + 7$
E) $- 10 y + 60$

Question 57

Simplify: $$7 n + 8 ( n + 2 ) - 8$$

A) $15 n + 16$
B) $17 n + 8$
C) $15 n + 8$
D) $17 n + 16$
E) $9 n - 8$

Question 58

Simplify: $$- 11 ( a + 3 )$$

A) $11 a - 8$
B) $- 11 a - 33$
C) $- 8 a - 33$
D) $- 11 a - 8$
E) $- 8 a + 3$

Question 59

Simplify the following expression. $$- 4 ( z + 10 )$$

A) $- 4 z + 40$
B) $- 4 z - 10$
C) $- 4 z + 10$
D) $- 4 z - 40$
E) $4 z + 40$

Question 60

Simplify the following expression. $$- ( x + 9 )$$

A) $- x + 9$
B) $- x - 9$
C) $x + 9$
D) $x - 9$
E) 9

Question 61

Find the circumference (perimeter) and area of a circle with radius 2.5 feet. Use $\pi$ from a calculator. Choices are rounded to the nearest tenth.

A) C = 15.7 ft; A = 19.6 ft²
B) C = 7.9 ft; A = 19.6 ft²
C) C = 5 ft; A = 6.3 ft²
D) C = 10 ft; A = 6.3 ft²
E) C = 19.6 ft; A = 15.7 ft²

Question 62

Use unit analysis to answer how many minutes are in 7 years, assuming that each year has 365 days.

A) 3,689,200 minutes
B) 3,679,200 minutes
C) 3,699,200 minutes
D) 3,709,200 minutes
E) 3,719,200 minutes

Question 63

Evaluate: -2³

A) 8
B) -8
C) $- \frac { 3 } { 2 }$
D) -9
E) 6

Question 64

Find the perimeter and area of a trapezoid: length of top is 2.9 cm; length of bottom (parallel to the top) is 5.8 cm; length of one slant side is 1.7 cm, length of the other slant side is 2.4 cm; and the height is 1.4 cm. Choices are rounded to the nearest tenth.

A) P = 14.2 cm; A = 6.1 cm²
B) P = 12.8 cm; A = 6.1 cm²
C) P = 14.2 cm; A = 2.9 cm²
D) P = 10.1 cm; A = 2.9 cm²
E) P = 12.8 cm; A = 9.0 cm²

Question 65

Simplify the expression without a calculator. $$\frac { 9 - 5 } { 6 - ( - 1 ) }$$

A) $\frac { 4 } { 5 }$
B) $\frac { 4 } { 7 }$
C) $\frac { 5 } { 9 }$
D) $\frac { 7 } { 4 }$
E) $\frac { 5 } { 4 }$

Question 66

Evaluate: (-2 )³(-4)²(-2)³

A) -256
B) -288
C) 1024
D) -32
E) 256

Question 67

Find the circumference (perimeter) and area of a circle with diameter 8 inches. Use $\pi$ from a calculator. Choices are rounded to the nearest tenth.

A) C = 50.3 in.; A = 64 in.²
B) C = 64 in.; A = 50.3 in.²
C) C = 25.1 in.; A = 201.1 in.²
D) C = 50.3 in.; A = 201.1 in.²
E) C = 25.1 in.; A = 50.3 in.²

Question 68

Simplify the expression without a calculator. $\sqrt { ( 7 - ( - 5 ) ) ^ { 2 } + ( - 4 - 1 ) ^ { 2 } }$

A) 13
B) 14
C) 15
D) 10
E) 9

Question 69

Evaluate the following expression. $$\frac { 30 + \sqrt { 225 } } { 3 }$$

A) 25
B) 35
C) 85
D) 105
E) 15

Question 70

Evaluate: $$\left( - \frac { 2 } { 5 } \right) ^ { 5 }$$

A) $\frac { 32 } { 3125 }$
B) $- \frac { 2 } { 625 }$
C) $- \frac { 2 } { 5 }$
D) $- \frac { 32 } { 3125 }$
E) $- \frac { 32 } { 5 }$

Question 71

Use unit analysis to change 8 cubic yards into cubic inches.

A) 373,248 cubic inches
B) 372,248 cubic inches
C) 375,248 cubic inches
D) 370,248 cubic inches
E) 377,248 cubic inches

Question 72

Simplify the expression without a calculator. $$| 2 - 8 | - | 8 - 7 |$$

A) 5
B) 6
C) 3
D) 8
E) 1

Question 73

Simplify the expression (6 ft)³. Use the definition of positive integer exponents.

A) 18 ft
B) 18 ft³
C) 216 ft
D) 36 ft³
E) 216 ft³

Question 74

Evaluate: 5(-3 )⁴

A) 405
B) -405
C) -60
D) $\frac { 4 } { 15 }$
E) 60

Question 75

Simplify the expression (9 cm)². Use the definition of positive integer exponents.

A) 18 cm²
B) 81 cm
C) 18 cm
D) 81 cm²
E) 9 cm²

Question 76

Simplify the expression. Use a calculator as needed. $$3.14 ( 5 ) ^ { 2 } \cdot 7$$

A) 550.62
B) 549.5
C) 550.95
D) 551.64
E) 546.83

Question 77

Evaluate: (-2 )⁴(-8)²

A) 128
B) 1024
C) -80
D) 8
E) -128

Question 78

Use unit analysis to answer how many ounces are in 3 tons. Round to the nearest whole number if necessary. 1 ton = 2,000 pounds
16 ounces = 1 pound

A) 96,000 ounces
B) 6,000 ounces
C) 48 ounces
D) 375 ounces
E) 2,019 ounces

Question 79

Use unit analysis to change 5,900,000 ounces into tons. Round your answer to one decimal place.

A) 184.4 tons
B) 174.4 tons
C) 164.4 tons
D) 154.4 tons
E) 224.4 tons

Question 80

Simplify the expression. Use a calculator as needed. $$2 ( 3.14 ) \cdot 5 \cdot 4 + 2 ( 3.14 ) ( 4 ) ^ { 2 }$$

A) 226.08
B) 224.96
C) 224.63
D) 228.22
E) 228.75