Deck 1: Variables, Real Numbers, and Mathematical Models

Question 1

Evaluate the algebraic expression for the given value(s).
$6 x - 2 y , \text { given } x = 5 , y = 2$

A) 34
B) 24
C) 28
D) 26

Answer 1

26

Question 2

Write the English phrase as an algebraic expression. Let the variable x represent the number.
six less than the product of 13 and a number

A) 6x - 13
B) 13x + 6
C) 6 - 13x
D) 13x - 6

Answer 2

13x - 6

Question 3

Evaluate the algebraic expression for the given value(s).
$3 x , \text { given } x = 4$

A) 12
B) 4
C) 3
D) 7

Answer 3

12

Question 4

Write the English phrase as an algebraic expression. Let the variable x represent the number.
Six times a number, decreased by fourteen

A) 6x + 14
B) 14 - 6x
C) 6x - 14
D) 6x - 84

Question 5

Evaluate the algebraic expression for the given value(s).
$\frac { 2 y - x + 20 } { 2 x - y } , \text { given } x = 5 , y = 3$

A) 3
B) 21
C) 53
D) 1

Question 6

Write the English phrase as an algebraic expression. Let the variable x represent the number.
five subtracted from a number

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

Question 7

Evaluate the algebraic expression for the given value(s).
$x + 9 , \text { given } x = 2$

A) 11
B) 7
C) 12
D) 18

Question 8

Write the English phrase as an algebraic expression. Let the variable x represent the number.
eight less than a number

A) 8 - x
B) $\frac { x } { 8 }$
C) x + 8
D) x - 8

Question 9

Evaluate the algebraic expression for the given value(s).
$\frac { 10 } { x } , \text { given } x = 5$

A) 3
B) 5
C) 2
D) 10

Question 10

Write the English phrase as an algebraic expression. Let the variable x represent the number.
five decreased by a number

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

Question 11

Evaluate the algebraic expression for the given value(s).
$\frac { 24 } { x } - \frac { 14 } { y } , \text { given } x = 4 , y = 7$

A) 3
B) 4
C) 12
D) 8

Question 12

Write the English phrase as an algebraic expression. Let the variable x represent the number.
The sum of a number and 138

A) x - 138
B) 138
C) 138x
D) x + 138

Question 13

Evaluate the algebraic expression for the given value(s).
5(x + y), given x = 6, y = 4

A) 120
B) 34
C) 10
D) 50

Question 14

Evaluate the algebraic expression for the given value(s).
7x + y, given x = 3, y = 2

A) 23
B) 19
C) 35
D) 12

Question 15

Write the English phrase as an algebraic expression. Let the variable x represent the number.
eight more than a number

A) x - 8
B) x + 8
C) x + 80
D) 8x

Question 16

Evaluate the algebraic expression for the given value(s).
$\frac { 13 x - 2 y } { x + 2 } , \text { given } x = 3 , y = 7$

A) 6
B) 7
C) 5
D) 8

Question 17

Evaluate the algebraic expression for the given value(s).
8 + 3x, given x = 6

A) 11
B) 26
C) 10
D) 36

Question 18

Evaluate the algebraic expression for the given value(s).
$x - 0 , \text { given } x = 3$

A) 4
B) 2
C) 0
D) 3

Question 19

Evaluate the algebraic expression for the given value(s).
$2 ( x + 2 ) \text {, given } 4$

A) 10
B) 12
C) 16
D) 4

Question 20

Evaluate the algebraic expression for the given value(s).
$\frac { 10 x + 20 } { 5 x } , \text { given } 4$

A) 2
B) 3
C) 1
D) 40

Question 21

Write the sentence as an equation. Let the variable x represent the number.
The sum of twice a number and 5 is 11.

A) x + 10 = 11
B) 10x = 11
C) 2x + 5 = 11
D) 2x - 5 = 11

Question 22

Write the sentence as an equation. Let the variable x represent the number.
Four times a number is 24.

A) 4x = 24
B) x + 4 = 24
C) x - 4 = 24
D) $\frac { 4 } { x } = 24$

Question 23

Write the English phrase as an algebraic expression. Let the variable x represent the number.
the sum of 40 divided by a number and that number divided by 40

A) $\frac { 40 + x } { 40 }$
B) $\frac { 40 } { x } - \frac { x } { 40 }$
C) $\frac { 40 } { x } + \frac { x } { 40 }$
D) $\frac { 40 + x } { x + 40 }$

Question 24

Write the sentence as an equation. Let the variable x represent the number.
Four times a number is equal to 25 decreased by the number.

A) 4 + x = 25 - x
B) 4x = 25 - x
C) 4x = x - 25
D) 4x = 25 + x

Question 25

Write the sentence as an equation. Let the variable x represent the number.
The product of 6 and a number, increased by 2, is 32.

A) 12x = 32
B) 6x + 2 = 32
C) 6x - 2 = 32
D) 6(x + 2) = 32

Question 26

Write the sentence as an equation. Let the variable x represent the number.
The quotient of 15 and a number is $\frac { 1 } { 4 }$ .

A) $\frac { 15 } { x } = \frac { 1 } { 4 }$
B) $15 x = \frac { 1 } { 4 }$
C) $\frac { x } { 15 } = \frac { 1 } { 4 }$
D) $x + 15 = \frac { 1 } { 4 }$

Question 27

Determine if the given value is a solution to the equation.
3a + 2 = 2a + 5; 3

A) solution
B) not a solution

Question 28

Write the sentence as an equation. Let the variable x represent the number.
Seven less than 4 times a number gives 5.

A) 7 - 4x = 5
B) $\frac { 4 x } { 7 } = 5$
C) x - 28 = 5
D) 4x - 7 = 5

Question 29

Determine if the given value is a solution to the equation.
3(w + 2) = 4(w - 1); 9

A) solution
B) not a solution

Question 30

Determine if the given value is a solution to the equation.
$\frac { r } { 4 } = 5 ; 15$

A) solution
B) not a solution

Question 31

Determine if the given value is a solution to the equation.
y - 2 = 1; 3

A) solution
B) not a solution

Question 32

Determine if the given value is a solution to the equation.
3z = 18; 6

A) not a solution
B) solution

Question 33

Write the sentence as an equation. Let the variable x represent the number.
The difference between 50 and a number is 10.

A) 50 + x = 10
B) 50 - x = 10
C) $\frac { 50 } { x } = 10$
D) x - 50 = 10

Question 34

Determine if the given value is a solution to the equation.
60 - y = 10; 60

A) solution
B) not a solution

Question 35

Determine if the given value is a solution to the equation.
$4 ( p - 1 ) = 2 p ; 2$

A) not a solution
B) solution

Question 36

Determine if the given value is a solution to the equation.
4m + 8 = 42; 8

A) not a solution
B) solution

Question 37

Write the sentence as an equation. Let the variable x represent the number.
Find the perimeter of a rectangle if the length, L, is 8 meters and the width, W, is 7 meters. Use the formula P = 2L + 2W.

A) 112 m
B) 23 m
C) 30 m
D) 15 m

Question 38

Write the English phrase as an algebraic expression. Let the variable x represent the number.
one more than the quotient of a number and 45

A) $45 x - 1$
B) $\frac { 45 } { x } + 1$
C) $45 x + 1$
D) $\frac { x } { 45 } + 1$

Question 39

Write the sentence as an equation. Let the variable x represent the number.
The product of 4 and a number increased by 5 is 32.

A) 4(x + 5) = 32
B) 4x + 5 = 32
C) 20x = 32
D) 4x - 5 = 32

Question 40

Determine if the given value is a solution to the equation.
x + 10 = 11; 1

A) not a solution
B) solution

Question 41

Write the fraction in lowest terms.
$\frac { 22 } { 33 }$

A) $\frac { 11 } { 3 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 22 } { 33 }$
D) $\frac { 2 } { 11 }$

Question 42

Write the fraction in lowest terms.
$$\frac { 104 } { 147 }$$

A) $\frac { 104 } { 147 }$
B) $\frac { 52 } { 104 }$
C) $\frac { 147 } { 52 }$
D) $\frac { 52 } { 73 }$

Question 43

Write the fraction in lowest terms.
$\frac { 374 } { 396 }$

A) $\frac { 374 } { 396 }$
B) $\frac { 17 } { 18 }$
C) $\frac { 132 } { 124 }$
D) $\frac { 124 } { 132 }$

Question 44

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 5 } { 5 } \cdot \frac { 19 } { 11 }$

A) $\frac { 3 } { 2 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 19 } { 11 }$
D) $\frac { 11 } { 19 }$

Question 45

Write the sentence as an equation. Let the variable x represent the number.
The formula S = P - 0.2P gives the sale price, S, of a shirt that was marked down 20% from the original price, P. Find the sale price of a shirt that originally cost $42.

A) $44.00
B) $33.60
C) $41.80
D) $50.40

Question 46

Write the sentence as an equation. Let the variable x represent the number.
22

A) 2 ·11
B) 10 ·4
C) 3 ·13
D) prime

Question 47

Write the fraction in lowest terms.
$\frac { 495 } { 605 }$

A) $\frac { 9 } { 11 }$
B) $\frac { 605 } { 495 }$
C) $\frac { 495 } { 605 }$
D) $\frac { 11 } { 9 }$

Question 48

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\left( 4 \frac { 1 } { 6 } \right) \left( 2 \frac { 2 } { 5 } \right)$$

A) 10
B) $8 \frac { 5 } { 30 }$
C) 11
D) 15

Question 49

Write the fraction in lowest terms.
$$\frac { 60 } { 105 }$$

A) $\frac { 60 } { 105 }$
B) $\frac { 4 } { 15 }$
C) $\frac { 4 } { 7 }$
D) $\frac { 15 } { 7 }$

Question 50

Write the fraction in lowest terms.
$\frac { 14 } { 47 }$

A) $\frac { 14 } { 47 }$
B) $\frac { 1 } { 47 }$
C) $\frac { 23 } { 7 }$
D) $\frac { 7 } { 23 }$

Question 51

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 4 } { 5 } \cdot 415$

A) $\frac { 172229 } { 5 }$
B) 328
C) $\frac { 1660 } { 5 }$
D) 332

Question 52

Write the fraction in lowest terms.
$\frac { 22 } { 26 }$

A) $\frac { 22 } { 26 }$
B) $\frac { 11 } { 13 }$
C) $\frac { 11 } { 2 }$
D) $\frac { 2 } { 13 }$

Question 53

Write the fraction in lowest terms.
$\frac { 30 } { 50 }$

A) $\frac { 30 } { 50 }$
B) $\frac { 3 } { 10 }$
C) $\frac { 10 } { 5 }$
D) $\frac { 3 } { 5 }$

Question 54

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$400 \cdot \frac { 2 } { 5 }$$

A) $\frac { 800 } { 5 }$
B) 140
C) 160
D) $\frac { 160002 } { 5 }$

Question 55

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 5 } { 9 } \cdot \frac { 7 } { 8 }$

A) $\frac { 12 } { 17 }$
B) $\frac { 63 } { 40 }$
C) $\frac { 72 } { 35 }$
D) $\frac { 35 } { 72 }$

Question 56

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$28 \cdot \frac { 4 } { 7 }$

A) 16
B) $\frac { 197 } { 35 }$
C) $\frac { 112 } { 7 }$
D) 20

Question 57

Write the fraction in lowest terms.
$\frac { 195 } { 208 }$

A) $\frac { 15 } { 16 }$
B) $\frac { 15 } { 13 }$
C) $\frac { 13 } { 16 }$
D) $\frac { 195 } { 208 }$

Question 58

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\frac { 7 } { 8 } \div \frac { 1 } { 2 }$$

A) $\frac { 7 } { 16 }$
B) $\frac { 9 } { 8 }$
C) $\frac { 4 } { 5 }$
D) $\frac { 7 } { 4 }$

Question 59

Write the fraction in lowest terms.
$\frac { 24 } { 42 }$

A) $\frac { 24 } { 42 }$
B) $\frac { 4 } { 6 }$
C) $\frac { 4 } { 7 }$
D) $\frac { 6 } { 7 }$

Question 60

Write the sentence as an equation. Let the variable x represent the number.
957

A) 3 ·3 ·29
B) 11 ·11 ·29
C) 3 ·11 ·29
D) prime

Question 61

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 5 } { 7 } - \frac { 1 } { 2 }$

A) $\frac { 1 } { 7 }$
B) $\frac { 3 } { 14 }$
C) $\frac { 4 } { 9 }$
D) $\frac { 4 } { 7 }$

Question 62

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 1 } { 6 } - \frac { 1 } { 13 }$

A) $\frac { 7 } { 78 }$
B) $\frac { 1 } { 78 }$
C) $\frac { 7 } { 6 }$
D) $\frac { 1 } { 6 }$

Question 63

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\frac { 5 } { 26 } + \frac { 4 } { 26 }$$

A) $\frac { 10 } { 27 }$
B) $\frac { 4 } { 13 }$
C) $\frac { 9 } { 26 }$
D) $\frac { 8 } { 25 }$

Question 64

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 5 } { 8 } + \frac { 1 } { 8 }$

A) $\frac { 2 } { 3 }$
B) $\frac { 2 } { 4 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 4 } { 5 }$

Question 65

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\frac { 1 } { 17 } \div \frac { 7 } { 10 }$$

A) $\frac { 10 } { 117 }$
B) $\frac { 10 } { 119 }$
C) $\frac { 9 } { 119 }$
D) $\frac { 8 } { 119 }$

Question 66

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\frac { 2 } { 13 } \div \frac { 3 } { 13 }$$

A) $\frac { 2 } { 3 }$
B) $\frac { 6 } { 169 }$
C) $\frac { 5 } { 26 }$
D) $\frac { 169 } { 6 }$

Question 67

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\frac { 5 } { 11 } + \frac { 5 } { 11 }$$

A) $\frac { 9 } { 11 }$
B) $\frac { 11 } { 12 }$
C) $\frac { 10 } { 11 }$
D) $\frac { 9 } { 10 }$

Question 68

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 8 } { 19 } \div \frac { 8 } { 11 }$

A) $\frac { 10 } { 19 }$
B) $\frac { 11 } { 17 }$
C) $\frac { 11 } { 19 }$
D) $\frac { 9 } { 19 }$

Question 69

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\frac { 7 } { 21 } - \frac { 3 } { 21 }$$

A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 4 } { 21 }$
D) $\frac { 4 } { 7 }$

Question 70

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\frac { 1 } { 6 } + \frac { 7 } { 10 }$$

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

Question 71

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\frac { 7 } { 8 } - \frac { 3 } { 8 }$$

A) $\frac { 5 } { 8 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 2 }$

Question 72

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\frac { 7 } { 19 } \div \frac { 9 } { 14 }$$

A) $\frac { 98 } { 169 }$
B) $\frac { 97 } { 171 }$
C) $\frac { 32 } { 57 }$
D) $\frac { 98 } { 171 }$

Question 73

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$\frac { 12 } { 70 } + \frac { 11 } { 70 }$$

A) $\frac { 24 } { 71 }$
B) $\frac { 23 } { 70 }$
C) $\frac { 22 } { 70 }$
D) $\frac { 22 } { 69 }$

Question 74

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 8 } { 25 } - \frac { 5 } { 25 }$

A) $\frac { 2 } { 3 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 3 } { 25 }$
D) $\frac { 13 } { 25 }$

Question 75

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 2 } { 19 } \div \frac { 5 } { 16 }$

A) $\frac { 32 } { 93 }$
B) $\frac { 6 } { 19 }$
C) $\frac { 31 } { 95 }$
D) $\frac { 32 } { 95 }$

Question 76

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 25 } { 42 } - \frac { 7 } { 42 }$

A) $\frac { 16 } { 21 }$
B) $\frac { 2 } { 7 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 3 } { 7 }$

Question 77

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 7 } { 8 } - \frac { 1 } { 4 }$

A) $\frac { 3 } { 4 }$
B) $\frac { 5 } { 8 }$
C) $\frac { 3 } { 16 }$
D) $\frac { 5 } { 2 }$

Question 78

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$$2 \frac { 8 } { 9 } \div 1 \frac { 2 } { 7 }$$

A) $2 \frac { 21 } { 81 }$
B) $3 \frac { 20 } { 81 }$
C) $2 \frac { 20 } { 80 }$
D) $2 \frac { 20 } { 81 }$

Question 79

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 5 } { 8 } + \frac { 1 } { 8 }$

A) $\frac { 2 } { 3 }$
B) $\frac { 2 } { 4 }$
C) $\frac { 4 } { 5 }$
D) $\frac { 3 } { 4 }$

Question 80

Perform the indicated operation. Where possible, reduce the answer to its lowest terms.
$\frac { 7 } { 8 } - \frac { 2 } { 8 }$

A) $\frac { 5 } { 8 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 3 } { 16 }$
D) $\frac { 5 } { 4 }$