Deck 2: The Real Numbers

Question 1

Reduce the fraction to lowest terms. $\frac { - 36 y z } { - 32 x y }$

A) $- \frac { 8 x } { 9 z }$
B) $\frac { 8 z } { x }$
C) $\frac { 9 y } { 8 x }$
D) $- \frac { 9 z } { 8 y }$
E) $\frac { 9 z } { 8 x }$

Answer 1

$\frac { 9 z } { 8 x }$

Question 2

Multiply the fractions below, and express the answer in reduced form. $\frac { 4 c } { 8 z } \cdot \frac { 6 z } { 33 c }$

A) $\frac { 2 } { 11 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 22 }$
D) $\frac { 1 } { 11 }$
E) none of these

Answer 2

$\frac { 1 } { 11 }$

Question 3

Reduce the fraction below to its lowest terms. $\frac { 65 a } { 40 a }$

A) $\frac { 13 } { 8 }$
B) $\frac { 26 } { 8 }$
C) $\frac { 13 } { 16 }$
D) none of these

Answer 3

$\frac { 13 } { 8 }$

Question 4

Reduce the fraction below to its lowest terms. $\frac { 45 } { 20 }$

A) $\frac { 9 } { 4 }$
B) $\frac { 27 } { 4 }$
C) $\frac { 9 } { 8 }$
D) none of these

Question 5

Multiply as indicated, and express your answer in reduced form. $\left( - \frac { 4 } { 14 } \right) \left( - \frac { 14 } { 24 } \right)$

A) $\frac { 1 } { 24 }$
B) $- \frac { 5 } { 6 }$
C) $\frac { 1 } { 6 }$
D) $\frac { 5 } { 6 }$
E) $- \frac { 1 } { 6 }$

Question 6

If the product of two numbers is 1, the numbers are said to be inverses of each other.

Question 7

Division of rational numbers can be expressed in terms of multiplication by the reciprocal.

Question 8

Reduce the fraction below to lowest terms. $\frac { 10 c } { 16 c }$

A) $\frac { 15 } { 16 }$
B) $\frac { 15 } { 8 }$
C) $\frac { 5 } { 8 }$
D) $\frac { 5 } { 16 }$
E) none of these

Question 9

Reduce the fraction below to lowest terms. $\frac { 20 b x } { 128 b }$

A) $\frac { 5 x } { 32 }$
B) $\frac { 5 x } { 64 }$
C) $\frac { 15 x } { 64 }$
D) $\frac { 5 } { 32 }$
E) none of these

Question 10

Divide as indicated, and express your answer in reduced form. $\frac { - 5 } { x } \div \frac { 9 } { x }$

A) $- \frac { 9 } { 5 }$
B) $\frac { 9 x } { 5 x }$
C) $- 45$
D) $- \frac { 5 } { 9 }$
E) $\frac { 5 x } { 9 }$

Question 11

Multiply the numbers below, and express the answer in reduced form. $\frac { 2 } { 5 } \cdot \frac { 32 } { 13 }$

A) $\frac { 64 } { 65 }$
B) $\frac { 64 } { 5 }$
C) $\frac { 2 } { 65 }$
D) none of these

Question 12

Divide the fractions below, and express the answer in reduced form. $\frac { 4 } { 5 } \div \frac { 3 } { 2 }$

A) $\frac { 4 } { 15 }$
B) $\frac { 8 } { 15 }$
C) $\frac { 8 } { 5 }$
D) none of these

Question 13

Reduce the fraction below to its lowest terms. $\frac { 55 a x } { 40 a }$

A) $\frac { 11 x } { 8 }$
B) $\frac { 11 x } { 16 }$
C) $\frac { 11 } { 8 }$
D) none of these

Question 14

Multiply as indicated, and express your answer in reduced form. $5 x y \cdot \frac { 7 } { x }$

A) $35 y$
B) $\frac { 35 } { x y }$
C) $\frac { 35 } { y }$
D) $\frac { 7 } { 5 x ^ { 2 } y }$
E) $35 x y$

Question 15

All integers, except 0, are rational numbers.

Question 16

Reduce the fraction to lowest terms. $\frac { 20 y } { 35 y }$

A) $\frac { 7 y } { 4 }$
B) $\frac { 4 } { 7 }$
C) $\frac { 6 } { 7 }$
D) $\frac { 6 } { 7 y }$
E) $\frac { 4 y } { 7 y }$

Question 17

Variables appearing in the denominator of a rational number represent nonzero integers.

Question 18

Multiply the fractions below, and express the answer in reduced form. $\frac { 8 b } { 12 y } \cdot \frac { 15 y } { 55 b }$

A) $\frac { 2 } { 11 }$
B) $\frac { 22 } { 11 }$
C) $\frac { 2 } { 22 }$
D) none of these

Question 19

Multiply as indicated, and express your answer in reduced form. $\frac { 3 } { 4 } \cdot \frac { - 14 } { 12 }$

A) $\frac { 8 } { 9 }$
B) $\frac { 9 } { 8 }$
C) $- \frac { 8 } { 7 }$
D) $- \frac { 7 } { 8 }$
E) $- \frac { 9 } { 8 }$

Question 20

Divide as indicated, and express your answer in reduced form. $\frac { 15 } { x } \div \frac { 21 } { y }$

A) $\frac { 5 x } { 7 y }$
B) $\frac { 5 y } { 7 x }$
C) $\frac { 5 } { 7 }$
D) $\frac { 7 x } { 5 y }$
E) $\frac { 7 y } { 5 x }$

Question 21

Reduce the fraction to lowest terms.

Question 22

Reduce the fraction below to its lowest terms.

Question 23

Perform the operations as indicated, and express your answer in lowest terms. $\left( - \frac { 5 } { 6 } \right) \left( \frac { 3 } { 5 } \right) \div \left( - \frac { 3 } { 2 } \right)$

A) $- \frac { 1 } { 6 }$
B) $3$
C) $- \frac { 1 } { 3 }$
D) $\frac { 1 } { 6 }$
E) $\frac { 1 } { 3 }$

Question 24

If it takes yards of material to make one dress, how much material is needed for 12 dresses? __________ yards

Question 25

Jonas left an estate valued at $900,000. His will states that three-fourths of the estate is to be divided equally among his three children. How much should each receive?

A) $125,500
B) $156,500
C) $149,500
D) $168,000
E) $225,000

Question 26

Multiply the numbers below, and express the answer in reduced form.

Question 27

Reduce the fraction below to lowest terms.

Question 28

Reduce the fraction below to its lowest terms.

Question 29

Reduce the fraction to lowest terms.

Question 30

Multiply the fractions below, and express the answer in reduced form.

Question 31

Perform the operations as indicated, and express your answer in lowest terms.

Question 32

Divide the numbers below, and express the answer in reduced form.

Question 33

If it takes $4 \frac { 1 } { 4 }$ yards of material to make one dress, how much material is needed for 16 dresses?

A) 68 yards
B) 70 yards
C) 67 yards
D) 64 yards
E) 80 yards

Question 34

Perform the operations as indicated, and express your answer in lowest terms. $\left( \frac { 4 x } { 5 y } \right) \left( \frac { 7 y } { x } \right) \left( \frac { 15 } { 16 x } \right)$

A) $\frac { 21 x } { 4 y }$
B) $\frac { 21 } { 4 x }$
C) $\frac { 4 } { 21 x }$
D) $\frac { 21 x } { 4 }$
E) $\frac { 4 x } { 21 }$

Question 35

A certain recipe calls for $\frac { 1 } { 4 }$ cup of sugar. To make one-fourth of the recipe, how much sugar is needed?

A) $\frac { 2 } { 4 }$ cup
B) $\frac { 2 } { 32 }$ cup
C) $\frac { 1 } { 48 }$ cup
D) $\frac { 1 } { 16 }$ cup
E) $\frac { 1 } { 32 }$ cup

Question 36

Reduce the fraction below to its lowest terms.

Question 37

Perform the operations as indicated, and express your answer in lowest terms. $\left( - \frac { 8 } { 9 } \right) \div \left( \frac { 7 } { 9 } \right) \left( - \frac { 21 } { 8 } \right)$

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

Question 38

A certain recipe calls for $\frac { 1 } { 8 }$ cup of sugar. To make one-half of the recipe, how much sugar is needed?

A) $\frac { 1 } { 16 }$ cup
B) $\frac { 2 } { 8 }$ cup
C) $\frac { 1 } { 32 }$ cup
D) none of these

Question 39

If it takes $5 \frac { 1 } { 4 }$ yards of material to make drapes for one window, how much material is needed for 7 windows?

A) $21 \frac { 3 } { 4 }$ yards
B) $39 \frac { 3 } { 4 }$ yards
C) $36 \frac { 3 } { 4 }$ yards
D) $12 \frac { 1 } { 4 }$ yards
E) $35 \frac { 1 } { 4 }$ yards

Question 40

Perform the operations as indicated, and express your answer in lowest terms. $\left( - \frac { 3 } { 10 } \right) \left( \frac { 18 } { 19 } \right) \left( - \frac { 20 } { 12 } \right)$

A) $- \frac { 10 } { 19 }$
B) $\frac { 9 } { 19 }$
C) $- \frac { 9 } { 19 }$
D) $\frac { 10 } { 19 }$
E) $\frac { 19 } { 9 }$

Question 41

A certain recipe calls for cup of sugar. To make one-half of the recipe, how much sugar is needed? Please enter your answer as a number without the units.

Question 42

Perform the operations as indicated, and express your answer in lowest terms.

Question 43

Multiply as indicated, and express your answer in reduced form.

Question 44

Multiply as indicated, and express your answer in reduced form.

Question 45

Add the fractions below, and express the answer in its lowest terms. $\frac { 10 } { 90 } + \frac { 1 } { 9 }$

A) $\frac { 2 } { 1 }$
B) $\frac { 2 } { 9 }$
C) $\frac { 9 } { 10 }$
D) none of these

Question 46

The least common multiple of the denominator is the called the least common denominator (LCD).

Question 47

Add the fractions below, and express the answer in lowest terms. $\frac { 2 } { 5 z } + \frac { 3 } { 11 a }$

A) $\frac { 22 a + 3 z } { 11 z }$
B) $\frac { 22 a + 15 z } { 55 z a }$
C) $\frac { 2 a + 15 z } { 5 a }$
D) $\frac { 2 a + 3 z } { 55 z a }$
E) none of these

Question 48

Add the fractions below, and express the answer in its lowest terms. $\frac { 4 } { 44 y } + \frac { 32 } { 44 y }$

A) $\frac { 1 } { 11 y }$
B) $\frac { 9 } { 11 y }$
C) $\frac { 8 } { 22 y }$
D) none of these

Question 49

Add the fractions below, and express the answer in its lowest terms. $\frac { 1 } { 8 y } + \frac { 10 } { y }$

A) $\frac { 81 } { 8 y }$
B) $\frac { 10 } { 8 }$
C) $\frac { 80 } { 16 y }$
D) none of these

Question 50

Only rational numbers with common denominators can be multiplied or divided.

Question 51

Add the fractions below, and express the answer in its lowest terms. $\frac { 4 } { 5 y } + \frac { 2 } { 3 b }$

A) $\frac { 4 b + 10 y } { 5 b }$
B) $\frac { 12 b + 2 y } { 3 y }$
C) $\frac { 12 b + 10 y } { 15 y b }$
D) none of these

Question 52

Multiply as indicated, and express your answer in reduced form.

Question 53

Perform the operations as indicated, and express your answer in lowest terms.

Question 54

Perform the operations as indicated, and express your answer in lowest terms.

Question 55

Prime factorization can be used to determine the least common denominator of two or more rational numbers.

Question 56

Equivalent fractions are fractions that have the same denominator.

Question 57

If it takes yards of material to make drapes for one window, how much material is needed for 5 windows? Express your answer as a mixed fraction.

Question 58

Divide as indicated, and express your answer in reduced form.

Question 59

Divide as indicated, and express your answer in reduced form.

Question 60

Add the fractions below, and express the answer in its lowest terms. $\frac { 8 } { 17 } + \frac { 4 } { 17 }$

A) $\frac { 12 } { 17 }$
B) $\frac { 8 } { 17 }$
C) $\frac { 4 } { 34 }$
D) none of these

Question 61

Subtract as indicated, and express your answer in lowest terms. $- \frac { 2 } { 17 } - \frac { 9 } { 68 }$

A) $\frac { 1 } { 3 }$
B) $\frac { 3 } { 4 }$
C) $\frac { 1 } { 4 }$
D) $- \frac { 1 } { 4 }$
E) $- \frac { 3 } { 4 }$

Question 62

Simplify the numerical expression and express your answer in reduced form. $\frac { 4 } { 5 } \div \frac { 9 } { 8 } + \frac { 8 } { 12 } \cdot \frac { 3 } { 9 } - \frac { 9 } { 12 }$

A) $\frac { 60 } { 13 }$
B) $\frac { 11 } { 60 }$
C) $\frac { 60 } { 11 }$
D) $- \frac { 13 } { 60 }$
E) $\frac { 13 } { 60 }$

Question 63

Subtract the fractions below, and express the answer in its lowest terms. $\frac { 4 } { 7 } - \frac { 1 } { 7 }$

A) $\frac { 5 } { 7 }$
B) $\frac { 3 } { 7 }$
C) $\frac { 3 } { 14 }$
D) $\frac { 5 } { 14 }$
E) none of these

Question 64

Simplify the numerical expression below, expressing the answer in its reduced form. $\frac { 1 } { 7 } + \frac { 6 } { 4 } \cdot \frac { 4 } { 30 } - \frac { 1 } { 20 } \cdot \frac { 4 } { 7 }$

A) $\frac { 6 } { 7 }$
B) $\frac { 5 } { 35 }$
C) $\frac { 11 } { 35 }$
D) none of these

Question 65

Add the fractions below, and express the answer in lowest terms. $\frac { 12 } { 26 y } + \frac { 10 } { 26 y }$

A) $\frac { 5 } { 26 y }$
B) $\frac { 6 } { 13 y }$
C) $\frac { 11 } { 13 y }$
D) $\frac { 6 } { 26 y }$
E) none of these

Question 66

Subtract as indicated, and express your answer in lowest terms. $- 3 - \frac { 4 } { 5 }$

A) $\frac { 5 } { 19 }$
B) $- \frac { 19 } { 5 }$
C) $\frac { 19 } { 5 }$
D) $- \frac { 5 } { 19 }$
E) $- \frac { 1 } { 19 }$

Question 67

Subtract the fractions below, and express the answer in its lowest terms. $\frac { 8 } { 7 } - \frac { 7 } { 7 }$

A) $\frac { 1 } { 7 }$
B) $\frac { 7 } { 14 }$
C) $\frac { 8 } { 7 }$
D) none of these

Question 68

Subtract as indicated, and express your answer in lowest terms. $\frac { 5 } { 8 } - \frac { 8 } { 9 }$

A) $- \frac { 19 } { 73 }$
B) $\frac { 19 } { 72 }$
C) $\frac { 5 } { 18 }$
D) $- \frac { 20 } { 73 }$
E) $- \frac { 19 } { 72 }$

Question 69

Simplify the algebraic expression by combining similar terms. $\frac { 2 } { 5 } n - \frac { 1 } { 4 } n + \frac { 7 } { 10 } n$

A) $\frac { 20 } { 17 } n$
B) $\frac { 17 } { 20 } n$
C) $\frac { 19 } { 20 } n$
D) $- \frac { 19 } { 20 } n$
E) $\frac { 20 } { 19 } n$

Question 70

Simplify the algebraic expression by combining similar terms. $\frac { 2 } { 7 } x + \frac { 1 } { 4 } y + \frac { 1 } { 3 } x + \frac { 7 } { 8 } y$

A) $\frac { 9 } { 8 } x + \frac { 13 } { 21 } y$
B) $\frac { 13 } { 21 } x + \frac { 8 } { 9 } y$
C) $\frac { 23 } { 21 } x y$
D) $\frac { 13 } { 21 } x + \frac { 9 } { 8 } y$
E) $\frac { 21 } { 23 } ( x + y )$

Question 71

Simplify the numerical expression and express your answer in reduced form. $\frac { 4 } { 5 } \div \frac { 8 } { 7 } + \frac { 6 } { 9 } \cdot \frac { 2 } { 6 } - \frac { 5 } { 9 }$

A) $\frac { 13 } { 30 }$
B) $- \frac { 13 } { 30 }$
C) $\frac { 30 } { 11 }$
D) $\frac { 11 } { 30 }$
E) $\frac { 30 } { 13 }$

Question 72

Subtract as indicated, and express your answer in lowest terms. $\frac { 5 } { 8 } - \frac { 4 } { 5 }$

A) $\frac { 7 } { 40 }$
B) $\frac { 1 } { 5 }$
C) $- \frac { 7 } { 40 }$
D) $- \frac { 7 } { 41 }$
E) $- \frac { 8 } { 41 }$

Question 73

Subtract as indicated, and express your answer in lowest terms. $- \frac { 1 } { 15 } - \frac { 11 } { 60 }$

A) $\frac { 3 } { 4 }$
B) $\frac { 1 } { 4 }$
C) $- \frac { 3 } { 4 }$
D) $- \frac { 1 } { 4 }$
E) $\frac { 1 } { 3 }$

Question 74

Simplify the numerical expression and express your answer in reduced form. $\frac { 1 } { 5 } + \frac { 3 } { 9 } \cdot \frac { 9 } { 21 } - \frac { 1 } { 14 } \cdot \frac { 2 } { 5 }$

A) $\frac { 4 } { 5 }$
B) $\frac { 7 } { 35 }$
C) $\frac { 11 } { 35 }$
D) $\frac { 6 } { 7 }$
E) none of these

Question 75

Simplify the numerical expression and express your answer in reduced form. $\frac { 63 } { 8 } \left( \frac { 5 } { 9 } - \frac { 1 } { 18 } \right)$

A) $\frac { 567 } { 16 }$
B) $\frac { 70 } { 8 }$
C) $\frac { 63 } { 16 }$
D) $\frac { 9 } { 16 }$
E) none of these

Question 76

Add as indicated, and express your answer in lowest terms. $7 + \frac { 3 } { x }$

A) $\frac { 7 x + 3 } { x }$
B) $7 x + 3$
C) $\frac { 7 + 3 x } { x }$
D) $\frac { 10 } { x }$
E) $10 x$

Question 77

Add as indicated, and express your answer in lowest terms. $\frac { 5 } { 4 y } + \frac { 5 } { 3 y }$

A) $\frac { 35 } { 12 }$
B) $\frac { 12 y } { 35 }$
C) $\frac { 35 } { 12 y }$
D) $\frac { 35 y } { 12 }$
E) $\frac { 12 } { 35 y }$

Question 78

Subtract the fractions below, and express the answer in its lowest terms. $\frac { 10 } { z } - \frac { 2 } { b }$

A) $\frac { 10 b + 2 z } { z b }$
B) $\frac { 10 b - 2 z } { z b }$
C) $\frac { 10 b - 2 z } { b }$
D) none of these

Question 79

Subtract as indicated, and express your answer in lowest terms. $- 4 - \frac { 2 } { 5 }$

A) $\frac { 22 } { 5 }$
B) $\frac { 5 } { 22 }$
C) $- \frac { 1 } { 22 }$
D) $- \frac { 22 } { 5 }$
E) $- \frac { 5 } { 22 }$

Question 80

Simplify the numerical expression below, expressing the answer in its reduced form. $\frac { 63 } { 2 } \left( \frac { 7 } { 9 } - \frac { 1 } { 18 } \right)$

A) $\frac { 13 } { 4 }$
B) $\frac { 91 } { 4 }$
C) $\frac { 98 } { 2 }$
D) none of these