Deck 1: Real Numbers and Algebraic Expressions

Question 1

Write each set in roster form.

-{x|x is an odd whole number less than 16}

Answer 1

{1, 3, 5, 7, 9, 11, 13, 15}

Question 2

Write each set in roster form.
-{x|x is an integer greater than 20}

Answer 2

{21, 22, 23, …}

Question 3

Write each set in roster form.
-{x|x is a natural number less than 9}

Answer 3

{1, 2, 3, 4, 5, 6, 7, 8}

Question 4

List the elements of the set $\left\{6, \sqrt{5}, 0, \frac{3}{4}, \frac{3}{7}, -285\right\}$ that are also elements of the given set.
-Natural numbers

Question 5

List the elements of the set $\left\{6, \sqrt{5}, 0, \frac{3}{4}, \frac{3}{7}, -285\right\}$ that are also elements of the given set.
-Rational numbers

Question 6

List the elements of the set $\left\{6, \sqrt{5}, 0, \frac{3}{4}, \frac{3}{7}, -285\right\}$ that are also elements of the given set.
-Integers

Question 7

List the elements of the set $\left\{6, \sqrt{5}, 0, \frac{3}{4}, \frac{3}{7}, -285\right\}$ that are also elements of the given set.
-Irrational numbers

Question 8

Determine whether each statement is true or false.

-Some integers are natural numbers.

Question 9

Determine whether each statement is true or false.

--3 $\in$ {x|x is an integer}

Question 10

Determine whether each statement is true or false.

- $\frac{3}{7}\notin\{x|x is a rational number\}$

Question 11

Determine whether each statement is true or false.

-{x|x is a day of the week starting with the letter L} is $\emptyset$

Question 12

Write each phrase as an algebraic expression.
-Eight more than five times a number.

Question 13

Write each phrase as an algebraic expression.
-Three times a number, divided by ten.

Question 14

Write each phrase as an algebraic expression.
-The difference of fourteen and a number.

Question 15

Write each phrase as an algebraic expression.
-Nine less than twice a number.

Question 16

Write each phrase as an algebraic expression.
-Twelve minus seven times a number.

Question 17

Write each phrase as an algebraic expression.
-The quotient of three and the sum of a number and five.

Question 18

Write each phrase as an algebraic expression.
-Six times the difference of a number and eleven.

Question 19

Write each phrase as an algebraic expression.
-Name a negative rational number that does not simplify to an integer.

Question 20

Write each sentence as an equation.
-The sum of 8 and twice x is -14.

Question 21

Write each sentence as an equation.
-The difference of y and 5 is the same as the product of y and 8.

Question 22

Write each sentence as an equation.
-The quotient of z and 7 is 5 more than three times z.

Question 23

Insert <, >, or = between each pair of numbers to form a true statement.
- $\frac{15}{7}~~~~~~~\frac{15}{8}$

Question 24

Insert <, >, or = between each pair of numbers to form a true statement.
-3.9 $~~~~$ 3.90

Question 25

Insert <, >, or = between each pair of numbers to form a true statement.
--4.1 $~~~~$ -4.01

Question 26

Insert <, >, or = between each pair of numbers to form a true statement.
--11.6 $~~~~$ 2.8

Question 27

Write the opposite (or additive inverse) of each number.
--5.6

Question 28

Write the opposite (or additive inverse) of each number.
- $\frac{3}{11}$

Question 29

Write the opposite (or additive inverse) of each number.
-0

Question 30

Write the reciprocal (or multiplicative inverse) of each number if one exists.
- $\frac{2}{3}$

Question 31

Write the reciprocal (or multiplicative inverse) of each number if one exists.
--10

Question 32

Write the reciprocal (or multiplicative inverse) of each number if one exists.
- $\frac{0}{7}$

Question 33

Use a commutative property to write an equivalent expression.
-m + n

Question 34

Use a commutative property to write an equivalent expression.
- $\frac{x}{3} \cdot \frac{y}{4}$

Question 35

Use an associative property to write an equivalent expression.
-3x + (y + 2z)

Question 36

Use an associative property to write an equivalent expression.
- $(1.5r) \cdot t$

Question 37

Use the distributive property to multiply.
-6(x + 9)

Question 38

Use the distributive property to multiply.
-7(2a - 3b)

Question 39

Use the distributive property to multiply.
- $\frac{1}{4}(16x - 7y)$

Question 40

Find the absolute value.
-|-9|

Question 41

Find the absolute value.
-|-12|

Question 42

Add or subtract as indicated
--23 + 10

Question 43

Add or subtract as indicated
- $-\frac{1}{2}+\left(-\frac{1}{4}\right)$

Question 44

Add or subtract as indicated
-1.2 - 3.4

Question 45

Add or subtract as indicated
- $-\frac{3}{8}-\left(-\frac{1}{16}\right)$

Question 46

Add or subtract as indicated
--2 - 8 + 3

Question 47

Add or subtract as indicated
--11 + (-9) - 12

Question 48

Multiply or divide as indicated
--3(-12)

Question 49

Multiply or divide as indicated
- $\frac{-48}{6}$

Question 50

Multiply or divide as indicated
-0 ÷ (-10)

Question 51

Multiply or divide as indicated
--5(-6)(-1)

Question 52

Multiply or divide as indicated
- $-\frac{3}{7} \cdot \frac{14}{9}$

Question 53

Multiply or divide as indicated
- $-\frac{5}{8} \div (-10)$

Question 54

Evaluate.
- $(-5)^3$

Question 55

Evaluate.
- $-12^2$

Question 56

Evaluate.
- $\left(-\frac{1}{3}\right)^4$

Question 57

Find each root.
- $\sqrt{121}$

Question 58

Find each root.
- $\sqrt[3]{27}$

Question 59

Find each root.
- $\sqrt{\frac{1}{36}}$

Question 60

Simplify each expression.
- $(-8)^2 + 3^3$

Question 61

Simplify each expression.
--4[9 - (-2)]

Question 62

Simplify each expression.
- $-7 \cdot 6 + (-3)(-4)$

Question 63

Simplify each expression.
- $-9(-\frac{2}{3})-5$

Question 64

Simplify each expression.
-3 - [(17 - 16) + (4 - 12)]

Question 65

Simplify each expression.
-15 - 2(-5) +9

Question 66

Simplify each expression.
- $\frac{(1-2)(-4)^2}{-1-7}$

Question 67

Simplify each expression.
- $(\sqrt[3]{1000})(-3) - (\sqrt{81})(-2)$

Question 68

Simplify each expression.
- $19-[(8-3)^2 + (-14-10)]^5$

Question 69

Simplify each expression.
- $\left(\frac{7.27 - 8.2}{6.9 - 6.6}\right)^2$

Question 70

For 11 and 12, evaluate each expression when x = 2 and y = -5.
- $+3x + y^2$

Question 71

For 11 and 12, evaluate each expression when x = 2 and y = -5.
- $\frac{2+4|x+y|}{2x-y}$

Question 72

For 11 and 12, evaluate each expression when x = 2 and y = -5.
-The algebraic expression $\frac{10x + 8000}{x}$ represents the cost per compact disc (in dollars) of producing x compact discs (CD's).
Complete the table.

Question 73

For 11 and 12, evaluate each expression when x = 2 and y = -5.
-As the number of CD's produced increases, does the cost per CD increase or decrease?

Question 74

Simplify.
--7 +5x +15 - 9x

Question 75

Simplify.
-9a - b + 8a - 7b

Question 76

Simplify.
-(3 - 2y) - (10 - 11y)

Question 77

Simplify.
-5(4n - 3) - 2(12n - 5)

Question 78

Simplify.
- $\frac{1}{3}(9x - 6) - \frac{1}{5}(30x - y)$

Question 79

Simplify.
--1.3(4.6x - 2.4) + 3.75x

Question 80

Use the product rule to simplify each expression.
- $4a^5 \cdot a^{11}$