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Section 1
Real Numbers
The numbers in the set $\left\{x \mid x=\frac{a}{b},\right.$ where $a, b$ are integers and $b \neq 0\}$ are called ________ numbers.
The value of the expression $4+5 \cdot 6-3$ is________.
The fact that $2 x+3 x=(2+3) x$ is a consequence of the ______________ Property.
Multiple ChoiceWhich of the following represents"the product of 5 and $x+3$ equals $6 " ?$(a) $5+(x+3)$(b) $5 \cdot x+3=6$(c) $5(x+3)=6$(d) None of these
Multiple ChoiceThe intersection of sets $A$ and $B$ is denoted by which of the following?(a) $A \cap B$(b) $A \cup B$(c) $A \subseteq B$(d) $A \varnothing B$
Multiple ChoiceChoose the correct name for the set of numbers $\{0,1,2,3, \ldots\}$(a) Counting numbers(b) Whole numbers(c) Integers(d) Irrational numbers
True or False Rational numbers have decimals that either terminate or are nonterminating with a repeating block of digits.
True or FalseThe Zero-Product Property states that the product of any number and zero equals zero.
True or FalseThe least common multiple of 12 and 18 is $6 .$
True or FalseNo real number is both rational and irrational.
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$A \cup B$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$A \cup C$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$A \cap B$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$A \cap C$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$(A \cup B) \cap C$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$$(A \cap B) \cup C$$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$$\bar{A}$$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$$\bar{C}$$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$$\overline{A \cap B}$$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$$\overline{B \cup C}$$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$$\bar{A} \cup \bar{B}$$
Use $U=$ universal set $=\{0,1,2,3,4,5,6,7,8,9\}, A=\{1,3,4,5,9\}, B=\{2,4,6,7,8\},$ and $C=\{1,3,4,6\}$ to find each set.$$\bar{B} \cap \bar{C}$$
List the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers.$$A=\left\{-6, \frac{1}{2},-1.333 \ldots(\text { the } 3 \text { 's repeat }), \pi, 2,5\right\}$$
List the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers.$$B=\left\{-\frac{5}{3}, 2.060606 \ldots \text { (the block 06 repeats) }, 1.25,0,1, \sqrt{5}\right\}$$
List the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers.$$C=\left\{0,1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right\}$$
List the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers.$$D=\{-1,-1.1,-1.2,-1.3\}$$
List the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers.$$E=\left\{\sqrt{2}, \pi, \sqrt{2}+1, \pi+\frac{1}{2}\right\}$$
List the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers.$$F=\left\{-\sqrt{2}, \pi+\sqrt{2}, \frac{1}{2}+10.3\right\}$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$18.9526$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$25.86134$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$28.65319$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$99.05249$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$0.06291$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$0.05388$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$9.9985$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$1.0006$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$\frac{3}{7}$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$\frac{5}{9}$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$\frac{521}{15}$$
Approximate each number (a) rounded and (b) truncated to three decimal places.$$\frac{81}{5}$$
Write each statement using symbols.The sum of 3 and 2 equals 5 .
Write each statement using symbols.The product of 5 and 2 equals $10 .$
Write each statement using symbols.The sum of $x$ and 2 is the product of 3 and 4 .
Write each statement using symbols.The sum of 3 and $y$ is the sum of 2 and 2 .
Write each statement using symbols.The product of 3 and $y$ is the sum of 1 and 2 .
Write each statement using symbols.The product of 2 and $x$ is the product of 4 and $6 .$
Write each statement using symbols.The difference $x$ less 2 equals $6 .$
Write each statement using symbols.The difference 2 less $y$ equals $6 .$
Write each statement using symbols.The quotient $x$ divided by 2 is $6 .$
Write each statement using symbols.The quotient 2 divided by $x$ is 6 .
Evaluate each expression.$$9-4+2$$
Evaluate each expression.$$6-4+3$$
Evaluate each expression.$$-6+4 \cdot 3$$
Evaluate each expression.$$8-4 \cdot 2$$
Evaluate each expression.$$18-5 \cdot 2$$
Evaluate each expression.$$100-10 \cdot 2$$
Evaluate each expression.$$4+\frac{1}{3}$$
Evaluate each expression.$$2-\frac{1}{2}$$
Evaluate each expression.$$6-[3 \cdot 5+2 \cdot(3-2)]$$
Evaluate each expression.$$2 \cdot[8-3(4+2)]-3$$
Evaluate each expression.$$4 \cdot(9+5)-6 \cdot 7+3$$
Evaluate each expression.$$1-(4 \cdot 3-2+2)$$
Evaluate each expression.$$10-[6-2 \cdot 2+(8-3)] \cdot 2$$
Evaluate each expression.$$2-5 \cdot 4-[6 \cdot(3-4)]$$
Evaluate each expression.$$(5-3) \frac{1}{2}$$
Evaluate each expression.$$(5+4) \frac{1}{3}$$
Evaluate each expression.$$\frac{4+8}{5-3}$$
Evaluate each expression.$$\frac{2-4}{5-3}$$
Evaluate each expression.$$\frac{3}{5} \cdot \frac{10}{21}$$
Evaluate each expression.$$\frac{5}{9} \cdot \frac{3}{10}$$
Evaluate each expression.$$\frac{6}{25} \cdot \frac{10}{27}$$
Evaluate each expression.$$\frac{21}{25} \cdot \frac{100}{3}$$
Evaluate each expression.$$\frac{3}{4}+\frac{2}{5}$$
Evaluate each expression.$$\frac{4}{3}+\frac{1}{2}$$
Evaluate each expression.$$\frac{7}{8}+\frac{4}{7}$$
Evaluate each expression.$$\frac{8}{9}+\frac{15}{2}$$
Evaluate each expression.$$\frac{5}{18}+\frac{1}{12}$$
Evaluate each expression.$$\frac{2}{15}+\frac{8}{9}$$
Evaluate each expression.$$\frac{5}{24}-\frac{8}{15}$$
Evaluate each expression.$$\frac{3}{14}-\frac{2}{21}$$
Evaluate each expression.$$\frac{3}{20}-\frac{2}{15}$$
Evaluate each expression.$$\frac{6}{35}-\frac{3}{14}$$
Evaluate each expression.$$\begin{array}{l}\frac{5}{18} \\\frac{11}{27}\end{array}$$
Evaluate each expression.$$\frac{\frac{5}{21}}{\frac{2}{35}}$$
Evaluate each expression.$$\frac{1}{3} \cdot \frac{4}{7}+\frac{17}{21}$$
Evaluate each expression.$$\frac{2}{3}+\frac{4}{5} \cdot \frac{1}{6}$$
Evaluate each expression.$$2 \cdot \frac{3}{4}+\frac{3}{8}$$
Evaluate each expression.$$3 \cdot \frac{5}{6}-\frac{1}{2}$$
Use the Distributive Property to remove the parentheses.$$6(x+4)$$
Use the Distributive Property to remove the parentheses.$$4(2 x-1)$$
Use the Distributive Property to remove the parentheses.$$x(x-4)$$
Use the Distributive Property to remove the parentheses.$$4 x(x+3)$$
Use the Distributive Property to remove the parentheses.$$2\left(\frac{3}{4} x-\frac{1}{2}\right)$$
Use the Distributive Property to remove the parentheses.$$3\left(\frac{2}{3} x+\frac{1}{6}\right)$$
Use the Distributive Property to remove the parentheses.$$(x+2)(x+4)$$
Use the Distributive Property to remove the parentheses.$$(x+5)(x+1)$$
Use the Distributive Property to remove the parentheses.$$(x+9)(2 x-7)$$
Use the Distributive Property to remove the parentheses.$$(3 x-1)(x+5)$$
Use the Distributive Property to remove the parentheses.$$(x-8)(x-2)$$
Use the Distributive Property to remove the parentheses.$$(x-4)(x-2)$$
Find $k$ if $3 x(x-5 k)=3 x^{2}-60 x$.
Find $k$ if $(x-k)(x+3 k)=x^{2}+4 x-12$.
Explain to a friend how the Distributive Property is used to justify the fact that $2 x+3 x=5 x$.
Explain to a friend why $2+3 \cdot 4=14$ whereas $(2+3) \cdot 4=20$
Explain why $2(3 \cdot 4)$ is not equal to $(2 \cdot 3) \cdot(2 \cdot 4)$.
Explain why $\frac{4+3}{2+5}$ is not equal to $\frac{4}{2}+\frac{3}{5}$.
Is subtraction commutative? Support your conclusion with an example.
Is subtraction associative? Support your conclusion with an example.
Is division commutative? Support your conclusion with an example.
Is division associative? Support your conclusion with an example.
If $2=x,$ why does $x=2 ?$
If $x=5,$ why does $x^{2}+x=30 ?$
Are there any real numbers that are both rational and irrational? Are there any real numbers that are neither? Explain your reasoning.
Explain why the sum of a rational number and an irrational number must be irrational.
A rational number is defined as the quotient of two integers. When written as a decimal, the decimal will either repeat or terminate. By looking at the denominator of the rational number, there is a way to tell in advance whether its decimal representation will repeat or terminate. Make a list of rational numbers and their decimals. See if you can discover the pattern. Confirm your conclusion by consulting books on number theory at the library. Write a brief essay on your findings.
The current time is 12 noon CST. What time (CST) will it be 12,997 hours from now?
Both $\frac{a}{0}(a \neq 0)$ and $\frac{0}{0}$ are undefined, but for different reasons. Write a paragraph or two explaining the different reasons.