Section 1
Real Numbers
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$-3$$
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$-420$$
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$\frac{3}{8}$$
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$-\frac{4}{125}$$
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$\sqrt{11}$$
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$-\sqrt{5}$$
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$-\sqrt{5}$$v
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$\frac{\pi}{2}$$
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$\frac{2}{\pi}$$
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$2 . \overline{421}$$
Classify the number as to type. (For example, $\frac{1}{2}$ is rational and real, whereas $\sqrt{5}$ is irrational and real.)$$\text { 2.71828... }$$
Indicate whether the statement is true or false.Every integer is a whole number.
Indicate whether the statement is true or false.Every integer is a rational number.
Indicate whether the statement is true or false.Every natural number is an integer.
Indicate whether the statement is true or false.Every rational number is a real number.
Indicate whether the statement is true or false.Every natural number is an irrational number
Indicate whether the statement is true or false.$$\text { Every irrational number is a real number. }$$
State the real number property that iustifies the statement$$(2 x+y)+z=z+(2 x+y)$$
State the real number property that iustifies the statement$$3 x+(2 y+z)=(3 x+2 y)+z$$
State the real number property that iustifies the statement$$u(3 v+w)=(3 v+w) u$$
State the real number property that iustifies the statement$$a^{2}\left(b^{2} c\right)=\left(a^{2} b^{2}\right) c$$
State the real number property that iustifies the statement$$u(2 v+w)=2 u v+u w$$
State the real number property that iustifies the statement$$(2 u+v) w=2 u w+v w$$
State the real number property that iustifies the statement$$(2 x+3 y)+(x+4 y)=2 x+[3 y+(x+4 y)]$$
State the real number property that iustifies the statement$$(a+2 b)(a-3 b)=a(a-3 b)+2 b(a-3 b)$$
State the real number property that iustifies the statement$$a-[-(c+d)]=a+(c+d)$$
State the real number property that iustifies the statement$$-(2 x+y)[-(3 x+2 y)]=(2 x+y)(3 x+2 y)$$
State the real number property that iustifies the statement$$0(2 a+3 b)=0$$
State the real number property that iustifies the statement$$\text { If }(x-y)(x+y)=0, \text { then } x=y \text { or } x=-y \text { . }$$
State the real number property that iustifies the statement$$\text { If }(x-2)(2 x+5)=0, \text { then } x=2 \text { or } x=-\frac{5}{2}$$
State the real number property that iustifies the statement$$\text { If } x(2 x-9)=0, \text { then } x=0 \text { or } x=\frac{9}{2} \text { . }$$
State the real number property that iustifies the statement$$\frac{(x+1)(x-3)}{(2 x+1)(x-3)}=\frac{x+1}{2 x+1}$$
State the real number property that iustifies the statement$$\frac{(2 x+1)(x+3)}{(2 x-1)(x+3)}=\frac{2 x+1}{2 x-1}$$
State the real number property that iustifies the statement$$\frac{a+b}{b} \div \frac{a-b}{a b}=\frac{a(a+b)}{a-b}$$
State the real number property that iustifies the statement$$\frac{x+2 y}{3 x+y} \div \frac{x}{6 x+2 y}=\frac{x+2 y}{3 x+y} \cdot \frac{2(3 x+y)}{x}=\frac{2(x+2 y)}{x}$$
State the real number property that iustifies the statement$$\frac{a}{b+c}+\frac{c}{b}=\frac{a b+b c+c^{2}}{b(b+c)}$$
State the real number property that iustifies the statement$$\frac{x+y}{x+1}-\frac{y}{x}=\frac{x^{2}-y}{x(x+1)}$$
Indicate whether the statement is true or false.$$\text { If } a b=1 \text { , then } a=1 \text { or } b=1 \text { . }$$
Indicate whether the statement is true or false.$$\text { If } a b=0 \text { and } a \neq 0 \text { , then } b=0 \text { . }$$
Indicate whether the statement is true or false.$$a-b=b-a$$
Indicate whether the statement is true or false.$$a \div b=b \div a$$
Indicate whether the statement is true or false.$$(a-b)-c=a-(b-c)$$
Indicate whether the statement is true or false.$$a \div(b \div c)=(a \div b) \div c$$