# ABCDEFGHIJKLMNOPQRSTUVWXYZ

#### Domain

The set of all real numbers for which a rational expression is defined. Also, the set of first components in the ordered pair set.

#### Divisor

The number by which another number is divided.

#### Division property of inequalities

Divide each side by a positive quantity. If $$a < b$$ and c is positive, then $$\frac{a}{c} < \frac{b}{c}$$. Divide each side by a negative quantity and reverse the inequality symbol. If $$a < b$$ and c is negative, then $$\frac{a}{c} > \frac{b}{c}$$.

#### Dividing one integer from another

Let $a$ and $b$ be integers. $$\frac{0}{a} >= 0$$, $$a \ne 0$$. $$\frac{a}{0}$$ is undefined. Like signs: $$\frac{a}{b} > 0$$, $$b \ne 0$$. Unlike signs: $$\frac{a}{b} < 0$$, $$b \ne 0$$.

#### Dividing rational expressions

Let $a$, $b$, $c$, and $d$ represent real numbers, variables, or algebraic expressions such that $$b \ne 0$$, $$c \ne 0$$, and $$d \ne 0$$. Then the quotient of $\frac{a}{b}$ and $\frac{c}{d}$ is $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b}•\frac{d}{c} = \frac{{ad}}{{bc}}$.

#### Dividing a polynomial by a monomial

Let $a$, $b$, and $c$ be real numbers, variables, or algebraic expressions, such that $$c \ne 0$$. $$1.{\rm{ }}\frac{{a + b}}{c} = \frac{a}{c} + \frac{b}{c}$$

$$2.{\rm{ }}\frac{{a – b}}{c} = \frac{a}{c} – \frac{b}{c}$$

#### Dividing fractions

Let $a$, $b$, $c$, and $d$ be integers with $$b \ne 0$$, $$c \ne 0$$, and $$d \ne 0$$. Then the quotient of $\frac{a}{b}$ and $\frac{c}{d}$ is $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b}•\frac{d}{c}$.

#### Dividend

The number that is being divided by another number.

#### Distributive property

$$a(b + c) = ab + ac{\rm{ }}(a + b)c = ac + bc$$
The distance $d$ between the two points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ in a coordinate plane is \sqrt {{{\left( {{x_2} – {x_1}} \right)}^2} + {{\left( {{y_2} – {y_1}} \right)}^2}} \$.