# 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

$$a(b + c) = ab + ac{\rm{ }}(a + b)c = ac + bc$$

#### Distance formula

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 $d = \sqrt {{{\left( {{x_2} – {x_1}} \right)}^2} + {{\left( {{y_2} – {y_1}} \right)}^2}}$.

#### Discriminant

The expression inside the radical of the Quadratic Formula, ${b^2} – 4ac$. 1. If ${b^2} – 4ac > 0$, the equation has two real solutions. 2. If ${b^2} – 4ac = 0$, the equation has one repeated real solution. 3. If ${b^2} – 4ac < 0$, the equation has no real solution.

#### Discount rate

When the discount is given as a percent of the original price.

#### Discount

The difference between the price a store pays for an item and the price they sell the item for.

#### Difference of two squares

Let $a$ and $b$ be real numbers, variables, of algebraic expressions. $${a^2} – {b^2} = \left( {a + b} \right)\left( {a – b} \right)$$

#### Difference

The result of subtracting one integer from another.

#### Dependent system

A system of equations with infinitely many solutions. Also, the slopes of the lines are equal because the lines are equal.

#### Denominator

The number below the fraction bar in a fraction.

#### Decision digit

When rounding a decimal, the decision digit is the digit in the first position you discard.

#### Dependent variable

The output of a function.

Glossary: D