#### 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

Multiplication distributes over addition.

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

#### 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.