#### 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

#### 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

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