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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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 \sqrt {{{\left( {{x_2} – {x_1}} \right)}^2} + {{\left( {{y_2} – {y_1}} \right)}^2}} $.
 
Glossary: D

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