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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