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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