#### Multiplying two integers

Repeated addition or subtraction. Let $a$ and $b$ be integers. $a•0 = 0 = 0•a$. Like signs: $a•b > 0$. Unlike Signs: $a•b < 0$.

#### Multiplying rational expressions

Let $a$, $b$, $c$, and $d$ represent real numbers, variables, or algebraic expressions such that \(b \ne 0\) and \(d \ne 0\). Then the product of \(\frac{a}{b}\) and \(\frac{c}{d}\) is \(\frac{a}{b}•\frac{c}{d} = \frac{{ac}}{{bd}}\).

#### Multiplying fractions

Let $a$, $b$, $c$, and $d$ be integers with \(b \ne 0\) and \(d \ne 0\). The product of \(\frac{a}{b}\) and \(\frac{c}{d}\) is \(\frac{a}{b}•\frac{c}{d} = \frac{{a•c}}{{b•d}}\).

#### Multiplicative inverse property

The product of a nonzero real number and its reciprocal is 1.

#### Multiplicative identity property

The product of 1 and a real number equals the number itself.

#### Multiplication property of inequalities

Multiply each side by a positive quantity. If \(a < b\) and $c$ is positive, then \(ac < bc\). Multiply each side by a negative quantity and reverse the inequality symbol. If \(a < b\) and $c$ is negative, then \(ac > bc\).

#### Monomial

A polynomial in $x$ with only 1 term.

#### Mixture problems

Real-life problems that involve combinations of two or more quantities that make up a new or different quantity.

#### Markup rate

When the markup is expressed as a percent of the cost.

#### Markup

The difference between the price a store sells an item for and the price they pay for the item.