Pre-Algebra Practice Problem Packet Vocabulary

Vocabulary and rule-based flashcards generated from the MTH0661 Pre-Algebra Practice Problem Packet transcript.

PEMDAS

An acronym for the order of operations: P = parentheses, E = exponents, Multiplication and Division at the same level solved left to right, and Addition and Subtraction at the same level solved left to right.

Equivalent Fractions Condition

Where $a$, $b$, $c$, and $d$ are real numbers, variables, or algebraic expressions and $b, d \neq 0$, $\frac{a}{b} = \frac{c}{d}$ if and only if $ad = bc$.

Rules of Signs for Fractions

The algebraic sign relationships for fractions showing that $-\frac{a}{b} = \frac{-a}{b} = \frac{a}{-b}$ and $-\frac{-a}{b} = \frac{-a}{-b} = \frac{a}{b}$.

Generating Equivalent Fractions

The rule stating that a fraction $\frac{a}{b}$ can be rewritten as $\frac{ac}{bc}$, where $c \neq 0$.

Adding or Subtracting with Like Denominators

The fraction operation rule stating that $\frac{a}{b} \pm \frac{c}{b} = \frac{a \pm c}{b}$.

Adding or Subtracting with Unlike Denominators

The fraction operation rule stating that $\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm cb}{bd}$, found by multiplying the top and bottom of each fraction by the other fraction's denominator.

Multiplying Fractions

The fraction operation rule stating that $\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}$, which requires multiplying the top times the top and the bottom times the bottom.

Dividing Fractions

The fraction operation rule stating that $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} = \frac{ad}{bc}$ (where $c \neq 0$), formed by reciprocating the fraction being divided by and changing to multiplication.

Prime Number

A number that is only divisible by itself and 1. Examples include 2, 3, 5, 7, and 13.

Greatest Common Factor (GCF)

The largest factor shared between two numbers.

Least Common Multiple (LCM)

The smallest multiple shared between two numbers.

Zero Exponent Rule

The rule stating that any non-zero number raised to the power of zero equals 1, such as $2^0 = 1$.

Negative Exponent Rule

The exponent rule demonstrating that a negative exponent indicates a reciprocal, such as $2^{-1} = \frac{1}{2}$.