Mathematics Fundamentals: Fractions, Exponents, and Order of Operations

Vocabulary flashcards generated from the lecture transcript covering core mathematical concepts such as rational numbers, least common denominators, mixed numbers, exponent rules, and order of operations.

Rational Number

A number of the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

Least Common Denominator (LCD)

The smallest number that evenly divides into both numbers or denominators.

Improper Fraction

A fraction of the form $\frac{p}{q}$ where $p$ is greater than $q$ ($p > q$).

Mixed Number

A representation of an improper fraction obtained by performing long division and expressing the result as a whole number with a remainder over the original denominator.

Equivalent Fractions Rule

The algebraic property stating that $\frac{a \times c}{b \times c} = \frac{a}{b}$, allowing fractions to be scaled by multiplying or dividing the numerator and denominator by the same non-zero value.

Even Exponent Behavior (Negative Base)

When a negative base $a$ is raised to an even power $n$, the result $a^n$ is always positive.

Odd Exponent Behavior (Negative Base)

When a negative base $a$ is raised to an odd power $n$, the result $a^n$ is always negative.

Product Rule of Exponents

The exponent property stating that when multiplying powers with identical bases, you add their exponents: $a^m \times a^n = a^{m+n}$.

Zero Exponent Rule

The exponent property stating that any non-zero real number $a$ raised to the power of zero equals one: $a^0 = 1$.

Negative Exponent Rule

The exponent property stating that a term with a negative exponent is equal to its reciprocal with a positive exponent: $a^{-n} = \frac{1}{a^n}$.

Power of a Power Rule

The exponent property stating that raising an exponential term to another power multiplies the exponents: $(a^m)^n = a^{m \times n}$.

Power of a Product Rule

The exponent property stating that raising a product of terms to a power applies that power to each factor: $(a \times b)^m = a^m \times b^m$.

Order of Operations

The set rule for evaluating mathematical expressions: resolve parentheses first, evaluate exponents second, perform multiplication and division from left to right third, and perform addition and subtraction from left to right last.