Math College Notes: Real Numbers, Fractions, and PEMDAS

Vocabulary flashcards covering key concepts from the lecture notes: real numbers, number types, fractions, LCD, and order of operations (PEMDAS).

Real numbers

The set of rational and irrational numbers; all numbers on the number line (including integers, fractions, and roots).

Rational numbers

Numbers that can be expressed as a ratio a/b of integers with b ≠ 0.

Irrational numbers

Numbers that cannot be written as a ratio of integers; decimal form is non-terminating and non-repeating (e.g., sqrt(2)).

Integers

All positive and negative whole numbers, including zero: …, -2, -1, 0, 1, 2, …

Whole numbers

Non-negative integers: 0, 1, 2, 3, …

Natural numbers

Positive integers: 1, 2, 3, … (some definitions include 0).

Fraction

A number expressed as a numerator over a nonzero denominator; the numerator is the top part and the denominator is the bottom part.

Numerator

The top part of a fraction; the number above the line.

Denominator

The bottom part of a fraction; the number below the line; cannot be zero.

Mixed number

A number consisting of a whole part and a proper fraction, e.g., 2 3/4.

Least Common Denominator (LCD)

The smallest common denominator used to add or subtract fractions (the least common multiple of the denominators).

Least Common Multiple (LCM)

The smallest common multiple of two or more integers.

PEMDAS

Order of operations: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Parentheses

Symbols used to group terms and indicate the order of operations.

Exponents

Powers; indicate repeated multiplication (e.g., a^n).

Commutative property

Order of addition or multiplication can be changed without changing the result: a + b = b + a; a × b = b × a.

Associative property

Grouping of numbers can be changed without changing the result: (a + b) + c = a + (b + c); (a × b) × c = a × (b × c).

Imaginary numbers

Numbers that involve the imaginary unit i, where i^2 = -1 (e.g., 3i).

Imaginary unit i

The symbol i with property i^2 = -1, the square root of -1.

Complex numbers

Numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit.

Square root of 2

An irrational number; the square root of 2 cannot be expressed as a ratio of integers.

Fraction vs. mixed number

A fraction is a numerator over a denominator; a mixed number combines a whole number and a proper fraction.