Module 1: Real Numbers

A complete set of vocabulary flashcards covering the types of real numbers, their algebraic properties, and the fundamental operations of fractions based on the MAT 160 Module 1 notes.

Irrational Numbers

Numbers that cannot be written as a ratio of integers and include non-terminating and non-repeating decimals.

Rational Numbers

Numbers that can be written as a ratio of integers $a$ and $b$ in the form $\frac{a}{b}$ where $b \neq 0$, including fractions, terminating decimals, and repeating decimals.

Integers

The set of numbers defined as $\{... , -3, -2, -1, 0, 1, 2, 3, ... \}$.

Whole Numbers

The set of numbers defined as $\{0, 1, 2, 3, ... \}$.

Natural Numbers

The set of numbers defined as $\{1, 2, 3, ... \}$.

Commutative Property of Addition

$$a + b = b + a$$

Commutative Property of Multiplication

$$a \cdot b = b \cdot a$$

Associative Property of Addition

$$(a + b) + c = a + (b + c)$$

Associative Property of Multiplication

$$(a \cdot b) \cdot c = a \cdot (b \cdot c)$$

Distributive Property

$$a(b + c) = ab + ac$$

Multiplication Property of Zero

$$a \cdot 0 = 0$$

Additive Identity Property

$$a + 0 = a$$

Multiplicative Identity Property

$$a \cdot 1 = a$$

Additive Inverse Property

$$a + (-a) = 0$$

Multiplication Inverse Property

$$a \cdot \frac{1}{a} = 1$$

Addition Property of Equality

$$a + c = b + c$$

Multiplication Property of Equality

$$a \cdot c = b \cdot c$$

Numerator

The value $a$ in a fraction of the form $\frac{a}{b}$.

Denominator

The value $b$ in a fraction of the form $\frac{a}{b}$ where $b \neq 0$.

Fundamental Principle of Fractions

The value of a fraction does not change when you multiply the numerator and denominator by the same number: $\frac{a}{b} = \frac{a}{b} \cdot 1 = \frac{a}{b} \cdot \frac{c}{c} = \frac{a \cdot c}{b \cdot c}$.

Simplest Form (Lowest Terms)

A state where the numerator and denominator of a fraction share no common factor other than $1$.

Multiplying Fractions

The process of multiplying the numerators and multiplying the denominators.

Reciprocal

The value obtained by "flipping" a fraction; the reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$ where $a, b \neq 0$.

Dividing Fractions

Equivalent to multiplying the first fraction by the reciprocal of the second fraction.

Adding and Subtracting Fractions

The process where each fraction is first written as an equivalent fraction with common denominators, followed by adding or subtracting the numerators over the common denominator.