Math 1.1 - Real Numbers and Algebra Flashcards

Study Notes

Number Types

Natural Numbers are positive integers starting from 1, such as 1, 2, 3, and so on.
Whole Numbers include all natural numbers plus zero, represented as 0, 1, 2, 3, etc.
Integers consist of all whole numbers and their negatives, e.g., -3, -2, -1, 0, 1, 2, 3.
Rational Numbers are numbers that can be expressed as fractions (m/n) where m and n are integers and n ≠ 0; they can also appear as terminating or repeating decimals.
Irrational Numbers cannot be expressed as fractions and are represented as non-repeating, non-terminating decimals.
Real Numbers encompass all rational and irrational numbers and are categorized as negative, zero, or positive.

Notation and Properties

Exponential Notation involves the format a^n, where 'a' is the base and 'n' represents the exponent.
The Order of Operations is essential for evaluating expressions correctly and follows PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Algebraic Properties

The Commutative Property of Addition states that numbers can be added in any order (a + b = b + a).
The Commutative Property of Multiplication indicates that the order of multiplication does not affect the product (ab = ba).
Subtraction and division are not commutative; the order does matter.
The Associative Property of Multiplication shows that changing the grouping of factors does not alter the product (a(bc) = (ab)c).
The Associative Property of Addition implies that changing the grouping of addends does not change the sum (a + (b + c) = (a + b) + c).
The Distributive Property states that a factor times a sum equals the sum of the factor multiplied by each term (a(b + c) = ab + ac).
The Identity Property of Addition claims that adding zero to any number keeps the number unchanged (a + 0 = a).
The Identity Property of Multiplication asserts that multiplying any number by one retains the original number (a * 1 = a).
The Inverse Property of Addition identifies that a number added to its opposite equals zero (a + (-a) = 0).
The Inverse Property of Multiplication states that every number has a multiplicative inverse (reciprocal), so a * (1/a) = 1.

Algebra Basics

A Constant is a value that does not change, such as the '5' in the expression x + 5.
A Variable represents a factor that can change, exemplified by 'x' in the expression x + 5.
An Algebraic Expression is a combination of constants and variables linked by algebraic operations including addition, subtraction, multiplication, and division.
An Equation is a mathematical statement that asserts two expressions are equal.
A Formula is a specific type of equation that expresses a relationship between constant and variable quantities.

Description

This quiz covers essential concepts of real numbers and algebra, including definitions of natural numbers, whole numbers, integers, and rational numbers. It's designed to help reinforce your understanding of these fundamental mathematical terms. Study these flashcards to master the basics of real numbers in algebra.