Math 302 Pre-Algebra Chapter 1 Flashcards

Number Systems

• Whole numbers include 0 and all positive integers (0, 1, 2, 3...).
• Natural numbers consist of positive integers starting from 1 (1, 2, 3...).

Number Representation

• Place value indicates the position of each digit in a number (e.g., ones, tens, hundreds).
• Standard form is the representation of whole numbers using digits (e.g., 1,245,659).
• Expanded form expresses each digit according to its place value (e.g., 5,762 = 5 thousands + 7 hundreds + 6 tens + 2 ones).

Addition and Subtraction

• An addend is any number involved in an addition operation.
• The Addition Property of Zero states that any number added to zero equals the number itself.
• The Commutative Property of Addition allows the addition of numbers in any order without affecting the sum.
• The Associative Property of Addition permits changing the grouping of numbers being added.
• Minuend refers to the first number in a subtraction problem, while Subtrahend is the number being subtracted.
• The Difference is the result of a subtraction operation, and the Subtraction Properties of Zero assert that any number minus itself equals zero.

Geometry

• A polygon is defined as a flat figure formed by straight line segments that connect at their ends.
• Perimeter is the total distance around a polygon, calculated by summing the lengths of its sides.

Mathematical Operations

• Rounding involves approximating a whole number.
• Exact refers to the total of a set of products.
• Repeated addition is a method of addition where the same number is added multiple times (e.g., 6 + 6 + 6 + 6).

Multiplication

• Factors are the numbers being multiplied together in a multiplication problem.
• Product is the result obtained from multiplying factors.
• The Multiplication Property of Zero states that multiplying any number by zero yields zero.
• The Multiplication Property of One asserts that any number multiplied by one remains unchanged.
• The Commutative Property of Multiplication allows for changing the order of factors without affecting the product.
• The Associative Property of Multiplication states that regrouping factors does not alter the product.
• The Distributive Property shows that multiplication is applied over addition.

Division

• Division is the process of splitting a quantity into equal parts.
• The Dividend is the number being divided, while the Divisor is the number used for division.
• The Quotient is the result of a division operation.
• Division Properties of One state that any number divided by itself equals one.
• Division Properties of Zero declare that zero divided by any number (except zero) equals zero.
• The result of any number divided by zero is classified as undefined.
• Long division is a method used when dividends are larger than divisors.

Statistics

• Average is calculated as the sum of a list of numbers divided by the total count of those numbers.

Exponents and Algebra

• An exponent indicates how many times a number (base) is multiplied by itself.
• Order of Operations is crucial in evaluating expressions, represented by P.E.M.D.A.S. (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction).
• Base refers to the number that is raised to a power in exponential notation.
• A variable represents a number in an algebraic expression, fitting a given pattern.
• An expression is a combination of numbers and operations, while an equation equates two expressions.
• Evaluating an expression involves substituting the variable with a number and solving for its value.
• The solution is the value of the variable that satisfies the equation's truth.

Set Theory

• A set is a collection of distinct numbers or objects, denoted by braces {}.