CHAPTER1: EXPRESSIONS,EQUATIONS, AND INEQUALITIES1.1 Patterns and Expressions1.2 Properties of Real Numbers
DEFINITIONS A mathematical quantity is anything that can be measured or counted. Quantities whose value stay the same are constants Quantities whose values change or vary are called variable quantities
DEFINITIONS A variable is a symbol, usually a letter, that represents one or more numbers. Examples: and A numerical expression is a mathematical phrase that contains numbers and operation symbols. Examples: and An algebraic expression is a mathematical phrase that contains one or more variables. Examples: and
SETS OF NUMBERS Real Numbers can be graphed on a number line and contain several subsets Natural Numbers are the counting numbers: 1, 2, 3, 4, … Whole numbers are the natural numbers and zero 0, 1, 2, 3, 4 …. Integers are the positive and negative whole numbers and zero
SETS OF NUMBERS Rational numbers are number that can be written as a ratio of two integers (this includes fractions, terminating decimals, and repeating decimals) Irrational Numbers cannot be written as a ratio of two integers and have decimal representations that do not terminate or repeat
SETS OF NUMBERSThis diagram shows how subsets of the real numbers are related.
EXAMPLE: CLASSIFY EACH NUMBER.
PROPERTIES OF REAL NUMBERS The properties of real numbers are relationships that are true for all real numbers (except in one case, zero) The opposite (additive inverse) of any number a is –a. The Additive Inverse: The sum of a number and its opposite is 0. The reciprocal (multiplicative inverse) of any nonzero number is The Multiplicative Inverse: The product of a number and its reciprocal is 1
A set is closed with respect to an operation if the operation can always be completed with elements in the set.Look for clues/key information: • Does the equation contain 0 or 1? • What is different about the left and right side of the equation?
EXAMPLE: NAME THE PROPERTY ILLUSTRATEDBY EACH EQUATION.