1.1/1.2 Properties of Real Numbers

1.1/1.2 Properties of Real Numbers

• 1.
  Chapter1: Expressions, Equations,and Inequalities1.1 Patterns and Expressions1.2 Properties of Real Numbers
• 2.
  DefinitionsA mathematical quantityis anything that can be measured or counted.Quantities whose value stay the same are constantsQuantities whose values change or vary are called variable quantities
• 3.
  DefinitionsA variable isa 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
• 4.
  Sets of NumbersRealNumbers can be graphed on a number line and contain several subsetsNatural Numbersare the counting numbers: 1, 2, 3, 4, …Whole numbersare the natural numbers and zero 0, 1, 2, 3, 4 ….Integers are the positive and negative whole numbers and zero
• 5.
  Sets of NumbersRationalnumbersare 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
• 6.
  Sets of NumbersThisdiagram shows how subsets of the real numbers are related.
• 7.
  Example: Graph eachnumber on the number line and classify each number.
• 8.
  Properties of RealNumbersThe 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.Thereciprocal (multiplicative inverse) of any nonzero number is The Multiplicative Inverse: The product of a number and its reciprocal is 1
• 9.
  Look for clues/keyinformation: Does the equation contain 0 or 1?
• 10.
  What isdifferent about the left and right side of the equation?
• 11.
  Example: Name theproperty illustrated by each equation.