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 quantity is 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 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
- 4. Sets of NumbersReal Numbers 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 NumbersRational numbersare 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 NumbersThis diagram shows how subsets of the real numbers are related.
- 7. Example: Graph each number on the number line and classify each number.
- 8. Properties of Real NumbersThe 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/key information: Does the equation contain 0 or 1?
- 10. What is different about the left and right side of the equation?
- 11. Example: Name the property illustrated by each equation.