Section 2 Properties of Real Numbers Chapter 1 Section 2 Properties of Real Numbers

Classifications of Numbers Imaginary Numbers will be introduced later.

Real Numbers – all the numbers you use in everyday life The largest classification we will deal with Include any number that you can tell me Ex: Split into Rational and Irrational Numbers

Real Numbers Irrational Numbers Numbers that cannot be written as ratios Decimals that never terminate and never repeat Square roots of positive non-perfect squares Ex: √2, -√7, √(8/11), , 1.011011101111011111…

Real Numbers Rational Numbers All the numbers that can be written as a ratio (fraction) This includes terminating and repeating decimals. Ex: 8, 10013, -54, 7/5, -3/25, 0, 0/6, -1.2, .09, .3333….

Real Numbers Rational Numbers Integers “Complete” numbers (no parts – fractions or decimals) Negative, Zero, and Positive Each negative is the additive inverse (or opposite) of the positive Ex: -543, 76, 9, 0, -34

Real Numbers Rational Numbers Integers Whole Numbers Zero and positive integers Ex: 0, 1, 2, 3, 4, …

Real Numbers Rational Numbers Integers Whole Numbers Natural Numbers Also known as Counting Numbers Think of young children Ex: 1, 2, 3, 4, 5, 6, …

Example: Name the set of numbers to which each number belongs. -2/3 rational, real

Example: Name the set of numbers to which each number belongs. 9.999… rational, real

Example: Name the set of numbers to which each number belongs. √6 irrational, real

Example: Name the set of numbers to which each number belongs. √100 natural, whole, integer, rational, real

Example: Name the set of numbers to which each number belongs. -23.3 rational, real

Properties of Real Numbers Property Addition Multiplication Commutative commute = to move a + b = b + a ab = ba Associative associate = regroup (a+b)+c = a+(b+c) (ab)c = a(bc) Identity a+0=a,0+a=a a*1=a, 1*a=a Inverse a+(-a)=0 a*(1/a)=1,a≠0 Distributive a(b+c) = ab + ac

Identify the property Example 5 Which Property is illustrated? 6 + (-6) = 0 Inverse Property of Addition (-4 ∙ 1) – 2 = -4 – 2 Identity Property of Multiplication

Try these Problems p. 7 Check Understanding Which Property is illustrated? (3 + 0) – 5 = 3 – 5 Identity Property of Addition -5 + [2 + (-3)] = (-5 + 2) + (-3) Associative Property of Addition

Homework P.15 #19-35, 49-56