Number Sets Rational (Q) – all numbers that can be expressed in the form where a and b are integers and. Irrational(I) – all non-terminating, non- repeating decimals Real(R) – all rational and irrational numbers
Venn Diagram The Real Numbers Natural Whole Integers RationalIrrational
Properties of Real Numbers Commutative: Real numbers can be added or multiplied in any order. ex. 6 + 7+ 5y = 5y + 6 + 7 Associative: Real numbers can be grouped in any order under the operations of addition or multiplication. ex. 2 + (½ + 9) = (2 + ½) + 9
The Distributive Property of Multiplication Over Addition: Multiplying a real number over a group of added real numbers gives the same result as it would if adding the real numbers first and then multiplying the result by the real number. (You can also distribute over subtraction.) ex. - 2(x + 7y) = -2x – 14y
Multiplicative Property of Zero: If the product of two or more quantities equals zero, then at least one of the quantities must equal zero. ex. If (x +7)(y – 8) = 0 then either (x +7)= 0 or (y – 8) = 0 Could both equal zero?