5.5 Real numbers and their properties p

Real numbers From 5.3 and 5.4 we learned that rational numbers are numbers that can be written as a fraction and irrational numbers are numbers that have non-terminating, non- repeating decimals The real numbers are made up of rational and irrational numbers

Subsets of real numbers NameDescriptionExamples Natural numbers Numbers used for counting {1,2,3,4,5,…} Whole numbers The natural numbers with 0 {0,1,2,3,4,5,…} IntegersThe whole numbers and the negatives of the natural numbers {…-3,-2,- 1,0,1,2,3,…} Rational numbers Fractions-17, 3, 0.4, ½, 0.666… Irrational numbers Non-terminating, non- repeating decimals

Example: To which sets do the following numbers belong:

Properties of real numbers PropertyMeaningExample Closurea + b and ab are real numbers = 5.1 5( ½ )=2 ½ Commutativea + b = b + a ab = ba = (5)=5(4) Associativea+(b+c) = (a+b)+c a(bc) = (ab)c 3+(2+5) = (3+2)+5 Distributivea(b + c) = ab + ac½ (4 + 6) = ½ (4)+ ½ (6)

Name the property illustrated 8(3) = 3(8) (4 +7) +2 = 4 + (7+2) 2( ) = (3 + 4) = 2 + (4 + 3)

Hw: p