1. 5.5 Real numbers and their properties p. 236-243

2. 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

3. 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

4. Example: To which sets do the following numbers belong:

5. Properties of real numbers PropertyMeaningExample Closurea + b and ab are real numbers 2 + 3.1 = 5.1 5( ½ )=2 ½ Commutativea + b = b + a ab = ba 3 + 2 = 2 + 3 4(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)

6. Name the property illustrated 8(3) = 3(8) (4 +7) +2 = 4 + (7+2) 2(3 + 1.5) = 6 + 3 2 + (3 + 4) = 2 + (4 + 3)

7. Hw: p