SETS OF NUMBERS

Objective - To recognize different sets of numbers and to identify a domain. Naturals - Natural counting numbers { 1, 2, 3… } Wholes - Natural counting numbers and zero { 0, 1, 2, 3… } Integers - Positive or negative natural numbers or zero { … -3, -2, -1, 0, 1, 2, 3… } Rationals - Any number which CAN be written as a fraction. Irrationals - Any decimal number which can’t be written as a fraction. A non-terminating and non-repeating decimal. Reals - Rationals & Irrationals

Real Numbers Rationals Irrationals 7 2.09 Examples: Any number which can be written as a fraction Non-terminating and non- repeating decimals which can’t be written as fractions. Examples: 7 2.09

Numbers which can be expressed in the form , where a and b are integers and b is not equal to 0, are call RATIONAL NUMBERS. Rational numbers may appear in different forms, but all of them can be written as a fraction in the form a over b. Rational Number Form

Real Numbers Rationals Irrationals 7 2.09 Examples: Examples: Any number which can be written as a fraction Non-terminating and non- repeating decimals which can’t be written as fractions. Examples: Examples: 7 2.09

…-3, -2, -1, 0, 1, 2, 3... …-3, -2, -1 Sets of Numbers Reals Rationals Irrationals - any number which can be written as a fraction. - non-terminating and non-repeating decimals , 7, -0.4 Fractions/Decimals Integers , -0.32, - 2.1 …-3, -2, -1, 0, 1, 2, 3... Negative Integers Wholes …-3, -2, -1 0, 1, 2, 3... Zero Naturals 1, 2, 3...

Reals Make a Venn Diagram that displays the following sets of numbers: Reals, Rationals, Irrationals, Integers, Wholes, and Naturals. Reals Rationals -2.65 Integers -3 -19 Wholes Irrationals Naturals 1, 2, 3...

Reals Rationals -2.65 -3 -19 Irrationals 1, 2, 3...

Reals Rationals -2.65 Integers -3 -19 Wholes Irrationals 1, 2, 3... Irrationals 1, 2, 3... 1, 2, 3...

Reals Rationals -2.65 Integers -3 -19 Wholes Irrationals Naturals Irrationals Naturals 1, 2, 3...

1) -6 Integer, Rational, Real 2) Rational, Real 3) 14 Identify all of the sets to which each number belongs. (Reals, Rationals, Irrationals, Integers, Wholes, Naturals) 1) -6 Integer, Rational, Real 2) Rational, Real 3) 14 Natural, Whole, Integer, Rational, Real 4) 6 Irrational, Real

Whole, Integer, Rational, Real Identify all of the sets to which each number belongs. (Reals, Rationals, Irrationals, Integers, Wholes, Naturals) 1) 0 Whole, Integer, Rational, Real 2) - 2.03 Rational, Real 3) Irrational, Real 4) Integer, Rational, Real

Graphing on Number Lines -5 5 10 -10 Name the set of numbers that is graphed. {-8, -4, 1, 5, 8} {-8, -4, 1, 5, 8}

Graphing Real Numbers on a Number Line Graph the following numbers on a number line. -4 -3 -2 -1 0 1 2 3 4

Cross-Products < < Set up the problem as follows: 16 15 Multiply the denominator on the right by the numerator on the left. Multiply the denominator on the left by the numerator on the right. 15 < 16 therefore, 3/8 is less than 2/5.