1. SETS OF NUMBERS

2. 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

3. 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

4. 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

5. 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

6. …-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...

7. 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...

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

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

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

11. 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

12. 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)
Rational, Real 3)
Irrational, Real 4)
Integer, Rational, Real

13. 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}

14. Graphing Real Numbers on a Number Line
Graph the following numbers on a number line.

15. 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.