1. Real number system
Standard: MFANSQ2 – Students will conceptualize positive and negative numbers including decimals and fractions.

2. The Real Number System
The Real Number System is divided into two categories: Rational and Irrational
Rational Numbers: numbers such as ½ and -3/1 that can be written as a ratio of two integers.
Irrational Numbers: real numbers such as √2 or , that are not rational.

3. The Real Number System
Rational Numbers: Includes integers, whole numbers, natural numbers, and numbers written as the ratio of two integers.
Integers: {… -3, -2, -1, 0, 1, 2, 3,…}
Whole Numbers: {0, 1, 2, 3, …}
Natural Numbers: {1, 2, 3, …}

4. The Real Number System Real Numbers Rational Numbers
Irrational Numbers
1/2 -2 3 2 3
2/3 3 4
-5 2
15%
-0.7
1.456

5. The Real Number System Real Numbers Rational Numbers
Irrational Numbers
1/2
Integers
2/3 -2 3 2 3 4
-5 2
-0.7 3
15%
1.456

6. The Real Number System Real Numbers Rational Numbers
Irrational Numbers
1/2
Integers
2/3 -2
Whole 3 2 3 4
-5 2 3
-0.7
15%
1.456

7. The Real Number System Real Numbers Rational Numbers
Irrational Numbers
1/2
Integers
2/3 -2
Whole 3 2
Natural 3 4 3
-5 2
-0.7
15%
1.456

8. Properties of Real Numbers

9. What does zero mean? Zero = nothing Zero is not positive or negative
Zero does not have an opposite number

10. Graphing Numbers on a Line
Graph the following on a number line and compare.
-3 and 2
-4 and -7
5 and -6

11. Finding the Absolute Value of a Number
The absolute value of a number is its distance from zero.
The notation for absolute value is |a|.
Using the number line, find the absolute value of each.
|5|
|-8|

12. Finding the Opposite of a Number
The opposite of a number is the same distance from zero (both numbers have the same absolute value).
Using the number line, find the opposite of the following:
Opposite of 2:
Opposite of -11:

13. Extension
What does -|-4|=?? Compare -|-4| and 4 using <, >, or =.

14. Real Numbers in the Real World
What number would represent the following situations?
A hawk descends at 150 miles per hour when striking its prey.
A skier wins a downhill race by skiing at 126 miles per hour.

15. Classwork/Homework