1. Algebra 2-1 Rational Numbers on a Number Line
A number line can be used to show the sets of natural numbers, whole numbers and integers.
Values greater than 0, or positive numbers, are listed to the right of 0, and values less than 0, or negative numbers, are listed to the left of 0.
Harbour

2. Algebra 2-1 Rational Numbers on a Number Line
Integers
Whole Numbers
Natural Numbers
– 4 – 3 – 2 –
| | | | | | | | |
Negative numbers
Positive numbers
Zero is neither negative nor positive
Harbour

3. Algebra 2-1 Rational Numbers on a Number Line
Another set of numbers you can display on a number line is the set of rational numbers.
A rational number is any number that can be written in the form , where a and b are integers and b ≠ 0.
Some examples of rational numbers:
Harbour

4. Algebra 2-1 Rational Numbers on a Number Line
A rational number can also be expressed as a decimal that terminates or as a decimal that repeats indefinitely: = = = = = = =
Harbour

5. Algebra 2-1 Rational Numbers on a Number Line
Obtain and secure this handout in your notes!
Harbour

6. Algebra 2-1 Rational Numbers on a Number Line
To graph a set of numbers means to draw, or plot, the points named by those numbers on a number line.
The number that corresponds to a point on a number line is called the coordinate of that point.
Harbour

7. Identify Coordinates on a Number Line
Name the coordinates of the points graphed on the number line.
The dots indicate each point on the graph.
Answer: The coordinates are {–9, –7, –6, –3}.
Example 1-1a

8. Identify Coordinates on a Number Line
Name the coordinates of the points graphed on the number line.
The bold arrow on the graph indicates that the graph continues infinitely in that direction.
Answer: The coordinates are {11, 12, 13, 14, …}.
Example 1-1b

9. Identify Coordinates on a Number Line
Name the coordinates of the points graphed on each number line. a. b.
Answer: {6, 9, 11, 12}
Answer: {–0.5, 0, 0.5, 1, 1.5, …}
Example 1-1c

10. Graph Numbers on a Number Line
Answer:
Example 1-2a

11. Graph Numbers on a Number Line
Answer:
Example 1-2b

12. Graph Numbers on a Number Line
Graph {integers less than –6 or greater than or equal to 1}.
Answer:
Example 1-2c

13. Graph Numbers on a Number Line
Graph each set of numbers.
a. {–5, 2, 3, 5} b.
Answer:
Answer:
Example 1-2d

14. Graph Numbers on a Number Line
c. {integers less than or equal to –2 or greater than 4}
Answer:
Example 1-2e

15. Algebra 2-1 Rational Numbers on a Number Line
On the number line, notice that –4 and 4 are on opposite sides of zero and they are the same distance from zero.
In mathematics, we say they have the same absolute value, 4.
– 4 – 3 – 2 –
| | | | | | | | |
Harbour

16. Algebra 2-1 Rational Numbers on a Number Line
The absolute value of a number n is the distance the number is from zero on the number line and is written | n |.
The absolute value of a number is always greater than or equal to zero.
Harbour

17. Absolute Values of Rational Numbers
Find .
unit from 0 in the negative direction.
Answer:
Absolute Values of Rational Numbers
Find .
0.25 is 0.25 unit from 0 in the positive direction.
Answer:
Example 1-3a

18. Absolute Values of Rational Numbers
Find each absolute value. a. b.
Answer:
Answer: 6.3
Example 1-3c

19. You can also evaluate expressions involving absolute value
You can also evaluate expressions involving absolute value. The absolute value bars serve as grouping symbols.
Expressions with Absolute Value
Replace y with 12.
Simplify.
Answer:
Example 1-4a

20. Expressions with Absolute Value
Answer: 10
Example 1-4b