1. 2.1 Integers & Rational Numbers
ALGEBRA 1
2.1 Integers & Rational Numbers

2. Vocabulary Whole numbers: Counting numbers starting with 0
Integers: positive and negative counting numbers and 0
Rational numbers: a number that can be written as a/b where a and b are both integers

3. Vocabulary
Opposites: two numbers that are the same distance from 0 on a number line but on opposite sides
Absolute value: the distance between a number and 0 on the number line

4. EXAMPLE 1
Graph and compare integers
Graph – 3 and – 4 on a number line. Then tell which number is greater.
On the number line, – 3 is to the right of – 4. So, –3 > – 4.
ANSWER

5. 1. Graph 4 and 0 on a number line. Then tell which number is greater.
GUIDED PRACTICE
1. Graph 4 and 0 on a number line.
Then tell which number is greater.
– – – – – – 4
On the number line, 4 is to the right of 0. So, 4 > 0.
ANSWER

6. 2. Graph 2 and -5 on a number line. Then tell which number is greater.
GUIDED PRACTICE
2. Graph 2 and -5 on a number line.
Then tell which number is greater.
– – – – – – 2 –5
On the number line, 2 is to the right of –4. So, 2 > –5.
ANSWER

7. 3. Graph -6 and -1 on a number line.
GUIDED PRACTICE
3. Graph -6 and -1 on a number line.
Then tell which number is greater.
– – – – – – –1 –6
On the number line, –1 is to the right of –6. So, –1 > –6.
ANSWER

8. EXAMPLE 2
Classify numbers
Tell whether each of the following numbers is a whole
number, an integer, or a rational number: 5, 0.6, -2 and -24.
Yes No
–24
0.6 5
Rational number?
Integer?
Whole number?
Number 2 3 –2

9. 1. Tell whether each of the following numbers is a whole
GUIDED PRACTICE
1. Tell whether each of the following numbers is a whole
number, an integer, or a rational number. Then order the numbers from least list to greatest.
3, –1.2, –2,0
Number
Whole number?
Integer?
Rational number? 3
Yes
–1.2 No –2
–2, –1.2, 0, 3 (Ordered the numbers from least to greatest).

10. – 2.1, – ,0.5 ,– 2.1.(Order the numbers from least to greatest). 3 4
GUIDED PRACTICE
2. Tell whether each of the following numbers is a whole
number, an integer, or a rational number. Then order the numbers from least list to greatest.
4.5, – , – 2.1, 0.5 3 4
Yes No
0.5
–2 .1
4.5
Rational number?
Integer?
Whole number?
Number 3 4 –
– 2.1, – ,0.5 ,– 2.1.(Order the numbers from least to greatest). 3 4

11. –2.8, –1.5, – 0.31, 3.6 (Ordered the numbers from least to greatest).
GUIDED PRACTICE
3. Tell whether each of the following numbers is a whole number, an integer, or a rational number. Then order the numbers from least list to greatest.
3.6, –1.5,–0.31, – 2.8
Yes No
–2.8
–0.31
3.6
Rational number?
Integer?
Whole number?
Number
–1.5
–2.8, –1.5, – 0.31, 3.6 (Ordered the numbers from least to greatest).

12. – , 0 , , 1.75. (Order the numbers from least to greatest).
GUIDED PRACTICE
4. Tell whether each of the following numbers is a whole number, an integer, or a rational number. Then order the numbers from least list to greatest.
Number
Whole Number?
Integer?
Rational Number?
1/6 No
Yes
1.75
-2/3 2 3 1 6
– , 0 , , (Order the numbers from least to greatest).

13. EXAMPLE 3
Order rational numbers
A star’s color index is a measure of the temperature of the star. The greater the color index, the cooler the star. Order the stars in the table from hottest to coolest.
Star
Rigel
Arneb
Denebola
Shaula
Color index
–0.03
0.21
0.09
– 0.22
SOLUTION
Begin by graphing the numbers on a number line.

14. EXAMPLE 3
Order rational numbers
Read the numbers from left to right: – 0.22, – 0.03, 0.09, 0.21.
ANSWER
From hottest to coolest, the stars are Shaula, Rigel,
Denebola, and Arneb.

15. EXAMPLE 4
Find opposites of numbers
a. If a = – 2.5, then – a = 2.5.
b. If a = , then – a = – . 3 4

16. EXAMPLE 5
Find absolute values of numbers 2 3
a. If a = – , then |a | = | | = -3
b. If a = 3.2, then |a| = |3.2| = 3.2.

17. If a = -7, then –a = 7 |a| = |-7| = 7
GUIDED PRACTICE
For the given value of a, find –a and |a|.
1. a = 5.3
If a = 5.3, then –a = – 5.3
|a| = |5.3| =
2. a = -7
If a = -7, then –a = 7 |a| = |-7| = 7
3. a =
If a = -4/9, then –a = 4/9 |a| = |-4/9| = 4/9