ALGEBRA 1
2.1 Integers & Rational Numbers
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
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
EXAMPLE 1 Graph and compare integers
Graph – 3 and – 4 on a number line. Then tell which
number is greater.
ANSWER
On the number line, – 3 is to the right of – 4. So, –3 > – 4.
GUIDED PRACTICE
1. Graph 4 and 0 on a number line.
Then tell which number is greater.
0
–6
–5
–4
–3
–2
–1
0
4
1
2
3
4
5
ANSWER
On the number line, 4 is to the right of 0. So, 4 > 0.
6
GUIDED PRACTICE
2. Graph 2 and -5 on a number line.
Then tell which number is greater.
–5
–6
–5
2
–4
–3
–2
–1
0
1
2
3
4
5
ANSWER
On the number line, 2 is to the right of –4. So, 2 > –5.
6
GUIDED PRACTICE
3. Graph -6 and -1 on a number line.
Then tell which number is greater.
–1
–6
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
ANSWER
On the number line, –1 is to the right of –6. So, –1 > –6.
EXAMPLE 2 Classify numbers
Tell whether each of the following numbers is a whole
2
number, an integer, or a rational number: 5, 0.6, -2 3 and -24.
Number
Whole
number?
Integer?
Rational
number?
5
Yes
Yes
Yes
0.6
2
–2
3
–24
No
No
Yes
No
No
Yes
No
Yes
Yes
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
Yes
Yes
–1.2
No
No
Yes
–2
No
Yes
Yes
0
Yes
Yes
Yes
–2, –1.2, 0, 3 (Ordered the numbers from least to greatest).
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, –
3
, – 2.1, 0.5
4
Number Whole
number?
Integer?
Rational
number?
4.5
No
No
Yes
– 3
No
No
Yes
–2 .1
No
No
Yes
0.5
No
No
Yes
4
3
– 2.1, – 4 ,0.5 ,– 2.1.(Order 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
Number
Whole
number?
Integer?
Rational
number?
3.6
No
No
Yes
–1.5
No
No
Yes
–0.31
No
No
Yes
–2.8
No
No
Yes
–2.8, –1.5, – 0.31, 3.6 (Ordered 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.
1
2
,1.75, ,0
6
3
Number
1/6
1.75
-2/3
0
Whole Number?
No
No
No
Yes
Integer?
No
No
No
Yes
Rational Number?
Yes
Yes
Yes
Yes
2
1
– 3 , 0 , 6 , 1.75. (Order the numbers from least to greatest).
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
Color index
Rigel
–0.03
Arneb
0.21
Denebola
0.09
Shaula
– 0.22
SOLUTION
Begin by graphing the numbers on a number line.
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.
EXAMPLE 4
Find opposites of numbers
a.
If a = – 2.5, then – a = 2.5.
b.
3
If a = 4 , then – a = – 3 .
4
EXAMPLE 5 Find absolute values of numbers
a.
2
2
If a = – , then |a | = | -3 | =
3
b.
If a = 3.2, then |a| = |3.2| = 3.2.
2
3
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| =
5.3
2. a = -7
If a = -7, then –a = 7
|a| = |-7| = 7
3. a =  4
9
If a = -4/9, then –a = 4/9
|a| = |-4/9| = 4/9