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2-2 Comparing and Ordering Rational Numbers
Evaluating
Algebraic Expressions
California
Standards
NS1.1 Read, write, and compare rational
numbers in scientific notation (positive and
negative powers of 10), compare rational
numbers in general.
Also covered: NS1.3
2-2 Comparing and Ordering Rational Numbers
Evaluating Algebraic Expressions
Vocabulary
least common denominator (LCD)
2-2 Comparing and Ordering Rational Numbers
Evaluating
Algebraic
Expressions
To compare
fractions
with unlike
denominators, you can find a common
denominator. This could be the least
common denominator (LCD), which is the
least common multiple of the denominators.
2-2 Comparing and Ordering Rational Numbers
Evaluating Algebraic Expressions
Remember!
The least common multiple
(LCM) of two numbers is the
smallest number, other than 0,
that is a multiple of both
numbers.
2-2 Comparing and Ordering Rational Numbers
Additional Example 1B: Comparing Fractions by
Finding a Common Denominator
Compare.
Write <, Algebraic
>, or =.
Evaluating
Expressions
2
4
3
5
Method 2: Find the least common denominator.
List multiples of 3 and
3; 3, 6, 9, 12, 15…
5. The LCM is 15.
5; 5, 10, 15
10
25
5
2

=
=
Write the fractions with
35
15
5
3
>
4
3
4

=
5
3
5
10 < 12 ,so
15
15
3
12
=
15
3
a common
denominator.
2 < 4
3
5
Compare the fractions.
2-2 Comparing and Ordering Rational Numbers
Check It Out! Example 1A
Compare. Write <, >, or =.
Evaluating
Algebraic Expressions
1
2
>
2
5
Method 1: Multiply to find a common denominator.
Multiply 2 and 5 to find
2  5 = 10
5
15
5
1

=
=
10
25
5
2
22
4
2
2

=
=
52
10
2
5
5 > 4 ,so 1 > 2
10
10
2
5
a common denominator.
Write the fractions
with a common
denominator.
Compare the fractions.
2-2 Comparing and Ordering Rational Numbers
Check It Out! Example 1B
Compare. Write <, >, or =.
Evaluating
Algebraic Expressions
2
3
3
4
Method 2: Find the least common denominator.
>
3; 3, 6, 9, 12, …
4; 4, 8, 12…
8
24
4
2

=
=
12
34
4
3
3
3
3

=
4
3
4
8 < 9 ,so
12
12
3
9
=
3
12
2 < 3
3
4
List multiples of 3 and
4. The LCM is 12.
Write the fractions with
a common
denominator.
Compare the fractions.
2-2 Comparing and Ordering Rational Numbers
Additional Example 2: Comparing by Using
Decimals
Evaluating
Compare.
Write <,Algebraic
>, or =.
Expressions
2
2
_ < 5_
A. 5
9
7
_
_ = 5.285714…
_ = 5.2 and 5 2
5 2
7
9
_
5.2 < 5.285714…, so 5
2
_
9
<5
Write the
fractions as
decimals.
2 Compare the
_
7
decimals.
2-2 Comparing and Ordering Rational Numbers
Additional Example 2: Comparing by Using
Decimals
Evaluating
Expressions
Compare.
Write <, Algebraic
>, or =.
2
B. –0.44 < – _
5
2
2 = –0.4
–_
Write - _
as decimal.
5
5
2
_ Compare the
–0.44 < –0.4, so –0.44 < –
5 decimals.
1 > 0.1
C. _
9
1
1 = 0.1
_
Write _
as decimal.
9
9
Compare the
1 > 0.1
0.1 > 0.1, so _
decimals.
9
2-2 Comparing and Ordering Rational Numbers
Check It Out! Example 2
Compare.
Write <,
>, or =.
Evaluating
Algebraic
Expressions
2
3
_ < 4_
A. 4
9
5
_
3 = 4.6
2 = 4.2 and 4 _
4 _
9
5
Write the fractions
as decimals.
2
3 Compare the
_
_
4.2 < 4.6, so 4 < 4
9
5
decimals.
2-2 Comparing and Ordering Rational Numbers
Check It Out! Example 2
Compare. Write <, >, or =.
Evaluating Algebraic Expressions
4
B. –0.80 = – _
5
4 = –0.8
–_
5
4
Write – _
as decimal.
5
4 Compare the
_
–0.80 = –0.8, so –0.80 = –
5 decimals.
5
_
C.
6
> 0.8
5
Write _
as decimal.
5 = 0.83
_
6
_
6
5 > 0.8
0.83 > 0.8, so _
6
Compare the
decimals.
2-2 Comparing and Ordering Rational Numbers
Evaluating Algebraic Expressions
To order fractions and decimals, you can
either write them all in the same form and
then compare them, or place them on a
number line. Recall that numbers increase
in value as you move from left to right
along a number line.
2-2 Comparing and Ordering Rational Numbers
Additional Example 3: Social Studies Application
14
The numbers __ , –3.4, 6.0, and –2.5
Evaluating4Algebraic Expressions
represent the percent changes in
populations for four states. List these
numbers in order from least to greatest.
Place the numbers on a number line and
read them from left to right. 14
__
4
–3.4
–4

–2.5

–3 –2
–1
0
1
2
3

6.0
4
5

6
The percent changes in population from least
14, and 6.0.
to greatest are –3.4, –2.5, __
4