Transcript Document

Comparing and Ordering
Comparing
and Ordering Rational Numbers
2-2
2-2 Rational Numbers
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
33
2-2 Comparing and Ordering Rational Numbers
Warm Up
Write each fraction as a decimal.
Course 3
1
1.
3
3
3.
4
0.3
2.
4
5
0.8
0.75
2
4.
3
0.6
2-2 Comparing and Ordering Rational Numbers
Problem of the Day
How much pie do you have if you take 2 of
5 total pieces?
0.4 pie
Course 3
2-2 Comparing and Ordering Rational Numbers
Learn to compare and order positive
and negative rational numbers
written as fractions, decimals, and
integers.
Course 3
2-2 Comparing and Ordering Rational Numbers
Vocabulary
least common denominator (LCD)
Course 3
2-2 Comparing and Ordering Rational Numbers
To compare or order rational numbers, first
write them in the same form. To compare
fractions, find a common denominator. This
could be the least common denominator
(LCD), which is the least common multiple
of the denominators.
Course 3
2-2 Comparing and Ordering Rational Numbers
Remember!
The least common multiple
(LCM) of two numbers is the
smallest number, other than 0,
that is a multiple of both
numbers.
Course 3
2-2 Comparing and Ordering Rational Numbers
Additional Example 1A: Comparing Fractions by
Finding a Common Denominator
Compare. Write <, >, or =.
5
7
>
6
10
Method 1: Multiply to find a common denominator.
Multiply 6 and 10 to find
6  10 = 60
5  10
50
10
5

=
=
6  10
60
10
6
42
76
6
7

=
=
10  6
60
6
10
50 > 42 ,so 5 > 7
60
60
6
10
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a common denominator.
Write the fractions
with a common
denominator.
Compare the fractions
2-2 Comparing and Ordering Rational Numbers
Additional Example 1B: Comparing Fractions by
Finding a Common Denominator
Compare. Write <, >, or =.
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
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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 =.
1
2
>
2
5
Method 1: Multiply to find a common denominator.
Multiply 2 and 5 to find
2  5 = 10
15
5
5
1

=
=
25
10
5
2
4
22
2
2

=
=
52
10
2
5
5 > 4 ,so 1 > 2
10
10
2
5
Course 3
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 =.
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

=
=
34
12
4
3
3
3
3

=
4
3
4
8 < 9 ,so
12
12
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3
9
=
12
3
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 2A: Comparing by Using
Decimals
Compare. Write <, >, or =.
A. 5
2
2
_
< 5_
9
7
_
_ = 5.285714…
_ = 5.2 and 5 2
5 2
7
9
_
5.2 < 5.285714…, so 5
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2
_
9
<5
Write the
fractions as
decimals.
2 Compare the
_
7
decimals.
2-2 Comparing and Ordering Rational Numbers
Additional Example 2B & 2C: Comparing by Using
Decimals
Compare. Write <, >, 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
_
C.
> 0.1
9
1 = 0.1
_
1
Write _
as decimal.
_> 0.1
0.1 > 0.1, so 1
9
Compare the
decimals.
9
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9
2-2 Comparing and Ordering Rational Numbers
Check It Out: Example 2A
Compare. Write <, >, or =.
A. 4
2
3
_
< 4_
9
5
_
_ = 4.6
_ = 4.2 and 4 3
4 2
5
9
4.2 < 4.6, so 4
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2
3
_
_
<4
9
5
Write the
fractions as
decimals.
Compare the
decimals.
2-2 Comparing and Ordering Rational Numbers
Check It Out: Example 2B & C
Compare. Write <, >, or =.
4
B. –0.80 = – _
5
4
4 = –0.8
–_
Write – _
as decimal.
5
5
4
_ Compare the
–0.80 = –0.8, so –0.80 = –
5 decimals.
5
_
C.
> 0.8
6
5 = 0.83
_
6
_
_ > 0.8
0.83 > 0.8, so 5
6
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5
Write _
as decimal.
6
Compare the
decimals.
2-2 Comparing and Ordering Rational Numbers
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.
Course 3
2-2 Comparing and Ordering Rational Numbers
Additional Example 3: Social Studies Application
14
The numbers __ , –3.4, 6.0, and –2.5
4
represent the percentage of change 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
Course 3
2-2 Comparing and Ordering Rational Numbers
Check It Out: Example 3
7
The numbers __ , 3.0, –2.2, and –3.9
2
represent the percentage of change 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.
7
__
–3.9
2
3.0
–2.2
–5

–4 –3

–2
–1
0
1
2
 
3
4
5
The percent changes in population from least
7 .
to greatest are –3.9, –2.2, 3.0, and __
2
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2-2 Comparing and Ordering Rational Numbers
Lesson Quiz
Compare. Write <, >, or =.
1
1. 4
2
2. – 9
6
3. –2
7
1
2
<
–0.29
>
7
–2
8
>
4. Sarah competed in a long-jump contest. Her
8
first jump was 3.75 m, her second jump was 3 m,
9
9
and her third jump was 3 11 m. Which jump was
the longest? second jump
Course 3