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Course Comparing and Ordering Rational Numbers Learn to compare and order positive and negative rational numbers written as fractions, decimals, and integers. TB P
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Course 3
2-2 Comparing and Ordering Rational Numbers
Warm UpWrite each fraction as a decimal.
1. 1 3 0.3 2. 4
5
3. 4.
0.8
0.753 4
23 0.6
Course 3
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.
TB P. 68-71
Course 3
2-2 Comparing and Ordering Rational Numbers
least common denominator (LCD)Vocabulary
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 =.
Multiply 6 and 10 to find a common denominator.
5 6
7 10
Write the fractions with a common denominator.
Compare the fractions.
Method 1: Multiply to find a common denominator.6 10 = 60
5 10 6 10=5
6 10 10 = 50
60 7 6 10 6=7
10 6 6 = 42
6050 60
5 6> 42
60 ,so 7 10>
>
Course 3
2-2 Comparing and Ordering Rational Numbers
Additional Example 1B: Comparing Fractions by Finding a Common Denominator
Compare. Write <, >, or =.
List multiples of 3 and 5. The LCM is 15.
2 3
4 5
Write the fractions with a common denominator.
Compare the fractions.
Method 2: Find the least common denominator.3; 3, 6, 9, 12, 15… 5; 5, 10, 15
2 5 3 5=2
3 5 5 = 10
154 3 5
3=4
5 3 3 = 12
1510 15
2 3< 12
15 ,so 4 5<
>
Course 3
2-2 Comparing and Ordering Rational Numbers
A. 5 5
Additional Example 2A: Comparing by Using Decimals
Compare. Write <, >, or =.
2 9 _ 2
7 _
Write the fractions as decimals.
5 = 5.2 and 5 = 5.285714… 2 9 _ 2
7 __
5.2 < 5.285714…, so 5 < 5 _ 2
9 _ 2
7 _ Compare the
decimals.
<
Course 3
2-2 Comparing and Ordering Rational Numbers
B. –0.44 –
Additional Example 2B & 2C: Comparing by Using Decimals
Compare. Write <, >, or =.2 5 _
– = –0.4 2 5 _
–0.44 < –0.4, so –0.44 < – 2 5 _ Compare the
decimals.
<
Write - as decimal.2 5 _
C. 0.1 1 9 _
Compare the decimals.
Write as decimal.1 9 _
>
1 9 _ = 0.1
0.1 > 0.1, so > 0.11 9
_
Course 3
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 ApplicationThe numbers , –3.4, 6.0, and –2.5 represent the percentage of change in populations for four states. List these numbers in order from least to greatest.
14 4__
–4 –3 –2 –1 0 1 2 3 4 5 6
–2.5
6.0
Place the numbers on a number line and read them from left to right.
–3.4
14 4__
14 4
The percent changes in population from least to greatest are –3.4, –2.5, , and 6.0.__
Course 3
2-2 Comparing and Ordering Rational Numbers
Lesson QuizCompare. Write <, >, or =.
1.
2. – –0.29
4. Sarah competed in a long-jump contest. Herfirst jump was 3.75 m, her second jump was 3 m,and her third jump was 3 m. Which jump was the longest?
3. –2 –2 >
>
<1 2
second jump
1 4
2 96 7
7 8
8 99
11
