1. Course 3 2-2 Comparing and Ordering Rational Numbers Warm Up Write each fraction as a decimal. 1. 1313 0.3 2. 4545 3. 4. 0.8 0.75 3434 2323 0.6

2. 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

3. 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

4. Course 3 2-2 Comparing and Ordering Rational Numbers least common denominator (LCD) Vocabulary

5. 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.

6. 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.

7. 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. 5656 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 = 5656  10 = 50 60 7  6 10  6 = 7 10  6 = 42 60 50 60 5656 > 42 60,so 7 10 > >

8. 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. 2323 4545 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 = 2323  5 = 10 15 4  3 5  3 = 4545  3 = 12 15 10 15 2323 < 12 15,so 4545 < >

9. Course 3 2-2 Comparing and Ordering Rational Numbers A. 5 5 Additional Example 2A: Comparing by Using Decimals Compare. Write, or =. 2929 _ 2727 _ Write the fractions as decimals. 5 = 5.2 and 5 = 5.285714… 2929 _ 2727 _ _ 5.2 < 5.285714…, so 5 < 5 _ 2929 _ 2727 _ Compare the decimals. <

10. Course 3 2-2 Comparing and Ordering Rational Numbers B. –0.44 – Additional Example 2B & 2C: Comparing by Using Decimals Compare. Write, or =. 2525 _ – = –0.4 2525 _ –0.44 < –0.4, so –0.44 < – 2525 _ Compare the decimals. < Write - as decimal. 2525 _ C. 0.1 1919 _ Compare the decimals. Write as decimal. 1919 _ > 1919 _ = 0.1 0.1 > 0.1, so > 0.1 1919 _

11. 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.

12. Course 3 2-2 Comparing and Ordering Rational Numbers Additional Example 3: Social Studies Application The 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. __

13. Course 3 2-2 Comparing and Ordering Rational Numbers Lesson Quiz Compare. Write, or =. 1. 2. – –0.29 4. Sarah competed in a long-jump contest. Her first 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 > > < 1212 second jump 1414 2929 6767 7878 8989 9 11