2-2 Warm Up Problem of the Day Lesson Presentation Comparing and Ordering Rational Numbers Course 3 Warm Up Problem of the Day Lesson Presentation

Warm Up Write each fraction as a decimal. 0.3 1 3 45 1. 2. 0.8 0.6 3 4 23 3. 0.75 4.

Problem of the Day How much pie do you have if you take 2 of 5 total pieces? 0.4 pie

Learn to compare and order positive and negative rational numbers written as fractions, decimals, and integers.

Vocabulary least common denominator (LCD)

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.

Remember! The least common multiple (LCM) of two numbers is the smallest number, other than 0, that is a multiple of both numbers.

Multiply 6 and 10 to find a common denominator. Additional Example 1A: Comparing Fractions by Finding a Common Denominator Compare. Write <, >, or =. 5 6 7 10 > Method 1: Multiply to find a common denominator. Multiply 6 and 10 to find a common denominator. 6  10 = 60 5  10 6  10 = 5 6  10 10 50 60 Write the fractions with a common denominator. 7  6 10  6 = 7 10  6 6 42 60 50 60 5 6 > 42 60 ,so 7 10 Compare the fractions

List multiples of 3 and 5. The LCM is 15. Additional Example 1B: Comparing Fractions by Finding a Common Denominator Compare. Write <, >, or =. 2 3 4 5 > Method 2: Find the least common denominator. List multiples of 3 and 5. The LCM is 15. 3; 3, 6, 9, 12, 15… 5; 5, 10, 15 2  5 3  5 = 2 3  5 5 10 15 Write the fractions with a common denominator. 4  3 5  3 = 4 5  3 3 12 15 10 15 2 3 < 12 15 ,so 4 5 Compare the fractions.

Multiply 2 and 5 to find a common denominator. 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 a common denominator. 2  5 = 10 1  5 2  5 = 1 2  5 5 5 10 Write the fractions with a common denominator. 2  2 5  2 = 2 5  2 2 4 10 5 10 1 2 > 4 10 ,so 2 5 Compare the fractions

List multiples of 3 and 4. The LCM is 12. 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… List multiples of 3 and 4. The LCM is 12. 2  4 3  4 = 2 3  4 4 8 12 Write the fractions with a common denominator. 3  3 4  3 = 3 4  3 3 9 12 8 12 2 3 < 9 12 ,so 3 4 Compare the fractions.

Additional Example 2A: Comparing by Using Decimals Compare. Write <, >, or =. 2 9 _ 2 7 _ A. 5 5 < 5 = 5.2 and 5 = 5.285714… 2 9 _ 2 7 Write the fractions as decimals. 5.2 < 5.285714…, so 5 < 5 _ 2 9 2 7 Compare the decimals.

Additional Example 2B & 2C: Comparing by Using Decimals Compare. Write <, >, or =. 2 5 _ B. –0.44 – < – = –0.4 2 5 _ Write - as decimal. 2 5 _ –0.44 < –0.4, so –0.44 < – 2 5 _ Compare the decimals. 1 9 _ C. 0.1 > 1 9 _ = 0.1 Write as decimal. 1 9 _ 0.1 > 0.1, so > 0.1 1 9 _ Compare the decimals.

_ _ _ _ Write the fractions as decimals. Compare the decimals. Check It Out: Example 2A Compare. Write <, >, or =. 2 9 _ 3 5 _ A. 4 4 < 4 = 4.2 and 4 = 4.6 2 9 _ 3 5 Write the fractions as decimals. 4.2 < 4.6, so 4 < 4 2 9 _ 3 5 Compare the decimals.

Check It Out: Example 2B & C Compare. Write <, >, or =. 4 5 _ B. –0.80 – = – = –0.8 4 5 _ Write – as decimal. 4 5 _ –0.80 = –0.8, so –0.80 = – 4 5 _ Compare the decimals. 5 6 _ C. 0.8 > 5 6 _ = 0.83 Write as decimal. 5 6 _ 0.83 > 0.8, so > 0.8 5 6 _ Compare the decimals.

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.

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 __ Place the numbers on a number line and read them from left to right.  14 4 __  –3.4 6.0  –2.5  –4 –3 –2 –1 0 1 2 3 4 5 6 14 4 The percent changes in population from least to greatest are –3.4, –2.5, , and 6.0. __

__ __ Check It Out: Example 3 7 2 The numbers , 3.0, –2.2, and –3.9 represent the percentage of change in populations for four states. List these numbers in order from least to greatest. 7 2 __ Place the numbers on a number line and read them from left to right.  7 2 __  –3.9 3.0  –2.2  –5 –4 –3 –2 –1 0 1 2 3 4 5 The percent changes in population from least to greatest are –3.9, –2.2, 3.0, and . 7 2 __

< > > Lesson Quiz Compare. Write <, >, or =. 1 4 1 2 1. 2 9 > 2. – –0.29 6 7 7 8 3. –2 –2 > 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? 8 9 9 11 second jump