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.

To compare fractions: Method 1: Multiply to find a common denominator. Method 2: Find the least common denominator. least common denominator (LCD): 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.

Example 1: Comparing Fractions by Finding a Common Denominator A. Compare. Write <, >, or =. 5 6 7 10 > Method 1: 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.

Example 1: Comparing Fractions by Finding a Common Denominator B. Compare. Write <, >, or =. 2 3 4 5 > Method 2: 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 1 A. Compare. Write <, >, or =. 1 2 2 5 > Method 1: 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 1 B. Compare. Write <, >, or =. 2 3 3 4 > Method 2: 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.

Example 2: 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.

Example 2: 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 2 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.

_ _ _ _ _ _ _ _ Write – as decimal. Compare the decimals. Check It Out: Example 2 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: write them all in the same form and compare them place them on a number line

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 3 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