Comparing and Ordering Rational Numbers 2 2 Rational

Comparing and Ordering Rational Numbers 2 -2 Rational Numbers Warm Up Problem of the Day Lesson Presentation 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 1 A: 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 50 5 10 10 5 = = 60 6 10 10 6 42 7 6 6 7 = = 60 10 6 6 10 50 > 42 , so 5 > 7 60 60 6 10 Course 3 a common denominator. Write the fractions with a common denominator. Compare the fractions

2 -2 Comparing and Ordering Rational Numbers Additional Example 1 B: 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 15 3 5 5 3 > 4 3 4 = 5 3 5 10 < 12 , so 15 15 Course 3 12 3 = 15 3 a common denominator. 2 < 4 3 5 Compare the fractions.

2 -2 Comparing and Ordering Rational Numbers Check It Out: Example 1 A Compare. Write <, >, or =. 1 2 > 2 5 Method 1: Multiply to find a common denominator. Multiply 2 and 5 to find 2 5 = 10 5 1 5 5 1 = = 10 2 5 5 2 4 2 2 = = 10 5 2 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 1 B 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 = = 12 3 4 4 3 3 = 4 3 4 8 < 9 , so 12 12 Course 3 9 3 = 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 2 A: Comparing by Using Decimals Compare. Write <, >, or =. A. 5 2 2 _ < 5_ 9 7 _ 2 = 5. 2 and 5 2 _ = 5. 285714… 5 _ 7 9 _ 5. 2 < 5. 285714…, so 5 Course 3 2 _ 9 <5 Write the fractions as decimals. 2 Compare the _ 7 decimals.

2 -2 Comparing and Ordering Rational Numbers Additional Example 2 B & 2 C: Comparing by Using Decimals Compare. Write <, >, or =. 2 B. – 0. 44 < – _ 5 2 = – 0. 4 –_ Write - _ as decimal. 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. 1 > 0. 1, so _ 9 Compare the decimals. 9 Course 3 9

2 -2 Comparing and Ordering Rational Numbers Check It Out: Example 2 A Compare. Write <, >, or =. A. 4 2 3 _ < 4_ 9 5 _ 2 = 4. 2 and 4 3 _ = 4. 6 4 _ 5 9 4. 2 < 4. 6, so 4 Course 3 2 3 _ _ <4 9 5 Write the fractions as decimals. Compare the decimals.

2 -2 Comparing and Ordering Rational Numbers Check It Out: Example 2 B & 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. 83 > 0. 8, so 5 6 Course 3 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 – 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 3. 2 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 Course 3

2 -2 Comparing and Ordering Rational Numbers Lesson Quiz Compare. Write <, >, or =. 1 1. 4 1 2 < 2 2. – 9 – 0. 29 > 7 – 2 8 > 6 3. – 2 7 4. Sarah competed in a long-jump contest. Her 8 first jump was 3. 75 m, her second jump was 3 9 m, 9 and her third jump was 3 11 m. Which jump was the longest? second jump Course 3