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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
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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.
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Problem of the Day How much pie do you have if you take 2 of 5 total pieces? 0.4 pie
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Learn to compare and order positive and negative rational numbers written as fractions, decimals, and integers.
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Vocabulary least common denominator (LCD)
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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.
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Remember! The least common multiple (LCM) of two numbers is the smallest number, other than 0, that is a multiple of both numbers.
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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 = 5 6 10 10 50 60 Write the fractions with a common denominator. 7 6 = 7 10 6 6 42 60 50 60 5 6 > 42 60 ,so 7 10 Compare the fractions
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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 = 4 5 3 3 12 15 10 15 2 3 < 12 15 ,so 4 5 Compare the fractions.
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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 = 2 5 2 2 4 10 5 10 1 2 > 4 10 ,so 2 5 Compare the fractions
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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 = 3 4 3 3 9 12 8 12 2 3 < 9 12 ,so 3 4 Compare the fractions.
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Additional Example 2A: Comparing by Using Decimals
Compare. Write <, >, or =. 2 9 _ 2 7 _ A < 5 = 5.2 and 5 = … 2 9 _ 2 7 Write the fractions as decimals. 5.2 < …, so 5 < 5 _ 2 9 2 7 Compare the decimals.
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Additional Example 2B & 2C: Comparing by Using Decimals
Compare. Write <, >, or =. 2 5 _ B. – – < – = –0.4 2 5 _ Write - as decimal. 2 5 _ –0.44 < –0.4, so –0.44 < – 2 5 _ Compare the decimals. 1 9 _ C > 1 9 _ = 0.1 Write as decimal. 1 9 _ 0.1 > 0.1, so > 0.1 1 9 _ Compare the decimals.
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_ _ _ _ Write the fractions as decimals. Compare the decimals.
Check It Out: Example 2A Compare. Write <, >, or =. 2 9 _ 3 5 _ A < 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.
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Check It Out: Example 2B & C
Compare. Write <, >, or =. 4 5 _ B. – – = – = –0.8 4 5 _ Write – as decimal. 4 5 _ –0.80 = –0.8, so –0.80 = – 4 5 _ Compare the decimals. 5 6 _ C > 5 6 _ = 0.83 Write as decimal. 5 6 _ 0.83 > 0.8, so > 0.8 5 6 _ Compare the decimals.
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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.
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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. __ 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 – 14 4 The percent changes in population from least to greatest are –3.4, –2.5, , and 6.0. __
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__ __ 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. __ 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 – The percent changes in population from least to greatest are –3.9, –2.2, 3.0, and . __
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< > > Lesson Quiz Compare. Write <, >, or =. 1 4 1 2 1.
2 9 > 2. – –0.29 6 7 7 8 3. – –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 m. Which jump was the longest? 8 9 9 11 second jump
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