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Comparing and Ordering Rational Numbers

5 • 11 9 • 11. Multiply the numerator and denominator by 11. =. 55 99. 54 99. 55 99. Multiply. =. 6 • 9 11 • 9. Multiply the numerator and denominator by 9. =. 54 99. =. Multiply. Since. >. >. ,. 5 9. 5 9. 5 9. 6 11. 6 11. 6 11. COURSE 3 LESSON 4-3.

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Comparing and Ordering Rational Numbers

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  1. 5 • 11 9 • 11 Multiply the numerator and denominator by 11. = 55 99 54 99 55 99 Multiply. = 6 • 9 11 • 9 Multiply the numerator and denominator by 9. = 54 99 = Multiply. Since > > , . 5 9 5 9 5 9 6 11 6 11 6 11 COURSE 3 LESSON 4-3 Comparing and Ordering Rational Numbers Which is greater, or ? Rewrite each fraction with the denominator 9 • 11 = 99. 4-3

  2. Multiples of 18: 18, 36 List multiples of each denominator to find their LCD. Multiples of 12: 12, 24, 36 = Multiply the numerator and denominator by 2. 7 • 2 18 • 2 = Simplify. 14 36 7 18 5 12 7 18 COURSE 3 LESSON 4-3 Comparing and Ordering Rational Numbers Which is greater, or ? Since the LCM of 18 and 12 is 36, the LCD of the fractions is 36. 4-3

  3. = Multiply the numerator and denominator by 3. 14 36 15 36 = Simplify. 5 • 3 12 • 3 Since > > , . 15 36 7 18 5 12 5 12 COURSE 3 LESSON 4-3 Comparing and Ordering Rational Numbers (continued) 4-3

  4. 0.636363 Eagles: Divide. Use a calculator. Seals: 0.666667 7 11 8 12 COURSE 3 LESSON 4-3 Comparing and Ordering Rational Numbers The Eagles won 7 out of 11 games while the Seals won 8 out of 12 games. Which team has the better record? Change each fraction to a decimal. Compare the two decimals. Since 0.666 > 0.636, the Seals have the better record. 4-3

  5. Write each fraction as a decimal. – 0.667 = –0.625 –0.95 < –0.625 < –0.175 < 0.667 < 1.7 So, –0.95 < – < –0.175 < < 1.7. 5 8 2 3 5 8 2 3 2 3 5 8 COURSE 3 LESSON 4-3 Comparing and Ordering Rational Numbers Order –0.175, , – , 1.7, –0.95 from least to greatest. Then graph each decimal on a number line. The order of the points from left to right gives the order of the numbers from least to greatest. 4-3

  6. 1 4 1 5 –0.3, – , 0, 0.17, COURSE 3 LESSON 4-3 Comparing and Ordering Rational Numbers Compare. Use <, >, or =. 1.2. 3.4. 0.35 5. Order 0.17, , –0.3, 0, and – from least to greatest. 5 12 8 15 4 5 8 11 > < 15 50 36 120 7 20 = = 1 5 1 4 4-3

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