1. 3-10 Comparing and Ordering Rational Numbers Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Learn to compare and order fractions and decimals. Course 2 3-10 Comparing and Ordering Rational Numbers

3. Which is greater, or ? 7979 2929 When two fractions have the same denominator, just compare the numerators. 7979 > 2929 because 7 > 2. = 7979 = 2929 Course 2 3-10 Comparing and Ordering Rational Numbers

4. Compare the fractions. Write. Additional Example 1A: Comparing Fractions A. 7979 5858 Both fractions can be written with a denominator of 72. 7979 = 7 · 8 9 · 8 = 56 72 5858 = 5 · 9 8 · 9 = 45 72 56 72 > 45 72, and so. 7979 > 5858 Write as fractions with common denominators. Course 2 3-10 Comparing and Ordering Rational Numbers

5. Additional Example 1B: Comparing Fractions Compare the fractions. Write. B. 2525 3737 – – 2525 – = –2 · 7 5 · 7 = –14 35 3737 – = –3 · 5 7 · 5 = –15 35 – 14 35 > – 15 35, and so – >. 2525 – 3737 Write as fractions with common denominators. Put the negative signs in the numerators. Both fractions can be written with a denominator of 35. Course 2 3-10 Comparing and Ordering Rational Numbers

6. Compare the fractions. Write. A. 5656 7878 Both fractions can be written with a denominator of 48. 5656 = 5 · 8 6 · 8 = 40 48 7878 = 7 · 6 8 · 6 = 42 48 40 48 < 42 48, and so. 5656 < 7878 Write as fractions with common denominators. Try This: Example 1A Course 2 3-10 Comparing and Ordering Rational Numbers

7. Compare the fractions. Write. B. 6868 5757 – – 6868 – = –6 · 7 8 · 7 = –42 56 5757 – = –5 · 8 7 · 8 = –40 56 – 42 56 < – 40 56, and so – <. 6868 – 5757 Write as fractions with common denominators. Put the negative signs in the numerators. Try This: Example 1B Both fractions can be written with a denominator of 56. Course 2 3-10 Comparing and Ordering Rational Numbers

8. To compare decimals, line up the decimal points and compare digits from left to right until you find the place where the digits are different. Course 2 3-10 Comparing and Ordering Rational Numbers

9. Compare the decimals. Write. Additional Example 2: Comparing Decimals 0.4270.425 0.427 0.425 0.427 > 0.425 Line up the decimal points. The tenths and hundredths are the same. Compare the thousandths: 7 5 7 > 5. Course 2 3-10 Comparing and Ordering Rational Numbers

10. Compare the decimals. Write. 0.5350.538 0.535 0.538 0.535 < 0.538 Line up the decimal points. The tenths and hundredths are the same. Compare the thousandths: 5 8 5 < 8. Try This: Example 2 Course 2 3-10 Comparing and Ordering Rational Numbers

11. Order the numbers from least to greatest. Additional Example 3: Ordering Fractions and Decimals 4545 0.93, and 0.9, 4545 = 0.80 Graph the numbers on a number line. 0 0.2 0.4 0.6 0.8 1 0.93 Write as decimals with the same number of places. 0.93 = 0.93 0.9 = 0.90 Course 2 3-10 Comparing and Ordering Rational Numbers

12. Additional Example 3 Continued The values on a number line increase as we move from left to right. 0.80 < 0.90 < 0.93 4545, 0.9, 0.93 Place the decimals in order. Order the numbers from least to greatest. 4545 0.93, and 0.9, 0 0.2 0.4 0.6 0.8 1 0.93 Course 2 3-10 Comparing and Ordering Rational Numbers

13. Order the numbers from least to greatest. Try This: Example 3 3535 0.84, and 0.7, 3535 = 0.60 Graph the numbers on a number line. 0 0.2 0.4 0.6 0.8 1 0.84 Write as decimals with the same number of places. 0.84 = 0.84 0.7 = 0.70 Course 2 3-10 Comparing and Ordering Rational Numbers

14. Try This: Example 3 Continued The values on a number line increase as we move from left to right. 0.60 < 0.70 < 0.84 3535, 0.7, 0.84 Place the decimals in order. Order the numbers from least to greatest. 3535 0.84, and 0.7, 0 0.2 0.4 0.6 0.8 1 0.84 Course 2 3-10 Comparing and Ordering Rational Numbers

15. Lesson Quiz: Part 1 Choose the greater number. 1. Place the numbers in order from least to greatest 3. 0.3, 0.32, 0.312 Insert Lesson Title Here 0.3, 0.312, 0.32 3737 or 4 10 5858 or 2323 2. 2323 3737 5656, 0.8, 0.826 0.8, 0.826, 5656 4. Course 2 3-10 Comparing and Ordering Rational Numbers

16. Lesson Quiz: Part 2 5. Dana’s cross-country team is getting ready for a big meet. On Monday they ran 3.7 miles, on Tuesday they ran 3 miles, and on Wednesday they ran miles. On which day did they run the greatest distance? Monday Insert Lesson Title Here 3838 11 4 Course 2 3-10 Comparing and Ordering Rational Numbers