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

Learn to compare and order fractions and decimals. Course Comparing and Ordering Rational Numbers

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

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

Additional Example 1B: Comparing Fractions Compare the fractions. Write. B – – 2525 – = –2 · 7 5 · 7 = – – = –3 · 5 7 · 5 = –15 35 – > – 15 35, and so – > – 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 Comparing and Ordering Rational Numbers

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

Compare the fractions. Write. B – – 6868 – = –6 · 7 8 · 7 = – – = –5 · 8 7 · 8 = –40 56 – < – 40 56, and so – < – 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 Comparing and Ordering Rational Numbers

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 Comparing and Ordering Rational Numbers

Compare the decimals. Write. Additional Example 2: Comparing Decimals > Line up the decimal points. The tenths and hundredths are the same. Compare the thousandths: > 5. Course Comparing and Ordering Rational Numbers

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

Order the numbers from least to greatest. Additional Example 3: Ordering Fractions and Decimals , and 0.9, 4545 = 0.80 Graph the numbers on a number line Write as decimals with the same number of places = = 0.90 Course Comparing and Ordering Rational Numbers

Additional Example 3 Continued The values on a number line increase as we move from left to right < 0.90 < , 0.9, 0.93 Place the decimals in order. Order the numbers from least to greatest , and 0.9, Course Comparing and Ordering Rational Numbers

Order the numbers from least to greatest. Try This: Example , and 0.7, 3535 = 0.60 Graph the numbers on a number line Write as decimals with the same number of places = = 0.70 Course Comparing and Ordering Rational Numbers

Try This: Example 3 Continued The values on a number line increase as we move from left to right < 0.70 < , 0.7, 0.84 Place the decimals in order. Order the numbers from least to greatest , and 0.7, Course Comparing and Ordering Rational Numbers

Lesson Quiz: Part 1 Choose the greater number. 1. Place the numbers in order from least to greatest , 0.32, Insert Lesson Title Here 0.3, 0.312, or or , 0.8, , 0.826, Course Comparing and Ordering Rational Numbers

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 Course Comparing and Ordering Rational Numbers