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2-11

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  1. Comparing and Ordering Rational Numbers 2-11 Course 2 Warm Up Problem of the Day Lesson Presentation

  2. Comparing and Ordering Rational Numbers 2-11 Course 2 Warm Up Write each mixed number as an improper fraction. 1.1 3. 1 23 8 3 4 7 8 7 4 2. 2 1 12 5 6 11 6 97 12 4. 8

  3. Comparing and Ordering Rational Numbers 2-11 Course 2 Learn to compare and order fractions and decimals.

  4. Comparing and Ordering Rational Numbers 2-11 Course 2 Insert Lesson Title Here Vocabulary rational number

  5. Comparing and Ordering Rational Numbers 2-11 Course 2 7 9 2 9 Which is greater, or ? When two fractions have the same denominator, just compare the numerators. 7 9 2 9 > because 7 > 2. 7 9 = 2 9 =

  6. Comparing and Ordering Rational Numbers 2-11 7 9 7 9 7 9 5 8 5 8 5 8 56 72 7 · 8 9 · 8 45 72 5 · 9 8 · 9 56 72 45 72 , and so . > > Course 2 Additional Example 1A: Comparing Fractions Compare the fractions. Write < or >. The LCM of the denominators 9 and 8 is 72. Write equivalent fractions with 72 as the denominator. = = = = Compare the numbers.

  7. Comparing and Ordering Rational Numbers 2-11 2 5 2 5 3 7 3 7 Course 2 Additional Example 1B: Comparing Fractions Compare the fractions. Write < or >. – – Cross Multiply the denominator Of the first fraction by the Numerator of the second fraction Second, Cross multiply the Denominator of the second fraction By the numerator of the first fraction Cross Multiply = – – -14 -15 -14 > -15 So -2/5 > -3/7

  8. Comparing and Ordering Rational Numbers 2-11 5 6 5 6 7 8 7 8 . < Course 2 Check It Out: Example 1A Compare the fractions. Write < or >.

  9. Comparing and Ordering Rational Numbers 2-11 6 8 6 8 6 8 5 7 5 7 Course 2 Check It Out: Example 1B Compare the fractions. Write < or >. – – Both fractions can be written with a denominator of 56. Write equivalent fractions with common denominators. Put the negative signs in the numerators. –6 · 7 8 · 7 –42 56 = – = –5 · 8 7 · 8 –40 56 = – = 5 7 42 56 40 56 – – < , and so – < . –

  10. Comparing and Ordering Rational Numbers 2-11 Course 2 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.

  11. Comparing and Ordering Rational Numbers 2-11 Course 2 Additional Example 2A: Comparing Decimals Compare the decimals. Write < or >. 0.427 0.425 Line up the decimal points. 0.427 7 The tenths and hundredths are the same. 0.425 5 Compare the thousandths: 7 > 5. Since 0.007 > 0.005, 0.427 > 0.425.

  12. Comparing and Ordering Rational Numbers 2-11 _ 0.73 = _ Since 0.03 is < 0.04, 0.73 < 0.734. Course 2 Additional Example 2B: Comparing Decimals Compare the decimals. Write < or >. 0.73 0.734 Line up the decimal points. 0.733… 3 The tenths and hundredths are the same. 0.734 4 Compare the thousandths: 3 < 4.

  13. Comparing and Ordering Rational Numbers 2-11 Course 2 Check It Out: Example 2A Compare the decimals. Write < or >. 0.535 0.538 Line up the decimal points. 0.535 5 The tenths and hundredths are the same. 0.538 8 Compare the thousandths: 5 < 8. Since 0.005 < 0.008, 0.535 < 0.538.

  14. Comparing and Ordering Rational Numbers 2-11 0.3 __ 0.33 = __ Since 0.003 is < 0.004, 0.33 < 0.334. Course 2 Check It Out: Example 2B Compare the decimals. Write < or >. 0.334 Line up the decimal points. 0.3333… 3 The tenths and hundredths are the same. 0.334 4 Compare the thousandths: 3 < 4.

  15. Comparing and Ordering Rational Numbers 2-11 Course 2 A rational number is a number that can be written as a fraction with integers for its numerator and denominator. When rational numbers are written in a variety of forms, you can compare the numbers by writing them all in the same form.

  16. Comparing and Ordering Rational Numbers 2-11 Remember! The values on a number line increase as you move from left to right. Course 2

  17. Comparing and Ordering Rational Numbers 2-11 0 0.2 0.4 0.6 0.8 1 Course 2 Additional Example 3: Ordering Fractions and Decimals 4 5 , 0.93, and 0.9 from least to greatest. Order Write as decimals with the same number of places. 4 5 = 0.80 0.93 = 0.93 0.9 = 0.90 Graph the numbers on a number line. 0.93 0.80 < 0.90 < 0.93 Compare the decimals in order. 4 5 From least to greatest, the numbers are , 0.9, 0.93.

  18. Comparing and Ordering Rational Numbers 2-11 0 0.2 0.4 0.6 0.8 1 Course 2 Check It Out: Example 3 3 5 Order , 0.84, and 0.7 from least to greatest. Write as decimals with the same number of places. 3 5 = 0.60 0.84 = 0.84 0.7 = 0.70 Graph the numbers on a number line. 0.84 0.60 < 0.70 < 0.84 Compare the decimals in order. 3 5 From least to greatest, the numbers are , 0.7, 0.84.

  19. Comparing and Ordering Rational Numbers 2-11 > < 5 6 0.8, 0.826, Course 2 Insert Lesson Title Here Lesson Practice Compare the fractions. Write > or <. 1. Compare the decimals. Write < or >. 3. 0.32 and 0.312 4 10 3 7 2 3 5 8 or 2. or > 5 6 4. Order , 0.8, 0.826 from least to greatest.