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

2. 2-11 Comparing and Ordering Rational Numbers Warm Up Write each mixed number as an improper fraction. 1. 1 3. 1 7474 23 8 11 6 3434 5656 2. 2 7878 4. 8 1 12 97 12

3. 2-11 Comparing and Ordering Rational Numbers Problem of the Day Hot dogs are sold in packs of 6. Buns are sold in bags of 8. What is the least number of hot dog packages and the least number of bun packages you would need to buy in order to have the same number of hot dogs and buns? 4 packages of hot dogs and 3 packages of buns

4. 2-11 Comparing and Ordering Rational Numbers Learn to compare and order fractions and decimals. 2-11

5. Comparing and Ordering Rational Numbers Vocabulary rational number

6. 2-11 Comparing and Ordering Rational Numbers Which is greater, or ? 7979 2929 When two fractions have the same denominator, just compare the numerators. 7979 > 2929 because 7 > 2. = 7979 = 2929

7. 2-11 Comparing and Ordering Rational Numbers Compare the fractions. Write. Additional Example 1A: Comparing Fractions 7979 5858 The LCM of the denominators 9 and 8 is 72. 7979 = 7 · 8 9 · 8 = 56 72 5858 = 5 · 9 8 · 9 = 45 72 56 72 > 45 72, and so. 7979 > 5858 Write equivalent fractions with 72 as the denominator. Compare the numerators.

8. 2-11 Comparing and Ordering Rational Numbers Additional Example 1B: Comparing Fractions Compare the fractions. Write. 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 equivalent fractions with 35 as the denominator. Put the negative signs in the numerators. Both fractions can be written with a denominator of 35.

9. 2-11 Comparing and Ordering Rational Numbers Compare the fractions. Write. 5656 7878 The LCM of the denominators 6 and 8 is 48. 5656 = 5 · 8 6 · 8 = 40 48 7878 = 7 · 6 8 · 6 = 42 48 40 48 < 42 48, and so. 5656 < 7878 Write equivalent fractions with 48 as the denominator. Check It Out: Example 1A Compare the numerators.

10. 2-11 Comparing and Ordering Rational Numbers Compare the fractions. Write. 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 equivalent fractions with common denominators. Put the negative signs in the numerators. Check It Out: Example 1B Both fractions can be written with a denominator of 56.

11. 2-11 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.

12. 2-11 Comparing and Ordering Rational Numbers Compare the decimals. Write. Additional Example 2A: Comparing Decimals 0.4270.425 0.427 0.425 Since 0.007 > 0.005, 0.427 > 0.425. Line up the decimal points. The tenths and hundredths are the same. Compare the thousandths: 7 5 7 > 5.

13. 2-11 Comparing and Ordering Rational Numbers Compare the decimals. Write. Additional Example 2B: Comparing Decimals 0.730.734 0.733… 0.734 Line up the decimal points. The tenths and hundredths are the same. Compare the thousandths: 3 4 3 < 4. 0.73 = _ Since 0.003 is < 0.004, 0.73 < 0.734.

14. 2-11 Comparing and Ordering Rational Numbers Compare the decimals. Write. 0.5350.538 0.535 0.538 Since 0.005 < 0.008, 0.535 < 0.538. Line up the decimal points. The tenths and hundredths are the same. Compare the thousandths: 5 8 5 < 8. Check It Out: Example 2A

15. 2-11 Comparing and Ordering Rational Numbers Check It Out: Example 2B Compare the decimals. Write. 0.334 0.3333… 0.334 Line up the decimal points. The tenths and hundredths are the same. Compare the thousandths: 3 4 3 < 4. 0.3 Since 0.003 is < 0.004, 0.3 < 0.334. 0.3 = 0.3 is a repeating decimal.

16. 2-11 Comparing and Ordering Rational Numbers 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.

17. 2-11 Comparing and Ordering Rational Numbers The values on a number line increase as you move from left to right. Remember!

18. 2-11 Comparing and Ordering Rational Numbers Order Additional Example 3: Ordering Fractions and Decimals 4545 0.93, and 0.9 from least to greatest., 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 0.80 < 0.90 < 0.93Compare the decimals in order. 4545 From least to greatest, the numbers are, 0.9, 0.93.

19. 2-11 Comparing and Ordering Rational Numbers Order, 0.84, and 0.7 from least to greatest. Check It Out: Example 3 3535 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 0.60 < 0.70 < 0.84Compare the decimals in order. 3535 From least to greatest, the numbers are, 0.7, 0.84.

20. 2-11 Comparing and Ordering Rational Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

21. 2-11 Comparing and Ordering Rational Numbers Lesson Quiz Compare the fractions. Write > or <. 1. Compare the decimals. Write. 3. 0.32 and 0.312 > 3737 and 4 10 5858 and 2323 2. < > 5656 0.8, 0.826, 5656 4. Order, 0.8, 0.826 from least to greatest.

22. 2-11 Comparing and Ordering Rational Numbers 1. Identify the symbol that compares the fractions and. A. < B. > C. = D. ≤ Lesson Quiz for Student Response Systems 4545 6 10

23. 2-11 Comparing and Ordering Rational Numbers 2. Identify the symbol that compares the fractions and. A. = B. ≥ C. < D. > Lesson Quiz for Student Response Systems 1313 3838

24. 2-11 Comparing and Ordering Rational Numbers 3. Identify the symbol that compares the decimals 0.52 and 0.511. A. < B. > C. = D. ≥ Lesson Quiz for Student Response Systems

25. 2-11 Comparing and Ordering Rational Numbers 4. Which of the following shows, 0.66, and 0.665 ordered from least to greatest? A.0.66, 0.665,C., 0.66, 0.665 B. 0.665, 0.66,D., 0.665, 0.66 Lesson Quiz for Student Response Systems 3535 3535 3535 3535 3535