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Comparing Fractions and Decimals Lesson Presentation

Engage students with warm-up problems, examples, and quizzes on converting mixed numbers, comparing fractions, and ordering decimals. Includes interactive activities to reinforce learning concepts effectively. Suitable for middle school math classes.

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Comparing Fractions and Decimals Lesson Presentation

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  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. 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 Learn to compare and order fractions and decimals.

  5. Vocabulary rational number

  6. 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 =

  7. 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 . > > 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 numerators.

  8. 2 5 2 5 2 5 3 7 3 7 Additional Example 1B: Comparing Fractions Compare the fractions. Write < or >. – – Both fractions can be written with a denominator of 35. Write equivalent fractions with 35 as the denominator. Put the negative signs in the numerators. –2 · 7 5 · 7 –14 35 = – = –3 · 5 7 · 5 –15 35 = – = 3 7 14 35 15 35 – – > , and so – > . –

  9. 5 6 5 6 5 6 7 8 7 8 7 8 40 48 5 · 8 6 · 8 42 48 7 · 6 8 · 6 40 48 42 48 , and so . < < Check It Out: Example 1A Compare the fractions. Write < or >. The LCM of the denominators 6 and 8 is 48. Write equivalent fractions with 48 as the denominator. = = = = Compare the numerators.

  10. 6 8 6 8 6 8 5 7 5 7 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 – < . –

  11. 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. 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.

  13. _ 0.73 = Since 0.003 is < 0.004, 0.73 < 0.734. 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.

  14. 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.

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

  16. 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. Remember! The values on a number line increase as you move from left to right.

  18. 0 0.2 0.4 0.6 0.8 1 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.

  19. 0 0.2 0.4 0.6 0.8 1 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.

  20. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  21. > < 5 6 0.8, 0.826, Lesson Quiz 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 and and 2. > 5 6 4. Order , 0.8, 0.826 from least to greatest.

  22. Lesson Quiz for Student Response Systems 1. Identify the symbol that compares the fractions and . A. < B. > C. = D. ≤ 6 10 4 5

  23. Lesson Quiz for Student Response Systems 2. Identify the symbol that compares the fractions and . A. = B. ≥ C. < D. > 3 8 1 3

  24. Lesson Quiz for Student Response Systems 3. Identify the symbol that compares the decimals 0.52 and 0.511. A. < B. > C. = D. ≥

  25. Lesson Quiz for Student Response Systems 3 5 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 3 5 3 5 3 5 3 5

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