Comparing Dissimilar Fractions
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Questions and Answers

Which symbol correctly compares the fractions $\frac{3}{5}$ and $\frac{5}{8}$?

  • >
  • < (correct)
  • $\approx$
  • =
  • What is the correct comparison between $\frac{7}{12}$ and $\frac{5}{9}$?

  • $\frac{7}{12} < \frac{5}{9}$
  • $\frac{7}{12} = \frac{5}{9}$
  • $\frac{7}{12} > \frac{5}{9}$ (correct)
  • Cannot be determined
  • Which of the following statements is true?

  • $\frac{2}{3} < \frac{3}{7}$
  • $\frac{3}{4} > \frac{5}{8}$ (correct)
  • $\frac{5}{6} > \frac{7}{8}$
  • $\frac{4}{9} = \frac{1}{2}$
  • Which comparison is incorrect?

    <p>$\frac{3}{5} &gt; \frac{7}{10}$ (C)</p> Signup and view all the answers

    How would you correctly compare $\frac{11}{15}$ and $\frac{2}{3}$?

    <p>$\frac{11}{15} &gt; \frac{2}{3}$ (C)</p> Signup and view all the answers

    Study Notes

    Comparing Dissimilar Fractions

    • Understand that dissimilar fractions have different denominators.
    • To compare dissimilar fractions, they must first be converted to equivalent fractions with a common denominator.
    • This process involves finding the least common multiple (LCM) of the denominators.
    • The LCM represents the smallest positive integer that is a multiple of two or more integers.
    • Once the LCM is determined, rewrite each fraction as an equivalent fraction using the LCM as the new denominator.
    • The numerators of the equivalent fractions are adjusted proportionally to maintain the same value as the original fraction.
    • After rewriting as equivalent fractions, compare the numerators of the converted fractions.
    • The fraction with the larger numerator is the larger fraction.

    Using the Symbols =, >, and <

    • The symbol "=" indicates equality, meaning the two fractions represent the same value.
    • The symbol ">" means "greater than". A fraction is greater than another if its value is larger.
    • The symbol "<" means "less than". A fraction is less than another if its value is smaller.

    Examples and Steps for Comparison

    • Example 1: Compare 2/3 and 3/4

    • Find the LCM of 3 and 4. The LCM is 12.

    • Rewrite 2/3 as an equivalent fraction with a denominator of 12: (2/3) * (4/4) = 8/12

    • Rewrite 3/4 as an equivalent fraction with a denominator of 12: (3/4) * (3/3) = 9/12

    • Compare the numerators: 9 > 8. Therefore, 3/4 > 2/3

    • Example 2: Compare 5/6 and 7/8

    • Find the LCM of 6 and 8. The LCM is 24.

    • Rewrite 5/6 as an equivalent fraction with a denominator of 24: (5/6) * (4/4) = 20/24.

    • Rewrite 7/8 as an equivalent fraction with a denominator of 24: (7/8) * (3/3) = 21/24

    • Compare the numerators: 21 > 20. Therefore, 7/8 > 5/6

    • Example 3: Compare 1/2 and 1/2

    • The LCM of 2 and 2 is 2.

    • Rewrite 1/2 as an equivalent fraction with a denominator of 2: (1/2) * (1/1) = 1/2.

    • Compare the numerators: 1 = 1. Therefore, 1/2 = 1/2

    Key Concepts

    • Identifying fractions as equivalent forms of the same value.
    • Finding the LCM efficiently.
    • Converting dissimilar fractions to equivalent fractions.
    • Using the correct symbol to represent the comparison relationship between fractions ( =, >, < ) based on their values.
    • Understanding the significance of a common denominator in the comparison of unlike fractions.

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    Description

    This quiz focuses on understanding and comparing dissimilar fractions by converting them to equivalent fractions with a common denominator. By utilizing the least common multiple (LCM) and adjusting numerators, you will learn how to accurately compare fractions. Test your knowledge on the symbols of inequality as well.

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