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Order fractions with unlike denominators

Fractions with unlike denominators can be compared by recognizing that denominator size alone does not determine magnitude: each fraction must be expressed in equivalent form with a common denominator, compared with benchmarks such as 0, 1/2, and 1, or located on a number line. Ordering follows from comparing equivalent numerators while preserving value, for positive proper fractions and mixed numbers; generalized rational-number ordering and abstract symbolic cases beyond this scope are not included.

Detailed Explanation: Order fractions with unlike denominators

To order fractions with unlike denominators, rewrite them with a common denominator. Then compare the numerators.

Example: Order 34\frac{3}{4}, 23\frac{2}{3}, and 58\frac{5}{8} from least to greatest.

  1. Find a common denominator.
    The least common denominator of 44, 33, and 88 is 2424.

  2. Rewrite each fraction with denominator 2424:

34=1824\frac{3}{4}=\frac{18}{24} 23=1624\frac{2}{3}=\frac{16}{24} 58=1524\frac{5}{8}=\frac{15}{24}

  1. Compare the numerators. Since

15<16<18,15<16<18,

we have

1524<1624<1824.\frac{15}{24}<\frac{16}{24}<\frac{18}{24}.

  1. Replace the equivalent fractions with the original fractions:

58<23<34\boxed{\frac{5}{8}<\frac{2}{3}<\frac{3}{4}}

Remember: A larger denominator does not automatically mean a larger fraction. Rewrite the fractions with a common denominator before comparing them.

Learn by doing: Order fractions with unlike denominators

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    Fraction Comparison - Basic - One Changed Denominator

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