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Compare fractions with unlike denominators

Unlike denominators partition the whole into different-sized parts, so comparing their numerical values requires recognizing equivalent fractions, using a common denominator, benchmarks such as 0, 1/2, and 1, or positions on a number line. The reasoning applies to positive proper and improper fractions, including mixed numbers, and avoids the misconception that a larger denominator alone makes a fraction larger; symbolic variables, negative fractions, and more advanced generalizations are not included.

Detailed Explanation: Compare fractions with unlike denominators

When fractions have unlike denominators, their pieces are different sizes, so compare them by rewriting them with a common denominator.

Example: Compare 34\frac{3}{4} and 56\frac{5}{6}.

  1. Find a common denominator.
    The least common multiple of 44 and 66 is 1212.

  2. Rewrite each fraction with denominator 1212:

34=3×34×3=912 \frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12} 56=5×26×2=1012 \frac{5}{6}=\frac{5\times2}{6\times2}=\frac{10}{12}
  1. Compare the numerators. Since 9<109<10,
912<1012. \frac{9}{12}<\frac{10}{12}.

Therefore,

34<56.\boxed{\frac{3}{4}<\frac{5}{6}}.

Remember: a larger denominator does not automatically mean a larger fraction. Rewrite the fractions so they describe the same-sized parts before comparing.

Learn by doing: Compare fractions with unlike denominators

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Fraction Comparison - Mixed - Two Changed Denominators


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