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Compare fraction strategies

Comparison of fractions involves reasoning about their values, not comparing numerators or denominators independently. A learner can select and justify strategies such as finding equivalent fractions with a common denominator, using benchmark fractions or a number line, and, when appropriate, comparing products from cross-multiplication; these methods apply to positive fractions and mixed numbers in familiar forms and support proportional reasoning and later algebraic comparison.

Detailed Explanation: Compare fraction strategies

To compare fractions, compare their values, not just their numerators or denominators. A helpful strategy is to rewrite the fractions with a common denominator.

Compare:

34and56\frac{3}{4} \quad \text{and} \quad \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 equivalent fractions:
912<1012\frac{9}{12}<\frac{10}{12}

Therefore,

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

Both fractions now describe parts of the same-sized whole: twelfths. Since 99 twelfths is less than 1010 twelfths, 34\frac{3}{4} is less than 56\frac{5}{6}.

Learn by doing: Compare fraction strategies

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    Fraction Comparison - Basic - Two Changed Denominators

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