Comparing Fractions Math Example 2

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Example 2

medium
Compare 59\frac{5}{9} and 712\frac{7}{12} using a common denominator.

Solution

  1. 1
    Find the LCD of 99 and 1212: multiples of 99: 9,18,27,36,…9, 18, 27, 36, \ldots; multiples of 1212: 12,24,36,…12, 24, 36, \ldots; LCD=36\text{LCD} = 36.
  2. 2
    Convert: 59=2036\frac{5}{9} = \frac{20}{36} and 712=2136\frac{7}{12} = \frac{21}{36}.
  3. 3
    Compare numerators: 20<2120 < 21, so 59<712\frac{5}{9} < \frac{7}{12}.

Answer

59<712\frac{5}{9} < \frac{7}{12}
Converting unlike fractions to a common denominator transforms a comparison of 'different-sized pieces' into a simple comparison of whole numbers. Always divide the LCD by each original denominator to find the scaling factor.

About Comparing Fractions

Determining which of two fractions is greater, less, or equal using common denominators, benchmarks, or cross-multiplication.

Learn more about Comparing Fractions →

More Comparing Fractions Examples

Example 1 easy

Compare [formula] and [formula] using the [formula], [formula], or [formula] symbol.

Example 3 easy

Compare [formula] and [formula] using cross-multiplication.

Example 4 hard

Without finding a common denominator, use benchmark reasoning to compare [formula] and [formula].

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