Ordering Fractions Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Order 56\frac{5}{6}, 34\frac{3}{4}, 712\frac{7}{12}, and 23\frac{2}{3} from least to greatest.

Solution

  1. 1
    Find the LCD of 6,4,12,36, 4, 12, 3: LCD=12\text{LCD} = 12.
  2. 2
    Convert each fraction: 56=1012\frac{5}{6} = \frac{10}{12}, 34=912\frac{3}{4} = \frac{9}{12}, 712=712\frac{7}{12} = \frac{7}{12}, 23=812\frac{2}{3} = \frac{8}{12}.
  3. 3
    Order the numerators: 7<8<9<107 < 8 < 9 < 10.
  4. 4
    So from least to greatest: 712<23<34<56\frac{7}{12} < \frac{2}{3} < \frac{3}{4} < \frac{5}{6}.

Answer

712<23<34<56\frac{7}{12} < \frac{2}{3} < \frac{3}{4} < \frac{5}{6}
Converting all fractions to a common denominator reduces the ordering problem to comparing whole-number numerators. The LCD is the most efficient choice of common denominator because it produces the smallest numerators.

About Ordering Fractions

Ordering fractions means arranging a set of fractions from least to greatest (or greatest to least) by converting them to a common denominator or to decimals so their sizes can be directly compared.

Learn more about Ordering Fractions →

More Ordering Fractions Examples

Example 1 easy

Order [formula], [formula], and [formula] from least to greatest.

Example 3 easy

Order [formula], [formula], and [formula] from greatest to least.

Example 4 hard

Arrange [formula], [formula], [formula], and [formula] from least to greatest.

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