Ordering Fractions Math Example 4

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

Example 4

hard
Arrange 49\frac{4}{9}, 512\frac{5}{12}, 718\frac{7}{18}, and 1136\frac{11}{36} from least to greatest.

Solution

  1. 1
    Find the LCD of 9,12,18,369, 12, 18, 36: LCD=36\text{LCD} = 36.
  2. 2
    Convert: 49=1636\frac{4}{9} = \frac{16}{36}, 512=1536\frac{5}{12} = \frac{15}{36}, 718=1436\frac{7}{18} = \frac{14}{36}, 1136=1136\frac{11}{36} = \frac{11}{36}.
  3. 3
    Order numerators: 11<14<15<1611 < 14 < 15 < 16.
  4. 4
    So: 1136<718<512<49\frac{11}{36} < \frac{7}{18} < \frac{5}{12} < \frac{4}{9}.

Answer

1136<718<512<49\frac{11}{36} < \frac{7}{18} < \frac{5}{12} < \frac{4}{9}
When denominators are all factors or multiples of a common number, you can find the LCD efficiently by inspection. Here all denominators divide 36, making the conversions clean.

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 2 medium

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

Example 3 easy

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

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