Math

How to Order Fractions From Least to Greatest

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How to Order Fractions From Least to Greatest

Fractions are hard to measure instantly and it is even more complex to order them from least to greatest. There are a couple of ways to order fractions. Here is a step by step guide on how to order fractions from least to greatest. 

How to Order Fractions With The Same Denominator

  1. Arrange the numerator in increasing order.

  2. Place the fractions in ascending order by comparing their numerators.

    For Example,

    \\\mathbf{Given \ Fractions: \frac{3}{5}, \frac{1}{5}, \frac{2}{5}} \\ \\\mathbf{\\Common \ Denominator \ is \ 5.} \\ \\\mathbf{\\Numerators \ in \ Increasing \ Order: 1 < 2 < 3} \\ \\\mathbf{\\Order \ the \ Fractions \ From \ Least \ to \ Greatest: \frac{1}{5}, \frac{2}{5}, \frac{3}{5}}

How to Order Fractions using Common Denominator

  1. Identify all the denominators of the fractions.

  2. Calculate the least common multiple of all the denominators.

  3. Rewrite each fraction as an equivalent fraction with the denominator.

  4. Place the fractions in ascending order by comparing their numerators.

    For Example, 

    \\\mathbf{\\Given \ Fractions: \frac{1}{2}, \frac{2}{3}, \frac{1}{4}, \frac{5}{6}} \\ \\\mathbf{\\Identify \ All \ the \ Denominators: 2, 3, 4, 6} \\ \\\mathbf{\\Calculate \ the \ LCM \ of \ all \ the \ Denominators: 12} \\\ \\\mathbf{\\Rewrite \ each \ Fraction \ as \ an \ equivalent \ fraction \ with \ the \ denominator:} \\ \\\mathbf{\\\frac{1}{2} \ X \ \frac{6}{6} = \frac{6}{12}, \frac{2}{3} \ X \ \frac{4}{4} = \frac{8}{12}, \frac{1}{4} \ X \ \frac{3}{3} = \frac{3}{12}, \frac{5}{6} \ X \ \frac{2}{2} = \frac{10}{12}} \\ \\\mathbf{\\Now, \ We \ have \ the \ Common \ Denominator \ which \ is \ 12.} \\ \\\mathbf{Arrange \ Numerators \ in \ Increasing \ Order: 3 < 6 < 8 < 10} \\ \\\mathbf{Order \ the \ Fractions \ From \ Least \ to \ Greatest: \frac{1}{4}, \frac{1}{2}, \frac{2}{3}, \frac{5}{6}}

How to Order Fractions by Changing Fractions to Decimals and then Ordering

  1. Convert all the fractions to decimals. 

  2. Arrange the decimals in ascending order.

  3. Rewrite the equivalent fractions of decimals to get the final answer. 

    For Example, 

    \\\mathbf{\\Given \ Fractions: \frac{2}{3}, \frac{3}{4}, \frac{1}{2}} \\ \\\mathbf{\\Convert \ all \ Fractions \ to \ Decimals: 0.66, 0.75, 0.50} \\ \\\mathbf{\\Arrange \ the \ Decimals \ in \ Ascending \ Order: 0.50,0.66, 0.75} \\ \\\mathbf{\\The \ Final \ Answer \ is: \frac{1}{2}, \frac{2}{3}, \frac{3}{4}}