# Ordering Fractions Calculator

Enter the fraction separated by comma and press the calculate button. The system will show the entered fractions in ascending and descending order.

Please enter fraction separated by comma , (example: 1/3,4/2,3/2,7/5) |

Ascending Order (Least to Greatest) |

Descending Order (Greatest to Least) |

To compare fractions the calculator first finds the least common denominator (LCD), converts the fractions to equivalent fractions using the LCD, then compares the numerators for equality.

There can be three cases as follows:

$$ \frac{14}{7} , \frac{8}{7}, \frac{17}{7}, \frac{25}{7}, \frac{51}{7} $$ In this case we compare the numerators and arrange the fractions in the order based on numerators as follows:

$$ \text {Ascending order : }\frac {8}{7}, \frac {14}{7}, \frac {17}{7}, \frac {25}{7} and \frac {51}{7} $$ $$ \text {Descending order: }\frac {51}{7}, \frac {25}{7}, \frac {17}{7}, \frac {14}{7} and \frac {8}{7} $$

$$ \frac {3}{2}, \frac {8}{3}, \frac {10}{9}, \frac {5}{4} $$ In this case We will derive the least common denominator (LCD) to achieve the fractions with same denominator. In other words this will become case 1 (like denominators)

So lets find the LCD for denominators 2, 3, 9 and 4 which is 36.

Now to find the equivalent fractions have denominator as 36 therefore

$$ \frac {3}{2} = \frac {(n \times 3)}{36} = \frac {(18 \times 3)}{(18 \times 2)} = \frac {54}{36} $$ $$ \frac {8}{3} = \frac {(n \times 8)}{36} = \frac {(12 \times 8)}{(12 \times 3)} = \frac {96}{36} $$ $$ \frac {10}{9} = \frac {(n \times 10)}{36} = \frac {(4 \times 10)}{(4 \times9)} = \frac {40}{36} $$ $$ \frac {5}{4} = \frac {(n \times 5)}{36} = \frac {(9 \times5)}{(9 \times 4)} = \frac {45}{36} $$ Now compare the derived numerators and arrange the fractions in the order based on derived numerators like :

$$ \text {Ascending order : } \frac {10}{9}, \frac {5}{4}, \frac {3}{2} and \frac {8}{3} $$ $$ \text {Descending order: } \frac {8}{3}, \frac {3}{2}, \frac {5}{4} and \frac {10}{9} $$

$$ \frac {1}{9}, \frac {1}{5}, \frac {1}{11}, \frac {1}{6} $$ If the fractions having like numerators, we will compare the denominators and arrange the fraction in order based on denominators. The important point is here that fraction with the smaller denominator is the larger fraction In this case we compare the denominators and arrange the fractions in the order based on denominators as follows:

$$ \text {Ascending order : } \frac {1}{11}, \frac {1}{9}, \frac {1}{6} and \frac {1}{5} $$ $$ \text {Descending order: } \frac {1}{5}, \frac {1}{6}, \frac {1}{9} and \frac {1}{11} $$

There can be three cases as follows:

**Case 1 : Order the fractions with like denominators**example :$$ \frac{14}{7} , \frac{8}{7}, \frac{17}{7}, \frac{25}{7}, \frac{51}{7} $$ In this case we compare the numerators and arrange the fractions in the order based on numerators as follows:

$$ \text {Ascending order : }\frac {8}{7}, \frac {14}{7}, \frac {17}{7}, \frac {25}{7} and \frac {51}{7} $$ $$ \text {Descending order: }\frac {51}{7}, \frac {25}{7}, \frac {17}{7}, \frac {14}{7} and \frac {8}{7} $$

**Case 2 : Order the fractions with unlike denominators**Example$$ \frac {3}{2}, \frac {8}{3}, \frac {10}{9}, \frac {5}{4} $$ In this case We will derive the least common denominator (LCD) to achieve the fractions with same denominator. In other words this will become case 1 (like denominators)

So lets find the LCD for denominators 2, 3, 9 and 4 which is 36.

Now to find the equivalent fractions have denominator as 36 therefore

$$ \frac {3}{2} = \frac {(n \times 3)}{36} = \frac {(18 \times 3)}{(18 \times 2)} = \frac {54}{36} $$ $$ \frac {8}{3} = \frac {(n \times 8)}{36} = \frac {(12 \times 8)}{(12 \times 3)} = \frac {96}{36} $$ $$ \frac {10}{9} = \frac {(n \times 10)}{36} = \frac {(4 \times 10)}{(4 \times9)} = \frac {40}{36} $$ $$ \frac {5}{4} = \frac {(n \times 5)}{36} = \frac {(9 \times5)}{(9 \times 4)} = \frac {45}{36} $$ Now compare the derived numerators and arrange the fractions in the order based on derived numerators like :

$$ \text {Ascending order : } \frac {10}{9}, \frac {5}{4}, \frac {3}{2} and \frac {8}{3} $$ $$ \text {Descending order: } \frac {8}{3}, \frac {3}{2}, \frac {5}{4} and \frac {10}{9} $$

**Case 3: Order the fractions with like numerators**example:$$ \frac {1}{9}, \frac {1}{5}, \frac {1}{11}, \frac {1}{6} $$ If the fractions having like numerators, we will compare the denominators and arrange the fraction in order based on denominators. The important point is here that fraction with the smaller denominator is the larger fraction In this case we compare the denominators and arrange the fractions in the order based on denominators as follows:

$$ \text {Ascending order : } \frac {1}{11}, \frac {1}{9}, \frac {1}{6} and \frac {1}{5} $$ $$ \text {Descending order: } \frac {1}{5}, \frac {1}{6}, \frac {1}{9} and \frac {1}{11} $$