Ordering Fractions Calculator: Ascending, Descending, Shows Work

Learn

How to order fractions using one of two methods.

How to Order Fractions

To arrange a list of fractions in ascending or descending order, it may help to use one of two methods; Decimals or Like Denominators.

The decimal method involves converting each fraction to a decimal, and then sorting by the decimals.

To convert a fraction to a decimal, you divide the numerator by the denominator. For example, the fraction 1/2 becomes the decimal 0.50 (1 divided by 2 = 0.50).

The second method for sorting fractions involves converting all fractions so they share the same denominator and then sorting by their numerators.

To convert a list of fractions with unlike denominators into fractions with like denominators, you first find the lowest number that all denominators will divide into evenly (Least Common Multiple or LCM).

Once you know the least common denominator for the group of fractions, you then convert each fraction by following these steps:

Divide the LCD by the denominator.
Multiply the numerator by the result in step #1. The result becomes the new numerator.
The LCD becomes the new denominator.

Ordering Fractions Examples

Example #1: Fractions Only
1/12	1/4	8/9	4/6	2/3

Here is how to order the fractions using two different methods.

Method #1: Convert fractions to decimals and then sort by the decimals.

Convert each fraction to a decimal by dividing the numerator by the denominator.

Convert to Decimals
Fraction	Decimal
1/12	0.083
1/4	0.250
8/9	0.889
4/6	0.667
2/3	0.667

Fraction decimal equivalents sorted in ascending order (smallest decimal to largest).

Decimals by Ascending Order
Fraction	Decimal
1/12	0.083
1/4	0.250
4/6	0.667
2/3	0.667
8/9	0.889

Fraction decimal equivalents sorted in descending order (largest decimal to smallest).

Decimals by Descending Order
Fraction	Decimal
8/9	0.889
4/6	0.667
2/3	0.667
1/4	0.250
1/12	0.083

Method #2: Convert fractions to like denominators, and then sort by their numerators.

To convert fractions to like denominators, start by finding the least common denominator (LCD) of all denominators (lowest number all 5 denominators divide into evenly), which in this case is 36. Next, for each fraction, divide the LCM by the denominator and then multiply that result by the numerator to get the converted numerator. Finally, use the LCM as the new denominator.

Convert to Like Denominators
Fractions	Conversion	Like Denominators
1/12	36 / 12 * 1 = 3	3/36
1/4	36 / 4 * 1 = 9	9/36
8/9	36 / 9 * 8 = 32	32/36
4/6	36 / 6 * 4 = 24	24/36
2/3	36 / 3 * 2 = 24	24/36

Fractions with like denominators sorted by their numerators in ascending order (smallest numerator to largest).

Numerators by Ascending Order
Fraction	Like Denominators
1/12	3/36
1/4	9/36
4/6	24/36
2/3	24/36
8/9	32/36

Fractions with like denominators sorted by their numerators in descending order (largest numerator to smallest).

Numerators by Descending Order
Fraction	Like Denominators
8/9	32/36
4/6	24/36
2/3	24/36
1/4	9/36
1/12	3/36

Example #2: Fractions and Mixed Numbers
1 6/7	1/9	1 1/3	1 1/8	2/5

Here is how to order the fractions and mixed numbers using two different methods.

Since one or more of your entries are mixed numbers, convert them to fractions by multiplying the denominator by the whole number, and then adding that result to the numerator to get the converted numerator.

Convert Mixed Numbers
Entry	Fraction
1 6/7	13/7
1/9	1/9
1 1/3	4/3
1 1/8	9/8
2/5	2/5