# Ordering Fractions Calculator: Ascending and Descending, and Shows Work This calculator will arrange a list of fractions and mixed numbers in both ascending and descending order.

Plus, the calculator will show its work so you can learn how to order fractions either by converting the fractions to decimals or by converting unlike denominators to like denominators.

If you would like to compare two fractions, please visit the Compare Fractions Calculator.

## Ordering Fractions Calculator

Order fractions and mixed numbers in ascending and descending order.

#### Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Enter fractions, separated by commas

#### Fraction list:

Enter each fraction or mixed number in your list, each separated by a comma. Enter fractions without spaces before or after the division sign (/). If entering a mixed number, enter the whole number, followed by a space, followed by the fraction (for two and one half, enter 2 1/2).

# fractions:# of fractions:Number of fractions:Number of fractions:

#### Number of fractions:

This is the number of different fractions detected by the calculator.

LCD:LCD:Least common denominator:Least common denominator:

#### Least common denominator:

This is the least common denominator of the entered fractions as calculated by the calculator.

Fractions in ascending order:

#### Fractions in ascending order:

Below you will see the fractions have been sorted from least to greatest (smallest to largest). Note that any mixed numbers will have been converted to fractions.

Fractions in descending order:

#### Fractions in descending order:

Below you will see the fractions have been sorted from greatest to least (largest to smallest). Note that any mixed numbers will have been converted to fractions.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

## 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:

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

#### Ordering Fractions Examples

Example #1: Fractions Only
1/121/48/94/62/3

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
FractionDecimal
1/120.083
1/40.250
8/90.889
4/60.667
2/30.667

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

Decimals by Ascending Order
FractionDecimal
1/120.083
1/40.250
4/60.667
2/30.667
8/90.889

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

Decimals by Descending Order
FractionDecimal
8/90.889
4/60.667
2/30.667
1/40.250
1/120.083

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
FractionsConversionLike Denominators
1/1236 / 12 * 1 = 33/36
1/436 / 4 * 1 = 99/36
8/936 / 9 * 8 = 3232/36
4/636 / 6 * 4 = 2424/36
2/336 / 3 * 2 = 2424/36

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

Numerators by Ascending Order
FractionLike Denominators
1/123/36
1/49/36
4/624/36
2/324/36
8/932/36

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

Numerators by Descending Order
FractionLike Denominators
8/932/36
4/624/36
2/324/36
1/49/36
1/123/36
Example #2: Fractions and Mixed Numbers
1 6/71/91 1/31 1/82/5

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
EntryFraction
1 6/713/7
1/91/9
1 1/34/3
1 1/89/8
2/52/5

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
FractionDecimal
13/71.857
1/90.111
4/31.333
9/81.125
2/50.400

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

Decimals by Ascending Order
FractionDecimal
1/90.111
2/50.400
9/81.125
4/31.333
13/71.857

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

Decimals by Descending Order
FractionDecimal
13/71.857
4/31.333
9/81.125
2/50.400
1/90.111

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 2520. 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
FractionsConversionLike Denominators
13/72520 / 7 * 13 = 46804680/2520
1/92520 / 9 * 1 = 280280/2520
4/32520 / 3 * 4 = 33603360/2520
9/82520 / 8 * 9 = 28352835/2520
2/52520 / 5 * 2 = 10081008/2520

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

Numerators by Ascending Order
FractionLike Denominators
1/9280/2520
2/51008/2520
9/82835/2520
4/33360/2520
13/74680/2520

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

Numerators by Descending Order
FractionLike Denominators
13/74680/2520
4/33360/2520
9/82835/2520
2/51008/2520
1/9280/2520

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".