Ordering Fractions Calculator

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Order Fractions
Enter fractions, mixed numbers, integers
(separated by commas)




answer will show inequalities and equalities
(<, >, and =)
Answer:
Rewriting as fractions or any negatives if necessary:
1/1, 1/2, 3/4, 9/12, 29/8, -12/16

The least common denominator (LCD) is: 48.

Rewriting as equivalent fractions with the LCD:
48/48, 24/48, 36/48, 36/48, 174/48, -36/48

Ordering these fractions by the numerator:
-36/48  <  24/48  <  36/48  =  36/48  <  48/48  <  174/48

Therefore, the order of your input is:
-12/16  <  1/2  <  3/4  =  9/12  <  1  <  3 5/8

Calculator Use

Compare and order fractions, integers and mixed numbers to find if the are equal, greater or less than each other. (=, > , or <) We also have calculators for fraction operations, simplifying fractions, mixed numbers operations, and comparing fractions. See additional notes below on ranking fractions.

How to Order Fractions, Integers and Mixed Numbers:

To compare and order fractions you can first convert all integers, mixed numbers (mixed fractions) and fractions into comparable values.  We do this by first converting all terms into fractions, finding the least common denominator (LCD), then rewriting each term as an equivalent fraction with the LCD.  Then all we need to do is compare the numerators of each fraction to put them in correct order from least to greatest or greatest to least.

Steps to compare and order fractions, integers and mixed numbers

  1. Convert integers and mixed numbers to improper fractions
  2. Find the LCD of the fractions
  3. Rewrite fractions as equivalent fractions using the LCD
  4. Order the new fractions by the numerator
  5. Match original inputs to the ordered fractions to see the final order

Example using this calculator default sample:

  • Input: 1, 1/2, 3/4, 3 5/8, -12/16
  • Convert integers and mixed numbers to improper fractions
    • 1/2, 3/4 and -12/16 are already fractions so we can use those as they are written.
    • 1 rewritten as a fraction can be 1/1.
    • 3 5/8 is the same as (3/1) + (5/8). Using the formula for adding fractions, ((n1*d2)+(n2*d1)) / (d1*d2), we get ((3*8)+(5*1)) / (1*8) = 29/8
    • Input rewritten as fractions is:  1/1, 1/2, 3/4, 29/8, -12/16
  • Now find the least common denominator (LCD) (or the least common multiple (LCM) of the denominators)
    • LCD = 16
  • Rewriting the fractions as equivalent fractions using the LCD
    • 16/16, 8/16, 12/16, 58/16, -12/16
  • Order these fractions from least to greatest numerator
    • -12 < 8 < 12 < 16 < 58 or
    • -12/16 < 8/16 < 12/16 < 16/16 < 58/16
  • Now ordering our original input to match (note that you will need to keep track of of which input corresponds to which equivalent fractions)
    • -12/16 < 1/2 < 3/4 < 1 < 3 5/8
 

Cite this content, page or calculator as:

Furey, Edward "Ordering Fractions Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.