How to solve it
- Find the LCM of all the denominators.
- Convert each fraction to that denominator.
- Sort the numerators from smallest to largest.
- Write the original fractions in that order.
12 = 4 × 3 = 3 × 4 = 6 × 2
3/4 = 9/12, 2/3 = 8/12, 5/6 = 10/12
8 < 9 < 10
2/3 < 3/4 < 5/6
Result: 2/3 < 3/4 < 5/6
Common mistake:Wrong: 1/3 < 1/4 < 1/5.Right: 1/5 < 1/4 < 1/3.A larger denominator does not make a larger fraction: it cuts the whole into smaller parts.
To order fractions, compare them by value and arrange them from least to greatest or from greatest to least. Type the list, choose the direction, and you get each value with its reduced fraction next to it. If you only have two values and want to see the reasoning, use compare fractions.
Worked example: four measurements
Four measurements differ from a reference value, in inches: 1/2, 0.25, 2/3 and −1/4. Order them from least to greatest.
- Write everything as a fraction. 0.25 is 25/100, which reduces to one fourth.
- Find a common denominator. The LCM of 2, 4 and 3 is 12.
- Convert each value. You get 6/12, 3/12, 8/12 and −3/12.
- Sort the numerators. −3 < 3 < 6 < 8.
- Write each value back the way you had it, in that order.
Result: −1/4 < 0.25 < 1/2 < 2/3.
Check: as decimals they are −0.25, 0.25, 0.5 and 0.6667 (error less than 0.0001), in the same order.
Which method to use for your list
The calculator always compares exact values, but by hand it pays to pick the shortest route based on what the fractions have in common. The table covers the most frequent cases.
| List | What you do | Example |
|---|---|---|
| Same denominator | Sort the numerators | 1/7 < 3/7 < 6/7 |
| Same numerator | The larger the denominator, the smaller the fraction | 3/8 < 3/5 < 3/4 |
| Close to one half | Compare double the numerator with the denominator | 9/20 < 1/2 < 6/11 |
| Different denominators | Rewrite with a common denominator | 7/12 < 9/12 < 10/12, that is, 7/12 < 3/4 < 5/6 |
| Improper fractions and mixed numbers | Convert to improper fractions or to a common denominator | 5/3 < 7/4 < 2 1/3 |
In the one-half row, 9/20 falls below because 2 × 9 = 18 is less than 20, and 6/11 falls above because 2 × 6 = 12 is more than 11. It is a useful shortcut when one of the fractions is the reference. The guide to benchmark fractions develops it with more cases.
What happens when two values are equal
The entries 0.5, 1/2 and 2/4 are written differently and have the same value. The calculator does not delete any of them: it leaves them together and in the order you typed them. This is called a stable sort, and it helps when each entry matches an answer or a measurement you still need to recognize.
With the list 5/8; 0.5; 2/4; −1/4, least to greatest gives −1/4; 0.5; 2/4; 5/8. Greatest to least gives 5/8; 0.5; 2/4; −1/4. Below the result, a line shows the equivalent values grouped together.
How decimals and mixed numbers are combined
A terminating decimal is first turned into a fraction: 0.125 is 125/1000, which reduces to 1/8. That way no rounding can change the order of two very close values. A mixed number is compared by its total value, which is the whole part plus the fraction.
For example, 1.4 equals 7/5 and 1 4/5 equals 9/5, so 1.4 = 7/5 < 1 4/5. A negative mixed number is written with the sign in front of everything: −1 4/5 is −9/5, not −1 + 4/5. To see the positions to scale, there is the fraction number line, and to find a value in between, the fraction between two fractions page.
Where to go next
If you want the average of the list rather than its order, the average of fractions calculator adds the values and divides by how many there are. If you have a decimal and want to see its fraction, decimal to fraction reduces it. To practice without a calculator, the compare and order worksheets include exercises with answers.
Source: Wikipedia, article Fraction, section “Comparing fractions”, which covers the same-denominator and same-numerator cases and cross multiplication (accessed October 17, 2026).
Frequently asked questions
How do you order fractions from greatest to least?
Do the same as for least to greatest, but read the result backward. With 5/6, 7/9 and 17/24 the common denominator is 72, giving 60/72, 56/72 and 51/72, so 5/6 > 7/9 > 17/24. In the calculator, change the “Order” field to “Largest to smallest” and select “Calculate”.
How do you order negative fractions?
Negatives come first, and among them the one farthest from zero goes first. With −2/3, −3/4 and −1/6, in twelfths they are −8/12, −9/12 and −2/12, so −3/4 < −2/3 < −1/6. That is the left-to-right order on the fraction number line.
Can I order repeating decimals like 0.6̅?
Convert them to fractions first, because a few decimal places are not enough to decide. Since 0.6̅ = 2/3, and 2 × 100 = 200 is less than 67 × 3 = 201, 0.6̅ < 0.67. The repeating decimal to fraction calculator makes that conversion.
How do I order fractions with different denominators without finding the LCM?
Compare them in pairs with cross products. For 4/9 and 5/11 you multiply 4 × 11 = 44 and 5 × 9 = 45; since 44 is less, 4/9 < 5/11. With many fractions it is shorter to use a common denominator, which the least common denominator calculator gives you.