Putting several fractions in order is like comparing two, repeated: once every fraction is written with the same denominator, you just sort the numerators. This calculator accepts a list of fractions, mixed numbers and decimals, finds their least common denominator, rewrites each one, and returns the list in increasing or decreasing order.
How to use the calculator
- Type the values separated by commas or on separate lines. Mixed numbers use a space (1 1/6), negatives use a minus sign, and decimals are fine (0.6).
- Choose Least to greatest or Greatest to least.
- The tape shows the ordered list with < or > signs, the smallest and largest values, and the common denominator.
- The table gives each value as you typed it, in lowest terms, over the common denominator and as a decimal.
The method
- Convert mixed numbers and decimals to fractions in lowest terms.
- Find the LCD of all the denominators.
- Rewrite each fraction over the LCD.
- Sort by the new numerators.
- Write the answer using the original fractions.
Worked example
Order 3/4, 2/3, 5/8, 1 1/6, 7/12 from least to greatest.
- 1 1/6 = 7/6. The denominators are 4, 3, 8, 6 and 12.
- LCD = 24 (8 = 2³ and 3 = 3, so 2³ × 3 = 24).
- Rewrite: 3/4 = 18/24, 2/3 = 16/24, 5/8 = 15/24, 7/6 = 28/24, 7/12 = 14/24.
- Sort the numerators: 14 < 15 < 16 < 18 < 28.
- Answer: 7/12 < 5/8 < 2/3 < 3/4 < 1 1/6.
Shortcuts for quick checks
- Anything over 1 is larger than every proper fraction, so mixed numbers like 1 1/6 go at the end of an increasing list.
- Negative values come first, and among negatives the one farther from zero is smaller.
- Use 1/2 as a benchmark. Fractions whose numerator is less than half the denominator are below 1/2; this splits a list into two smaller groups.
- Same numerators: larger denominators mean smaller fractions, so 1/8 < 1/6 < 1/4.
Common mistakes
- Sorting by denominator alone. A larger denominator does not always mean a smaller fraction: 7/8 has a larger denominator than 2/3, yet it is the larger fraction. Always compare full values.
- Forgetting to scale the numerator. Rewriting 3/4 as ?/24 means multiplying the 3 by 6, not just changing the 4.
- Treating rounded decimals as exact. 0.67 is not equal to 2/3; type 2/3 if that is what you mean.
To compare just two fractions with cross-multiplication, use the comparing fractions calculator. The fractions number line shows the same order visually, and the average of fractions calculator finds the mean of a list.
Frequently asked questions
How do you order fractions from least to greatest?
Rewrite every fraction over a common denominator, usually the least common denominator, then order them by their numerators. For 3/4, 2/3 and 5/8 the LCD is 24, giving 18/24, 16/24 and 15/24, so the order is 5/8 < 2/3 < 3/4.
Can I mix fractions, decimals and mixed numbers?
Yes. Separate the values with commas or new lines; 1 1/6, 0.6 and −2/5 are all accepted. Each one is converted to an exact fraction before sorting, so 0.6 is treated as 3/5.
What if two fractions are equal?
They are placed next to each other with an equals sign between them, and they keep the order in which you typed them. For example 1/2, 2/4 and 0.5 all have the same value.
Is it faster to convert to decimals?
Often, yes, but repeating decimals such as 2/3 = 0.666… must be carried far enough to separate close values. The common-denominator method is exact and is the one most teachers ask for.