Compare & Order Fractions
Compare and order up to four fractions from smallest to largest, showing decimal equivalents and the LCD. Leave unused fields at 0.
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How to use this calculator
- 1
Enter up to four fractions — numerator and denominator for each. Set numerator to 0 to skip a slot.
- 2
The fractions are ordered from smallest to largest with their decimal values.
- 3
The LCD is computed and each fraction is rewritten with the LCD as denominator.
Frequently asked questions
How do I skip a fraction I don’t need?
Set its numerator to 0 in slots 2, 3 or 4. Those slots are then ignored, which is why the default has a fourth fraction of 0/1 that does not appear in the result. Slot 1 is never skipped. If its numerator is 0, it is treated as the fraction 0/d and appears in the ordering.
Why can I not compare a fraction equal to zero in slots 2 to 4?
Because a zero numerator is the skip signal there. To compare against zero, place 0 in slot 1, for example 0/5 and 1/3, which the calculator orders as 0/5 < 1/3 with an LCD of 15. A slot with zero numerator in positions 2 to 4 is dropped before sorting.
What counts as an error?
A zero denominator in any slot that is in use, decimals or other non-whole numbers in numerators or denominators, or fewer than two usable fractions. A zero denominator in a skipped slot (numerator 0) is ignored. Enter decimals as fractions first, for example 0.75 as 3/4.
What does the LCD mean here, and is it always the smallest possible?
It is the least common multiple of the denominators exactly as you typed them. For 1/2, 2/5 and 3/7 it is 70, and the fractions become 35/70, 28/70 and 30/70. Fractions are not reduced first, so 2/4 and 1/2 give an LCD of 4, which is not the smallest denominator that would show their equality.
How are equal fractions shown in the ordering?
With an equals sign instead of a less-than sign. Entering 1/2 and 2/4 gives "1/2 = 2/4", with decimals 0.5 for both. Comparison uses cross-multiplication on whole numbers, so ties are not distorted by decimal rounding.
Can it compare negative fractions?
Yes. Put the minus on the numerator or on the denominator. A negative denominator is moved to the numerator before comparing, so 1/−3 is treated as −1/3. 1/3 against −1/2 returns −1/2 < 1/3 with LCD 6, written as −3/6 and 2/6.
Are the decimals exact?
They are rounded to six places, so 3/7 shows as 0.428571 and 2/3 as 0.666667. The order itself does not rely on those decimals. The LCD versions (numerators over the common denominator) are exact integers.
Does it simplify fractions or handle mixed numbers?
No. It does not reduce fractions to lowest terms, and it has no field for mixed numbers. Convert 1 3/4 to the improper fraction 7/4 before entering it.
Compare and order fractions — LCD and sorted results
How the comparison is made
To compare a/b with c/d without decimals, cross-multiply: a/b is smaller than c/d exactly when a × d is smaller than c × b (for positive denominators). The calculator sorts that way, then finds the least common denominator, which is the least common multiple of all the denominators, and rewrites every fraction over it. Equal numerators over the same denominator are easy to read: the larger numerator is the larger fraction.
| Slot | Numerator 0 | Denominator 0 |
|---|---|---|
| 1 | Kept, treated as 0/d | Error |
| 2 to 4 | Slot skipped | Error if numerator is not 0 |
Worked examples
Each case is a run of the calculator.
| Fractions | Order, smallest first | LCD | Over the LCD |
|---|---|---|---|
| 1/2, 2/5, 3/7 | 2/5 < 3/7 < 1/2 | 70 | 28/70, 30/70, 35/70 |
| 3/4, 5/8, 7/10, 2/3 | 5/8 < 2/3 < 7/10 < 3/4 | 120 | 75, 80, 84, 90 over 120 |
| 5/6, 7/9, 11/12 | 7/9 < 5/6 < 11/12 | 36 | 28/36, 30/36, 33/36 |
| 1/2, 2/4 | 1/2 = 2/4 | 4 | 2/4, 2/4 |
Why the answer can be surprising
People often compare 3/7 and 1/2 by looking at the numerators and denominators separately, which does not work. Over a common denominator of 70 the same fractions are 30/70 and 35/70, which settles it: 3/7 is smaller. The default set shows another trap, because 2/5 has a larger denominator than 1/2 and the smaller value, while 3/7 sits in the middle. A larger denominator makes each piece smaller, but only for a fixed numerator.
Negative values and zero
A negative fraction is always smaller than a positive one. Entering 1/3 and −1/2 returns −1/2 < 1/3, with LCD 6 and values −3/6 and 2/6. Zero is only comparable from slot 1, since a zero numerator in slots 2 to 4 means the slot is skipped. Putting 0/5 first and 1/3 second gives 0/5 < 1/3 over an LCD of 15.
Limits of the LCD shown
The LCD is computed from the denominators as typed, without reducing each fraction. If you enter 2/4 and 1/2, you see 4 rather than 2. Reduce fractions yourself first when you want the smallest possible common denominator for a worksheet answer. Inputs must be whole numbers, and the form orders at most four fractions at a time. The LCD can grow quickly when the denominators share no factors: denominators of 7, 9, 11 and 13 would already need 9009, so expect large numerators in the rewritten fractions.
Learn more from an authoritative source:
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