How to use
Use this page to decide which of two fractions is greater, or whether they are equal. It compares a single pair rather than sorting a list. This helps when checking portions, probabilities or signed rational values without rounding them first.
Type an integer, a fraction such as 7/12, or a mixed number such as -2 1/3. Put one space between the whole and fractional parts. The leading minus sign applies to the entire mixed number: -2 1/3 means -(2 + 1/3), not -2 + 1/3. Use 0 for zero. For an ordinary fraction the denominator may be negative; the answer moves that sign to the numerator.
Examples appear in gray and work directly with Calculate. Focusing any numeric field clears all examples together. If you leave the numeric fields without entering anything, the examples return. Once you type or paste in any field, examples will not return, even if you delete that entry. Your own values use the normal dark text. Empty or invalid inputs leave an unfinished diagram with axes and no calculated points. Valid values update the diagram. Calculate confirms the detailed result for copying; editing invalidates that confirmed result. Clear empties the inputs without restoring examples.
Method and interpretation
After normalization, both denominators are positive. Compare the exact integer cross-products ad and bc for A = a/b and B = c/d. Multiplying both values by the same positive denominator product preserves order. The result uses <, > or =, and the calculation shows the two integers that establish it. The common number line adds a visual interpretation without deciding the result.
The drawing uses a bounded scale and never creates one element for every denominator unit. Labels occupy separate rows, so equal or very close values may share a horizontal position without hiding their names. The exact fraction text is authoritative. A small gap on the drawing is not evidence that two fractions are equal. Use the picture to understand position and sign, and the arithmetic to establish an exact answer.
Examples
5/8 > 7/12 because 5 × 12 = 60 and 7 × 8 = 56. The denominators differ, so comparing 5 and 7 alone would give the wrong conclusion.
-3/4 < -2/3 because -3 × 3 = -9 and -2 × 4 = -8. On the number line, the more negative value lies farther to the left.
Limits and troubleshooting
Each integer component accepts at most 100 digits, excluding its sign. Decimal input, thousands separators, expressions and variables are outside this page. For mixed numbers, use a positive denominator and a fractional numerator smaller than that denominator. Rewrite 2 5/3 as 3 2/3 or 11/3. A denominator of zero is always invalid; change it to the intended nonzero value before calculating.
Frequently asked questions
Can different fractions be equal?
Yes. For 2/3 and 4/6 the cross-products match. The result is equality even though the input notation differs.
Are large fractions compared as decimals?
No. The comparison uses exact integers throughout, including values beyond ordinary floating-point integer precision.
Why do unequal points look aligned?
Finite screen resolution can merge very close positions. Read the exact inequality and cross-products rather than inferring equality from the drawing.
How are negative denominators handled?
Their signs move to the numerators before comparison, making the shared denominator product positive.