How to use
Use this page to check a two-fraction calculation in homework, a recipe adjustment or a measurement. Enter A and B, select the arithmetic sign, then calculate. The operand order matters for subtraction and division.
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
For a/b ± c/d, form (ad ± bc)/(bd). Multiplication gives ac/(bd). Division multiplies by the reciprocal, ad/(bc), and requires c ≠ 0. The displayed calculation retains the intermediate numerator and denominator, then divides both by their greatest common divisor. The number line locates both operands and the reduced answer on the same scale.
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
1/6 + 3/4 = 11/12. The cross-products give (4 + 18)/24 = 22/24, which reduces by 2. This is useful when adding portions expressed with different denominators.
-2 1/3 ÷ 7/9 = -3. First rewrite A as -7/3; multiplying by 9/7 gives -63/21. Dividing a negative value by a positive value keeps the result negative.
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
Why are denominators not added?
They measure the size of a part. Addition requires equal-sized parts, so denominators are combined before the numerators are added.
Can I divide by 0/5?
No. Although its denominator is valid, that entire fraction equals zero and has no reciprocal.
Does a mixed answer replace the exact fraction?
No. Both representations express the same rational value. Use whichever fits your next step.
Does the drawing show multiplication as area?
No. It shows operand and result positions. Use the calculation steps for the operation itself.