Fraction calculator

Add or subtract with a shared denominator

For 1/2 + 1/3, enter 1 and 2 for the first fraction, then 1 and 3 for the second. Select +. Halves and thirds first become sixths: changing a denominator requires changing its numerator by the same factor. Adding the denominators would give the wrong answer.

For 5/6 - 1/4, use twelfths. Keep the order of the fields when subtracting: reversing the two fractions changes the sign of this answer.

• 1/2 + 1/3 = 3/6 + 2/6 = 5/6
• 5/6 - 1/4 = 10/12 - 3/12 = 7/12

Keep the negative sign attached to the fraction

For -3/4, enter -3 in the first numerator field and 4 in its denominator. Adding 1/6 leaves a negative result that is closer to zero.

A negative denominator is supported too: 1/(-2) equals -1/2. The output moves the sign to the numerator so its denominator is positive. Two negative input fields make that fraction positive.

• -3/4 + 1/6 = -9/12 + 2/12 = -7/12
• 1/(-2) + 1/3 = -1/2 + 1/3 = -1/6

Multiply directly; divide by the reciprocal

Choose * to multiply. Multiply the numerators and denominators, then reduce by their greatest common divisor. Here -18/30 reduces to -3/5. No common denominator is needed.

Choose / to divide. Inverting the second fraction makes 3/4 divided by 2/3 equal 9/8. An answer larger than one is valid. The tool keeps the improper fraction; it does not automatically format this as 1 1/8.

• (-2/3) × (9/10) = -18/30 = -3/5
• 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8

Convert mixed numbers before entering them

There is no separate whole-number field. Convert 1 1/2 to (1 × 2 + 1)/2 = 3/2, and 2 1/3 to 7/3. Enter those four integers rather than typing “1 1/2” into one number field.

The result 23/6 is also 3 5/6: dividing 23 by 6 leaves remainder 5. That interpretation is shown here, not by the result formatter. For a negative mixed number, -(1 1/2) becomes -3/2.

• 1 1/2 + 2 1/3 → 3/2 + 7/3 = 9/6 + 14/6 = 23/6

Distinguish a zero value from an invalid denominator

A numerator may be zero: 0/5 is valid. A denominator may never be zero. When dividing, the second numerator must also be nonzero because division by 0/5 still means division by zero. The tool reports an error instead of infinity.

Each input must be an integer from -1,000,000 through 1,000,000. Do not enter decimal numerators, units or thousands separators. An empty field is not zero. Simplify an oversized fraction yourself before using the tool, then check all four inputs against these bounds.

• 0/5 + 0/7 = 0/1

Use the fraction when the decimal repeats

The output includes a reduced fraction and a decimal rounded to at most 12 significant digits. The decimal for 5/6 cannot show all its repeating sixes. Copying that decimal into another calculation uses a rounded value; keeping 5/6 preserves the intended fraction.

Check the operation, signs and four input fields before copying an answer. For a longer expression, handle one pair at a time and carry the fraction forward. These examples explain arithmetic; they do not infer measurement units or the tolerance of a physical project.