Reciprocal Calculator
This reciprocal calculator is able to determine the reciprocal of any number (except 0, of course).
Result2/3in lowest terms
Mixed number2/3
Decimal0.66666667
Percentage66.666667%
Reducing to lowest terms
| Original | 24/36 |
| Greatest common divisor | 12 |
| Divide both by 12 | 2/3 |
| Numerator factors | 2^3 × 3 |
| Denominator factors | 2^2 × 3^2 |
The method
divide both parts by their greatest common divisor
The rules in one place
- Adding and subtracting needs a common denominator first. The lowest common denominator keeps the numbers smallest, but any common denominator works.
- Multiplying needs no common denominator at all — multiply across the top and across the bottom.
- Dividing means multiplying by the reciprocal: flip the second fraction and multiply.
- Reducing divides top and bottom by their greatest common divisor. It never changes the value.
Why lowest terms matter
6/8 and 3/4 are the same number, but 3/4 is easier to compare, easier to check and conventional in an answer. Reducing also keeps later arithmetic small: multiplying unreduced fractions makes the numbers grow fast, and cancelling first avoids that.