Fraction operations and reducing to lowest terms
A fraction represents a numerator divided by a nonzero denominator. This calculator performs addition, subtraction, multiplication, and division, then simplifies the result by dividing the numerator and denominator by their greatest common divisor.
Why addition differs from multiplication
For addition and subtraction, use a common denominator: a/b + c/d = (ad + bc)/(bd). For multiplication, multiply numerators and denominators: (a/b)(c/d) = ac/bd. To divide by a fraction, multiply by its reciprocal: (a/b) ÷ (c/d) = ad/bc, provided the divisor is not zero.
Worked example
1/2 + 1/3 = 3/6 + 2/6 = 5/6. By contrast, 1/2 × 1/3 = 1/6. Enter whole-number numerators and denominators for conventional fractions; denominators cannot be zero, and division is undefined when the second fraction equals zero.
Tips for accurate results
To add or subtract fractions, convert them to a common denominator first. To multiply, multiply numerators and denominators across. To divide, multiply by the reciprocal of the second fraction. Reduce the answer by dividing the top and bottom by their greatest common divisor, and convert improper fractions to mixed numbers if you prefer.
Common mistakes and limits
A frequent error is adding the denominators, as in 1/2 + 1/3 = 2/5, when the correct result is 5/6. Another is forgetting to convert mixed numbers to improper fractions before multiplying or dividing. Check your answer by estimating it as a decimal.