Fraction Calculator Examples
Practice adding, subtracting, multiplying, dividing, and simplifying fractions.
Quick Answer
a/b + c/d = (ad + bc)/(bd); a/b ÷ c/d = ad/(bc)When to Use This
Choose the operation before manipulating denominators. Addition needs equal-sized parts; multiplication combines factors; division asks how many of one fraction fit into another. All input denominators must be nonzero.
Step-by-Step Method
- Enter each numerator and nonzero denominator.
- For addition/subtraction, rewrite the fractions over a common denominator.
- For multiplication multiply numerators and denominators; for division multiply by the reciprocal of the nonzero second fraction.
- Reduce the final fraction by its greatest common divisor.
Calculator Tips and Limits
- Use the operator selector in the fraction tool rather than changing denominators to imitate a different operation.
- An improper fraction is a valid exact answer; a mixed number is another display of the same value.
Worked Examples
Add unequal denominators
2/3 + 3/4 becomes 8/12 + 9/12. Add the numerators to get 17/12, or 1 5/12. Since the inputs are each below 1 and total above 1, this size is plausible.
Divide the same inputs
(2/3) ÷ (3/4) = (2/3) × (4/3) = 8/9. Check by multiplying back: (8/9) × (3/4) = 24/36 = 2/3.
Common Mistakes
Adding the denominators
2/3 + 3/4 is not 5/7. Convert to equal-sized parts and retain the common denominator.
Dividing by a zero fraction
A fraction such as 0/5 is zero, so it cannot be the divisor even though its own denominator is valid.
FAQ
Must I use the least common denominator?
No, any common multiple works. The least common denominator usually keeps the numbers smaller.
Can I simplify before multiplying?
Yes. Cancel common factors across the product before multiplying, provided you divide a numerator and denominator by the same nonzero factor.
References and corrections
OpenStax: Prealgebra 2e — further reading. The worked examples on this page are CalcSolver explanations. Read our calculation and correction method, or report an error with the input and expected result.