Fraction Calculator Guide: Add, Subtract, Multiply & Divide Fractions with Steps
A fraction calculator adds, subtracts, multiplies, and divides fractions, and converts between mixed and improper forms. It also simplifies results using the greatest common divisor (GCD).
What is Fraction Calculator?
The fraction calculator handles arithmetic on exact rational numbers and returns simplified fractions (and decimals if requested). It is ideal for homework, woodworking, and recipes where exactness matters.
How to Use the Fraction Calculator
- Select operation (add, subtract, multiply, divide) or convert (mixed <-> improper).
- Enter fractions as
a/b
or mixedw a/b
. - Calculate to get a simplified fraction (and optional decimal).
- Show steps to see common denominators and reduction by GCD.
- Copy result into your worksheet or plan.
Formulas & Methods
- Addition/Subtraction:
a/b +- c/d = (ad +- bc) / bd
-> reduce bygcd(ad +- bc, bd)
- Multiplication:
a/b * c/d = ac / bd
(cancel common factors early). - Division:
a/b / c/d = a/b * d/c = ad / bc
(c, d != 0). - GCD (Euclid): while
b != 0
, set(a, b) <- (b, a mod b)
; result isa
. - Improper <-> Mixed:
w a/b = (wb + a)/b
;n/d = (n // d) + (n % d)/d
.
Assumptions & limitations
- Denominators must be non-zero.
- Results are reduced to lowest terms by GCD.
- Decimal views use specified precision; exact value remains rational.
Examples
Example A — Add
2/3 + 3/8 = (16 + 9)/24 = 25/24 = 1 1/24
.
Example B — Divide
5/6 / 10/9 = 5/6 * 9/10 = 45/60 = 3/4
.
| Operation | Input | Output |
|---|---|---|
| Subtract | 7/10 - 1/4
| 28/40 - 10/40 = 18/40 = 9/20
|
| Multiply | 3/5 * 5/12
| 15/60 = 1/4
|
| Convert | 17/5
| 3 2/5
|
Pro Tips & Best Practices
- Cross-cancel before multiplying to keep numbers small.
- Always reduce to lowest terms for clean answers.
- Convert mixed numbers to improper before operations to avoid mistakes.
- Keep units consistent when fractions represent measurements (inches vs cm).
Related Calculators
FAQ
Q: How do I add or subtract fractions?
A: Find a common denominator, convert each fraction, then add/subtract numerators and simplify.
Q: How do I multiply fractions?
A: Multiply numerators together and denominators together; simplify before or after.
Q: How do I divide fractions?
A: Multiply by the reciprocal of the divisor: a/b / c/d = a/b * d/c.
Q: How do I simplify a fraction?
A: Divide numerator and denominator by their greatest common divisor (GCD).
Q: Can I convert to/from mixed numbers?
A: Yes—improper <-> mixed conversions are supported.
Call to Action
Enter two fractions or a mixed number and get a clean, simplified result—toggle steps to learn the method as you go.