Fraction Calculator
Add, subtract, multiply, and divide fractions. Get the simplified fraction, decimal value, mixed number, and calculation steps.
First fraction
Second fraction
Results
The Fraction Calculator adds, subtracts, multiplies, or divides two fractions and reduces the result. Fractions preserve exact ratios that a rounded decimal can hide, making them useful for measurements, recipes, algebra, and classroom work.
Why cross-multiplication works for addition
Addition and subtraction require a common denominator. Multiplication combines the numerators and denominators directly, while division multiplies by the reciprocal of the second fraction. The final numerator and denominator should be divided by their greatest common factor.
For addition, a/b + c/d = (ad + bc)/bd. For multiplication, multiply numerators and denominators; division multiplies by the reciprocal.
Enter the values in their mathematical roles
Enter each numerator and denominator with its sign, then choose the operation. Keep a negative sign attached to one part of the fraction rather than both. Review the unreduced result before simplification when you need to show the method.
The governing relationship
For addition, a/b + c/d = (ad + bc)/bd. For multiplication, multiply numerators and denominators; division multiplies by the reciprocal.
A compact example
2/3 + 1/4 = 8/12 + 3/12 = 11/12.
Valid inputs and boundary cases
A denominator can never be zero. Whole numbers may be written over 1, and mixed numbers should first be converted to improper fractions. When measurements use different units, convert them before combining the fractions.
Read the answer in context
Denominators cannot be zero, and a final fraction should be reduced by its greatest common factor.
An independent check
For addition, confirm the converted fractions represent the same original values. For division, multiply the answer by the divisor to recover the dividend. A decimal estimate can check whether the sign and magnitude are reasonable.
Errors that change the answer
- Adding denominators during fraction addition
- Forgetting to invert the divisor
- Cancelling terms across addition or subtraction
- Leaving a common factor in the final answer
- Using zero as a denominator
Continue with a related calculator
Continue with the Scientific Calculator or Mixed Number Calculator. For everyday arithmetic and order-of-operations checks, use the Basic Calculator.
What this numerical result cannot decide
The result is exact only when the entered fractions are exact. A fraction created from a rounded measurement does not restore lost precision. Word problems may also require a unit, mixed-number form, or interpretation beyond the arithmetic.
A second way to understand the method
The expression a/b + c/d becomes ad/bd + bc/bd because each fraction is multiplied by a form of 1. Once the denominators match, the numerators can be combined. Using the least common denominator can keep intermediate numbers smaller, but any nonzero common denominator produces an equivalent final fraction after reduction.
Reduce before multiplying when possible
In a product such as 14/15×25/28, common factors can be cancelled between a numerator and denominator before multiplication. Dividing 14 and 28 by 14, and 25 and 15 by 5, leaves 1/3×5/2=5/6. This keeps intermediate values small without changing the product. Cancellation is valid across multiplication, not across addition.
Fractions in measurement problems
Attach units to the final value and decide whether the context calls for a proper fraction, mixed number, or decimal. When adding lengths such as 2 3/8 in and 1 5/16 in, convert mixed numbers and find a common denominator before combining. Measurement tolerances may matter more than the exact arithmetic.
Fraction Calculator FAQ
Should the answer always be a proper fraction?
No. An improper fraction is valid and can also be written as a mixed number.
Can negative fractions be simplified?
Yes. Reduce the absolute values and place one negative sign in front of the fraction.
Why is my denominator larger after addition?
Creating a common denominator can enlarge intermediate values; reduction may make the final numbers smaller.
For additional worked mathematics, see the free OpenStax Prealgebra 2e reference.
