Math calculator
Fraction Calculator - Add, Subtract, Multiply & Divide
Add, subtract, multiply, or divide proper, improper, and negative fractions with simplified results and visible working steps.
Fraction arithmetic with working steps
Choose the operation, preserve the denominator rules, and simplify the result
Addition and subtraction need a common denominator. For a/b + c/d, cross-multiplication gives (ad + bc)/bd; the calculator then reduces the result by the greatest common divisor. For example, 3/4 + 2/5 becomes 15/20 + 8/20 = 23/20, or 1 3/20.
Multiplication works directly across the numerators and denominators. Division uses the reciprocal of the second fraction: 2/3 divided by 4/5 becomes 2/3 x 5/4 = 10/12 = 5/6. Division is undefined when the second fraction is zero.
Keep exact fractions while working instead of converting to rounded decimals too early. A negative sign can be entered with either part of a fraction, but a denominator can never be zero. Convert mixed numbers to improper fractions before entering them.
| Reference | Value or meaning |
|---|---|
| Add | a/b + c/d = (ad + bc) / bd |
| Subtract | a/b - c/d = (ad - bc) / bd |
| Multiply | a/b x c/d = ac / bd |
| Divide | a/b divided by c/d = ad / bc, where c is not zero |
| Simplify | Divide numerator and denominator by their greatest common divisor |
Checks before using the result
- Confirm that neither denominator is zero.
- Select the intended addition, subtraction, multiplication, or division operation.
- Convert mixed numbers such as 2 1/3 to improper fractions such as 7/3.
- Use the decimal result only as a convenience; retain the simplified fraction when an exact value matters.
Formulaa/b + c/d = (ad + bc) / bd; a/b x c/d = ac / bd; a/b divided by c/d = ad / bc
Formula
Fraction arithmetic formulas
a/b + c/d = (ad + bc) / bd; a/b x c/d = ac / bd; a/b divided by c/d = ad / bc
For addition, 1/2 + 1/3 = (1x3 + 1x2) / 6 = 5/6. For division, 2/3 divided by 4/5 = 10/12 = 5/6.
AssumptionsReview the assumptions and exclusions that define what this calculator does and does not include.
Assumptions and exclusions
Calculation notes
Review the assumptions and exclusions that define what this calculator does and does not include.
- Effective year
- Current rules
- Last verified
- 2026-06-18
Use calculator results as estimates and verify important decisions with official sources.
Assumptions
- Each denominator must be a nonzero whole number.
- The selected operation is applied to the two entered fractions before the result is reduced.
- Negative signs may be entered with either numerator and are normalized in the result.
Not included
- Decimal approximations beyond the displayed precision.
- Symbolic algebra containing variables.
- Undefined division by a zero fraction.
FAQ8 common questions for this calculator.
FAQs
Does the fraction calculator simplify results?+
Yes. It divides the result's numerator and denominator by their greatest common divisor so the final fraction is in lowest terms.
How do I add fractions with different denominators?+
Use a common denominator. The calculator cross-multiplies the numerators, combines them, and then reduces the resulting fraction.
How do I divide one fraction by another?+
Keep the first fraction, multiply by the reciprocal of the second fraction, and simplify. The second fraction cannot equal zero.
Can this calculator use negative fractions?+
Yes. Enter a negative numerator or denominator. The result is normalized so any negative sign appears with the numerator.
Can I enter mixed numbers?+
Convert each mixed number to an improper fraction first. For example, 1 1/2 becomes 3/2 before calculation.
How does the Fraction Calculator calculate the result?+
For the Fraction Calculator, it uses the Fraction arithmetic formulas: a/b + c/d = (ad + bc) / bd; a/b x c/d = ac / bd; a/b divided by c/d = ad / bc. For addition, 1/2 + 1/3 = (1x3 + 1x2) / 6 = 5/6. For division, 2/3 divided by 4/5 = 10/12 = 5/6.
What information do I need to use the Fraction Calculator?+
Enter the numerator and nonzero denominator for each fraction, then choose addition, subtraction, multiplication, or division. Convert mixed numbers to improper fractions before entering them.
How accurate is the Fraction Calculator?+
Fraction arithmetic is exact for integer numerators and nonzero integer denominators. The calculator reduces the result to lowest terms; only the optional decimal display can be rounded.
RelatedNearby math calculators for the next step after Fraction Calculator.
Math guide
How to use the Fraction Calculator
Choose addition, subtraction, multiplication, or division, then enter the two numerators and denominators. Read the exact simplified fraction first and use the decimal result only when an approximate form is useful.
- 1
Enter two fractions
Enter each numerator and a nonzero denominator. Convert mixed numbers to improper fractions before entering them.
- 2
Choose the operation
Select addition, subtraction, multiplication, or division. For division, the second fraction must not equal zero.
- 3
Check the simplified result
Review the working steps and reduced fraction. Keep the fraction form when an exact answer matters, and use the decimal as a secondary reference.