Quick answer
To add, subtract, multiply or divide fractions, enter the numerator and denominator of each fraction and choose the operation. The result is reduced to lowest terms and also shown as a decimal and a mixed number.
Fractions are combined with a few fixed rules. The calculator applies them exactly with whole-number arithmetic, so the answer is a true fraction rather than a rounded decimal.
Related tools: Inch Fraction Calculator: Convert decimal inches to the nearest fractional inch. Fraction to Decimal Calculator: Convert a fraction to a decimal, showing repeating digits. Percent to Fraction Calculator: Convert a percentage to a simplified fraction.
How to use the Fraction Calculator
- Enter numerator 1 (a whole number).
- Enter denominator 1 (a whole number). It starts at 1.
- Choose operation: + Add, − Subtract, × Multiply and ÷ Divide.
- Enter numerator 2 (a whole number).
- Enter denominator 2 (a whole number). It starts at 1.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Numerator 1 | A whole number | — |
| Denominator 1 | A whole number | starts at 1 |
| Operation | Choose one: + Add; − Subtract; × Multiply; ÷ Divide | Starts at + Add |
| Numerator 2 | A whole number | — |
| Denominator 2 | A whole number | starts at 1 |
Formula and method
Formula
a/b + c/d = (ad + bc)/bd; a/b × c/d = ac/bd; a/b ÷ c/d = ad/bc; then divide by the GCD
IEEE-754 double precision; shown to at most 6 decimal places.
Combine using the rule above, then reduce by the greatest common divisor and keep the denominator positive.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Numerator 1 = 1; Denominator 1 = 2; Operation = + Add; Numerator 2 = 1; Denominator 2 = 3.
| Result | Value |
|---|---|
| Result | 5/6 |
| Decimal | 0.833333 |
| Mixed number | 5/6 |
Example 2
Inputs: Numerator 1 = 3; Denominator 1 = 4; Operation = − Subtract; Numerator 2 = 1; Denominator 2 = 4.
| Result | Value |
|---|---|
| Result | 1/2 |
| Decimal | 0.5 |
| Mixed number | 1/2 |
Example 3
Inputs: Numerator 1 = 1; Denominator 1 = 2; Operation = ÷ Divide; Numerator 2 = 1; Denominator 2 = 4.
| Result | Value |
|---|---|
| Result | 2 |
| Decimal | 2 |
| Mixed number | 2 |
The first line is the headline result (result). Below it the fraction Calculator lists decimal and mixed number, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
The four rules
Each rule is followed by division of the numerator and denominator by their greatest common divisor.
| Operation | Rule |
|---|---|
| Add | a/b + c/d = (ad + bc) / bd |
| Subtract | a/b − c/d = (ad − bc) / bd |
| Multiply | a/b × c/d = ac / bd |
| Divide | a/b ÷ c/d = ad / bc |
Worked examples
1/2 + 1/3 = (1 × 3 + 2 × 1) / (2 × 3) = 5/6, which is 0.833333 as a decimal.
3/4 − 1/4 = (3 × 4 − 4 × 1) / (4 × 4) = 8/16, which reduces to 1/2 by dividing both numbers by 8.
How the result changes with numerator 1
Holding every other input at the first worked example, this table changes only numerator 1. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Numerator 1 | Result | Decimal | Mixed number |
|---|---|---|---|
| 1 | 5/6 | 0.833333 | 5/6 |
| 2 | 4/3 | 1.333333 | 1 1/3 |
| 4 | 7/3 | 2.333333 | 2 1/3 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Denominator 1: entering "0" shows "Denominator must not be 0." beside that field and no result.
- Numerator 2: entering "0" shows "Cannot divide by zero." beside that field and no result.
Choosing between the Fraction Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Inch Fraction Calculator](/math/inch-fraction-calculator/) | decimal inches and nearest | Nearest fraction |
| [Fraction to Decimal Calculator](/math/fraction-to-decimal-calculator/) | numerator and denominator | Decimal |
| [Percent to Fraction Calculator](/math/percent-to-fraction-calculator/) | percent | Fraction |
| [Fraction Simplifier](/math/fraction-simplifier/) | numerator and denominator | Simplified |
| [Decimal to Fraction Calculator](/math/decimal-to-fraction-calculator/) | decimal | Fraction |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- A denominator of 0 is invalid
- Dividing by a zero fraction is invalid
- Negative numerators are allowed
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for denominator 1 and numerator 2 to confirm this.
Frequently asked questions
How do you add fractions with different denominators?
Cross-multiply: a/b + c/d = (ad + bc)/bd, then reduce by the greatest common divisor. For 1/2 + 1/3 that gives 5/6.
Why does division by a fraction give an error sometimes?
Dividing by a fraction whose numerator is zero means dividing by zero, which is undefined, and a denominator of 0 is never allowed.
What does the Fraction Calculator calculate?
Add, subtract, multiply and divide fractions with simplified and mixed-number results. It returns Result, Decimal and Mixed number.
What formula does the Fraction Calculator use?
a/b + c/d = (ad + bc)/bd; a/b × c/d = ac/bd; a/b ÷ c/d = ad/bc; then divide by the GCD. Combine using the rule above, then reduce by the greatest common divisor and keep the denominator positive.
What do I need to enter in the fraction Calculator?
You enter Numerator 1, Denominator 1, Operation, Numerator 2 and Denominator 2.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. A denominator of 0 is invalid.
What are the limits of this calculator?
A denominator of 0 is invalid. Dividing by a zero fraction is invalid. Negative numerators are allowed.
What does the “Operation” option change?
It sets how the fraction is worked out. The choices are + Add, − Subtract, × Multiply and ÷ Divide.
What is an example of a fraction result?
With numerator 1 1, denominator 1 2, operation + Add, numerator 2 1 and denominator 2 3, the result is 5/6.
Related calculators
- Inch Fraction Calculator — Convert decimal inches to the nearest fractional inch.
- Fraction to Decimal Calculator — Convert a fraction to a decimal, showing repeating digits.
- Percent to Fraction Calculator — Convert a percentage to a simplified fraction.
- Fraction Simplifier — Reduce a fraction to lowest terms.
- Decimal to Fraction Calculator — Convert a terminating decimal to a simplified fraction.
- Fraction to Ratio Calculator — Convert a fraction to a ratio.
- Mixed Number to Fraction Calculator — Convert a mixed number to an improper fraction.
- Fraction to Mixed Number Calculator — Convert an improper fraction to a mixed number.
- Equivalent Fractions Calculator — Fractions equal to a given fraction.
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.