Fraction Calculator
Add, subtract, multiply, or divide any two fractions or mixed numbers. Type each fraction naturally — for example 1 2/3 for one and two-thirds, or 3/4 for three-quarters. The calculator shows the full step-by-step solution and the result in both improper and mixed number form.
Calculate
Result
Step-by-Step Solution
How to Enter Fractions
This calculator accepts fractions in all common written forms:
| What you mean | Type this |
|---|---|
| Three-quarters | 3/4 |
| One and two-thirds | 1 2/3 |
| Negative five-eighths | -5/8 |
| Negative two and a half | -2 1/2 |
| Whole number five | 5 |
How the Calculator Works
Adding and Subtracting
To add or subtract fractions with different denominators, both fractions must first be rewritten with a common denominator. This calculator uses the Least Common Denominator (LCD), which is the smallest multiple shared by both denominators. Once the denominators match, the numerators are added or subtracted and the result is simplified to lowest terms.
For mixed numbers like \(1\,\dfrac{2}{3}\), the calculator converts them to improper fractions first (\(\dfrac{5}{3}\)), performs the operation, then converts the result back to mixed number form if applicable.
Multiplying
Multiplying fractions requires no common denominator. The numerators are multiplied together and the denominators are multiplied together:
$$\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d}$$The result is then simplified by dividing both the numerator and denominator by their greatest common divisor.
Dividing
Dividing by a fraction is the same as multiplying by its reciprocal. The second fraction is flipped (numerator and denominator swapped) and then multiplied:
$$\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c} = \dfrac{a \times d}{b \times c}$$Simplifying the Result
Every result is reduced to lowest terms using the Euclidean algorithm to find the Greatest Common Divisor (GCD). If the result is an improper fraction (numerator larger than denominator), it is also shown as a mixed number.
Related Calculators
Need to work with fractions in a different way? Try these related tools:
- Simplify Fraction — reduce any fraction to its lowest terms with a step-by-step GCD walkthrough
- Fraction to Decimal Calculator — convert any fraction or mixed number to its decimal equivalent
- Decimal to Fraction Calculator — convert a decimal back to a fraction in lowest terms
Frequently Asked Questions
- Can I use whole numbers?
- Yes. Enter any whole number and it will be treated as a fraction with denominator 1.
For example, entering
5is the same as \(\dfrac{5}{1}\). - What happens if I divide by zero?
- The calculator will display an error. A fraction with a denominator of zero is mathematically undefined.
- Are the results always in lowest terms?
- Yes. Every result is automatically simplified by dividing both parts by their GCD.
- Does it handle negative fractions?
- Yes. Put a minus sign in front of either value — for example
-3/4or-1 2/3. - What is the difference between an improper fraction and a mixed number?
- An improper fraction has a numerator larger than its denominator (e.g. \(\dfrac{7}{4}\)). A mixed number expresses the same value as a whole number plus a proper fraction (e.g. \(1\,\dfrac{3}{4}\)). Both representations are shown in the result.
