Fraction Calculator
A fraction calculator simplifies one of the most common pain points in arithmetic — performing operations on fractions with different denominators. Whether you are adding cooking measurements, solving algebra problems, or splitting quantities, this tool handles the full calculation instantly. It shows the result as a fraction, simplifies it to lowest terms, and converts to decimal so you can cross-check your answer easily.
Fraction Bar Visual
How to Use the Fraction Calculator
- Select the operation tab — Add, Subtract, Multiply, or Divide — at the top of the calculator. The operator symbol between the fractions updates automatically, so you can confirm the selected operation before entering values.
- Enter the numerator and denominator for the first fraction on the left. The numerator is the top number, and the denominator is the bottom number. Negative numerators are allowed for values such as -3/4.
- Enter the numerator and denominator for the second fraction on the right. Denominators cannot be zero because division by zero is undefined in arithmetic.
- Click Calculate, or edit any field to update automatically. The result appears as an unsimplified fraction, simplified fraction, decimal, and mixed number when applicable.
- Read the step-by-step working box below the result. It shows the LCM method for addition and subtraction, direct multiplication for products, and the reciprocal rule for division.
Fraction Formulas
Subtraction: a/b - c/d = (ad - bc) / bd
Multiplication: a/b x c/d = ac / bd
Division: a/b ÷ c/d = a/b x d/c = ad / bc
Addition and subtraction require the fractions to describe pieces of the same size. That is why the calculator first finds a common denominator, usually the least common multiple of the two denominators. After converting both fractions to equivalent fractions with that denominator, only the numerators are added or subtracted. Multiplication is more direct: multiply the numerators together and multiply the denominators together. Division uses the reciprocal of the second fraction, meaning the second fraction is flipped before multiplication. After any operation, the result should be simplified. Simplification divides the numerator and denominator by their greatest common divisor, or GCD. The GCD is the largest whole number that divides both values exactly. This page uses the Euclidean algorithm for that step, repeatedly taking remainders until the remainder is zero.
Worked Example
Problem: 3/4 + 2/3. Step 1: find the least common multiple of 4 and 3. The LCM is 12. Step 2: convert 3/4 to twelfths by multiplying top and bottom by 3, giving 9/12. Step 3: convert 2/3 to twelfths by multiplying top and bottom by 4, giving 8/12. Step 4: add the numerators: 9 + 8 = 17, so the result is 17/12. Step 5: simplify. GCD(17, 12) is 1, so the fraction is already in lowest terms. Step 6: convert to a mixed number: 1 and 5/12. Step 7: convert to decimal: 17 ÷ 12 = 1.416667. Answer: 3/4 + 2/3 = 17/12 = 1 5/12.
Common Fraction Reference Table
| Fraction | Simplified | Decimal | Percentage |
|---|---|---|---|
| 2/4 | 1/2 | 0.5 | 50% |
| 3/6 | 1/2 | 0.5 | 50% |
| 4/8 | 1/2 | 0.5 | 50% |
| 2/6 | 1/3 | 0.333 | 33.33% |
| 3/4 | 3/4 | 0.75 | 75% |
| 4/6 | 2/3 | 0.667 | 66.67% |
| 5/10 | 1/2 | 0.5 | 50% |
| 6/9 | 2/3 | 0.667 | 66.67% |
| 3/12 | 1/4 | 0.25 | 25% |
| 8/12 | 2/3 | 0.667 | 66.67% |
Fraction Calculator FAQ
What is a fraction
A fraction represents part of a whole or a ratio between two quantities. The top number is the numerator, which tells how many parts are being considered. The bottom number is the denominator, which tells how many equal parts make up the whole. For example, 3/4 means three parts out of four equal parts. A proper fraction has a numerator smaller than the denominator, such as 2/5. An improper fraction has a numerator equal to or larger than the denominator, such as 7/4. A mixed number combines a whole number and a fraction, such as 1 3/4.
How do you add fractions with different denominators
To add fractions with different denominators, first find a common denominator. The most efficient common denominator is usually the least common multiple of the two denominators. Convert each fraction to an equivalent fraction using that denominator, then add only the numerators. For example, to add 1/4 and 1/6, the LCM of 4 and 6 is 12. Convert 1/4 to 3/12 and 1/6 to 2/12. Then add 3 + 2 to get 5/12. The denominator stays 12 because the parts are now the same size.
What is a simplified or reduced fraction
A simplified fraction is a fraction written in lowest terms. That means the numerator and denominator have no common factor greater than 1. For example, 12/18 can be reduced because both numbers are divisible by 6. Dividing 12 and 18 by 6 gives 2/3, which is the simplified form. Simplifying does not change the value of the fraction; it only writes the same value more clearly. This is why school answers, recipe adjustments, and algebra steps usually expect simplified fractions. The calculator uses the greatest common divisor to reduce answers automatically.
How do you divide fractions
Dividing fractions uses the reciprocal rule, often remembered as “keep, change, flip.” Keep the first fraction, change division to multiplication, and flip the second fraction. For example, 3/4 ÷ 2/5 becomes 3/4 × 5/2. Then multiply the numerators to get 15 and the denominators to get 8, so the result is 15/8. The reciprocal works because dividing by a fraction asks how many groups of that fractional size fit into the first quantity. Division by a zero numerator is not allowed because it would mean dividing by zero.
What is the difference between a proper fraction and an improper fraction
A proper fraction is less than one whole because its numerator is smaller than its denominator. Examples include 1/2, 3/5, and 7/10. An improper fraction is equal to or greater than one because its numerator is at least as large as its denominator. Examples include 5/4, 9/8, and 12/6. Improper fractions are often converted into mixed numbers for readability. For example, 17/12 is the same as 1 5/12. Both forms are mathematically correct, but improper fractions are often easier in algebra while mixed numbers are easier in everyday measurement.