Fraction calculator
Add, subtract, multiply or divide two fractions or mixed numbers. The answer is simplified and shown as an improper fraction, a mixed number and a decimal, with every step of the working.
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First fraction
Leave empty (or 1) for a whole number. Cannot be 0.
Second fraction
Leave empty (or 1) for a whole number. Cannot be 0.
Result
9/4 = 2 1/4
Result (simplified)
- Calculation1 1/2 + 3/4 = 9/4
- Improper fraction9/4
- Mixed number2 1/4
- Decimal2.25
How the answer was found
Mixed numbers are first turned into improper fractions. To add or subtract, both fractions are rewritten over the least common denominator (LCD); to multiply, numerators and denominators are multiplied; to divide, you multiply by the reciprocal of the second fraction. The result is then reduced by the greatest common divisor (GCD).
Step-by-step working
| Step | Working |
|---|---|
| 1. Write as improper fractions | 1 1/2 = (1×2 + 1)/2 = 3/2 |
| 2. Find the least common denominator | LCD(2, 4) = 4 |
| 3. Rewrite over the LCD | 3/2 = 6/4 |
| 4. Add the numerators | (6 + 3)/4 = 9/4 |
| 5. Simplify with the GCD | GCD(9, 4) = 1 → already in lowest terms |
| 6. Convert to a mixed number | 9/4 = 2 1/4 |
| 7. Convert to a decimal | 9/4 = 2.25 |
About this tool
How to add and subtract fractions
Fractions can only be added or subtracted when they share a denominator. Find the least common denominator (LCD), the smallest number both denominators divide into, rewrite each fraction over it, then add or subtract the numerators. Example: 1/2 + 3/4 → LCD 4 → 2/4 + 3/4 = 5/4 = 1 1/4.
How to multiply and divide fractions
To multiply, multiply the numerators together and the denominators together: 2/3 × 3/4 = 6/12 = 1/2. To divide, flip the second fraction (its reciprocal) and multiply: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3. You can't divide by a fraction equal to zero.
Mixed numbers and improper fractions
A mixed number such as 1 1/2 is turned into an improper fraction by multiplying the whole number by the denominator and adding the numerator: (1 × 2 + 1)/2 = 3/2. To go back, divide: 9/4 = 2 remainder 1, so 2 1/4.
Simplifying
Every answer is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD): 6/12 has GCD 6, so it becomes 1/2. Need a percentage instead? Use the percentage calculator, or compare quantities with the ratio calculator.
Formula
a/b + c/d = (a·d + c·b) / (b·d), or use the LCD of b and da/b − c/d = (a·d − c·b) / (b·d)a/b × c/d = (a·c) / (b·d)a/b ÷ c/d = a/b × d/c = (a·d) / (b·c), c ≠ 0Mixed number w n/d = (w·d + n) / dSimplify: divide numerator and denominator by GCD(numerator, denominator)
How it is calculated
- Enter the first fraction: an optional whole number, the numerator and the denominator.
- Choose the operation: add, subtract, multiply or divide.
- Enter the second fraction the same way (leave the whole number empty for a simple fraction).
- Read the simplified result as an improper fraction, mixed number and decimal, with the full working below.
Questions
How do you add fractions with different denominators?
Rewrite both fractions over the least common denominator, then add the numerators. For 1/3 + 1/4 the LCD is 12, so 4/12 + 3/12 = 7/12.
How do you divide fractions?
Keep the first fraction, flip the second one and multiply: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. Dividing by a fraction equal to zero is undefined.
How do I convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator: 17/5 = 3 remainder 2, so 3 2/5.
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For 18/24 the GCD is 6, so 18/24 = 3/4. When the GCD is 1 the fraction is already in lowest terms.