Fraction Calculator
Add, subtract, multiply, and divide fractions with full step-by-step solutions.
The fraction calculator performs addition, subtraction, multiplication, and division of fractions and mixed numbers, displaying results in simplified form, as a mixed number, as a decimal, and as a percentage. Each calculation includes a step-by-step solution showing the least common denominator, GCD simplification, and mixed number conversion — following standard secondary school curriculum methods.
How to Use the Fraction Calculator
- 1Enter the numerator and denominator for the first fraction using the stacked input boxes.
- 2Click Toggle Mixed number if your fraction includes a whole number component.
- 3Select the operation: +, -, times, or divide.
- 4Enter the second fraction in the same way.
- 5Click Calculate to see the simplified answer, mixed number form, decimal, and percentage.
- 6Expand Step-by-Step Solution to see the full working.
Worked Example: Adding Fractions with Unlike Denominators
Using the calculator's own default fractions, 1/2 + 3/4, the two denominators (2 and 4) don't match, so the tool first finds the least common denominator: LCD(2, 4) = 4.
Both fractions get rewritten over that denominator — 1/2 becomes 2/4, and 3/4 stays 3/4 — then the numerators add directly: 2/4 + 3/4 = 5/4. Since 5 and 4 share no common factor, that's already fully simplified.
The calculator also converts the result to a mixed number (1 1/4), a decimal (1.25), and a percentage (125.00%) — three different ways of expressing the exact same value, useful depending on whether you're handing the answer to a math teacher, a spreadsheet, or a recipe.
Worked Example: Multiplying Mixed Numbers
Multiplication works differently from addition, and mixed numbers add an extra step. Take 1 1/2 × 2/3. First, the mixed number 1 1/2 is converted to an improper fraction: (1 × 2 + 1)/2 = 3/2.
From there, multiplication is a straight-across operation — no common denominator needed. Multiply the numerators: 3 × 2 = 6. Multiply the denominators: 2 × 3 = 6. That gives 6/6, which simplifies (GCD = 6) to a clean 1 — displayed as 1/1, the whole number 1, the decimal 1, and 100.00%.
The key contrast with the addition example above: multiplying never required matching denominators. That step exists only for addition and subtraction.
The #1 Fraction Mistake: Adding (or Dividing) Straight Across
A very common shortcut students try — and the calculator's step-by-step view is designed to catch — is adding fractions the same way you multiply them: numerator plus numerator, denominator plus denominator. For 1/2 + 1/3, that wrong method gives (1 + 1)/(2 + 3) = 2/5 (0.4). The correct answer, found via the LCD of 6, is 3/6 + 2/6 = 5/6 (≈0.83) — a completely different value. The same instinct causes trouble in reverse with division: dividing fractions is not a straight-across operation either. Instead of dividing numerator by numerator, you flip the second fraction and multiply — 2/3 ÷ 4/5 becomes 2/3 × 5/4. Addition/subtraction need a common denominator first; multiplication and division never do, but division requires that extra flip step. Mixing up which rule applies to which operation is where most fraction errors come from.
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Frequently Asked Questions
How do you add fractions?
Find the Least Common Denominator (LCD). Convert each fraction to an equivalent fraction with the LCD. Add the numerators. Simplify by dividing by the GCD. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. Example: 2/3 x 3/4 = 6/12 = 1/2.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second. Example: 2/3 divided by 4/5 = 2/3 x 5/4 = 10/12 = 5/6.
What is a mixed number?
A mixed number combines a whole number and a fraction, like 2 and 1/2. Toggle Mixed number mode in this calculator to enter mixed numbers.
How do you simplify a fraction?
Divide both the numerator and denominator by their Greatest Common Divisor (GCD). Example: 6/8 with GCD of 2 simplifies to 3/4.