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Fraction Calculator

Free fraction calculator with step-by-step working. Add, subtract, multiply, divide and simplify fractions or mixed numbers — instant decimal and percentage.

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* lcm = least common multiple

How to Calculate Fractions?

Fractions represent parts of a whole number. They consist of a numerator (top number) and a denominator (bottom number). Understanding fraction operations is essential for many mathematical calculations.

Adding Fractions:

  • Find a common denominator for both fractions
  • Convert both fractions to have the same denominator
  • Add the numerators and keep the common denominator

3/4 + 1/2 = (3×2 + 1×4)/(4×2) = 10/8 = 5/4

Multiplying Fractions:

  • Multiply the numerators together
  • Multiply the denominators together

5/6 × 2/3 = (5×2)/(6×3) = 10/18 = 5/9

Simplifying Fractions:

  • Find the greatest common divisor (GCD) of numerator and denominator
  • Divide both numerator and denominator by the GCD

12/18 = (12÷6)/(18÷6) = 2/3

Common fraction values

FractionDecimalPercentage
1/20.550%
1/30.333...33.33%
1/40.2525%
1/50.220%
2/30.666...66.67%
3/40.7575%
4/50.880%

About this fraction calculator

Use this calculator for any of the four fraction operations — addition, subtraction, multiplication and division — on either simple fractions like 3/4 or mixed numbers like 1 1/2. Every result is automatically reduced to its lowest terms using the greatest common divisor, and the equivalent decimal value is shown alongside the fraction. The step-by-step box below the result shows exactly which common denominator was used and how each numerator was scaled, so the calculator works as both a fast answer machine and a study aid.

Frequently Asked Questions

Find the least common denominator (LCD) of the two fractions, rewrite each fraction with that denominator, then add the numerators. For example, 1/3 + 1/4: the LCD is 12, so 1/3 becomes 4/12 and 1/4 becomes 3/12. The sum is (4 + 3)/12 = 7/12. This calculator does the LCD step for you and shows the working in the calculation steps box.

Subtraction works exactly like addition once the denominators match. Find the LCD, rewrite each fraction, then subtract the numerators while keeping the common denominator. Example: 5/6 − 1/4 → LCD = 12, so 10/12 − 3/12 = 7/12. If the result has a common factor with the denominator, simplify it (here 7/12 is already in lowest terms).

Multiply the numerators together to get the new numerator, multiply the denominators together to get the new denominator, then simplify. Example: 2/3 × 4/5 = (2×4)/(3×5) = 8/15. You can also cancel common factors before multiplying to keep the numbers smaller — for instance 3/8 × 4/9 simplifies to 3/8 × 4/9 → (1/2)·(1/3) = 1/6 after cancelling the 4 with 8 and the 3 with 9.

Dividing by a fraction is the same as multiplying by its reciprocal — flip the second fraction (swap its numerator and denominator) and multiply. Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8 as a mixed number. The classic mnemonic is 'keep, change, flip': keep the first fraction, change the operation to multiplication, and flip the second.

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. Example: 18/24 — GCD(18, 24) = 6, so 18/24 = (18÷6)/(24÷6) = 3/4. This calculator simplifies every result automatically; the simplified fraction is what appears in the result row, and the decimal value next to it confirms equivalence (3/4 = 0.75).

A mixed number combines a whole number with a fraction, like 2 1/3. To convert it into an improper fraction, multiply the whole number by the denominator and add the numerator: 2 × 3 + 1 = 7, giving 7/3. To go the other way (improper → mixed), divide the numerator by the denominator: 7/3 → quotient 2, remainder 1, so 2 1/3. Turn on the 'Mixed Fractions' switch to enter and read results in mixed form.

Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75, and 0.75 × 100 = 75%. Some fractions produce repeating decimals — 1/3 = 0.333..., 2/7 = 0.285714... — in which case the calculator rounds to several decimal places. The reference table at the bottom of the page lists the most common values (halves, thirds, quarters, fifths) so you can look them up without computing.

Recipes scale up or down with fractions (doubling 3/4 cup of sugar means 1 1/2 cups). Construction and woodworking use fractional inches constantly (a board that is 2 3/8 inches plus a 1/2-inch cleat is 2 7/8 inches thick). Financial calculations like compounded discounts (taking 1/3 off and then another 1/4 off the reduced price) need fraction multiplication. Music time signatures, gear ratios, and odds in probability are all fractions in disguise.
Fraction Calculator — Free fraction calculator with step-by-step working. Add, subtract, multiply, divide and simplify fractions or mixed numb
Fraction Calculator
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