Adding and Subtracting Fractions Calculator

Add or subtract two fractions, even with different denominators. Enter each numerator and denominator and choose an operation to get the simplified result, mixed number, and decimal equivalent.

Quick Facts

Method
Least common denominator (LCD)
Both fractions are rewritten over the LCD of their denominators before the numerators are added or subtracted.
Simplifying
Divide by the GCD
The combined fraction is reduced to lowest terms by dividing numerator and denominator by their greatest common divisor.

Your Results

Calculated
Result (simplified)
-
Fraction in lowest terms
Mixed number
-
Whole number + proper fraction
Decimal equivalent
-
Rounded to 6 places
Common denominator
-
LCD used to combine the fractions

Ready

Enter two fractions and choose add or subtract, then press Calculate.

How the Adding and Subtracting Fractions Calculator works

This calculator adds or subtracts two fractions, even when they have different denominators, by converting both to a common denominator before combining the numerators. The result is automatically simplified to lowest terms and shown as a fraction, a mixed number, and a decimal.

Formula and method

To add or subtract two fractions a/b and c/d, first find the least common denominator (LCD) — the least common multiple of b and d. Rewrite each fraction over that denominator, then combine the numerators:

a/b ± c/d = (a·(LCD/b) ± c·(LCD/d)) / LCD

The LCD itself is found from LCD = (b × d) ÷ GCD(b, d), where GCD is the greatest common divisor of b and d. Once the numerators are combined over the LCD, the fraction is reduced by dividing both numerator and denominator by their GCD, and converted to a mixed number whenever the numerator is larger than the denominator.

Common sources of error

  • Adding the denominators directly: 1/2 + 1/3 is not 2/5 — denominators are never added or subtracted, only numerators once both fractions share a common denominator.
  • Using the product instead of the LCD: multiplying the denominators (b × d) always produces a valid common denominator, but not always the smallest one, which can leave the answer unsimplified.
  • Forgetting to simplify: a correct but unreduced answer like 6/8 should be simplified to 3/4 by dividing numerator and denominator by their GCD (2).

Checking your result

Convert the original fractions and your answer to decimals as a quick check: 3/4 (0.75) plus 1/6 (0.1667) should land close to 0.9167, matching 11/12. Also confirm the sign and size make sense — subtracting a positive fraction should produce a result smaller than the first fraction, and the denominator of the simplified answer must always divide evenly into the LCD you started with.

Applications

Adding and subtracting fractions comes up whenever a quantity is measured in parts of a whole: combining ingredient amounts in a recipe, adding lengths of wood measured in inches and fractions of an inch, tracking portions of a budget, or working through algebra and word problems in a classroom. Keep each numerator and denominator paired together as one number, and always finish by checking whether the result can be simplified further.

Frequently Asked Questions

How do you add fractions with different denominators?
Find the least common denominator (LCD) of the two denominators, rewrite each fraction over that denominator by multiplying its numerator and denominator by the same factor, then add or subtract the numerators and keep the LCD as the denominator. Finally, simplify the result to lowest terms.
What is the least common denominator (LCD)?
The LCD is the least common multiple of the two denominators — the smallest number that both denominators divide into evenly. It can be calculated as (b × d) ÷ GCD(b, d), where GCD is the greatest common divisor of denominators b and d.
How do I convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The whole-number quotient becomes the whole part of the mixed number, and the remainder becomes the new numerator placed over the original denominator. For example, 11/4 divides to 2 remainder 3, so it becomes 2 3/4.
Can the result be negative?
Yes. If you subtract a larger fraction from a smaller one, the result is negative, such as −1/6. This calculator accepts negative numerators for both fractions and reports a negative simplified result, mixed number, and decimal when that happens.

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