Adding Fractions Calculator

Add two fractions and get the sum reduced to lowest terms, as a decimal, and as a mixed number, using the common-denominator method.

Quick Facts

Method
Common-denominator addition: a/b + c/d = (a×d + b×c) / (b×d)
The result is automatically reduced using the greatest common divisor (GCD).
Least common denominator
Smallest number both denominators divide into evenly
Using the LCD instead of b×d keeps numbers smaller but gives the same final answer.

Your Results

Calculated
Sum (simplified)
-
a/b + c/d reduced to lowest terms
Decimal equivalent
-
Sum expressed as a decimal
Mixed number
-
Whole number plus remaining fraction
Least common denominator
-
LCD used to combine the fractions

Ready

Enter two fractions and press Calculate.

How the Adding Fractions Calculator works

This calculator adds two fractions using the standard common-denominator method taught in arithmetic: rewrite both fractions over the same denominator, add the numerators, then simplify. It also converts the result to a decimal and, if the sum is improper, to a mixed number.

Formula and method

For fractions a/b and c/d, the sum is a/b + c/d = (a×d + b×c) / (b×d). This calculator uses the least common denominator (LCD) of b and d rather than the raw product b×d, which keeps the intermediate numbers smaller but produces the exact same final answer once reduced. The LCD is found from the greatest common divisor (GCD): LCD = |b × d| ÷ GCD(b, d). Each fraction's numerator is then multiplied by whatever factor turns its denominator into the LCD, the two adjusted numerators are added, and the sum is divided by its own GCD with the LCD to reduce it to lowest terms.

Common sources of error

  • Adding denominators directly: 1/2 + 1/3 is not 2/5 — denominators must be equalized first, then only the numerators are added.
  • Zero denominator: a denominator of 0 makes a fraction undefined; this calculator rejects it.
  • Skipping simplification: an unsimplified sum like 6/8 is mathematically equal to 3/4 but should be reduced — this calculator always reduces automatically.

Checking your result

Multiply the simplified numerator and denominator back up and confirm they match the unsimplified sum before reduction. Check the decimal view against a quick estimate — 1/2 + 1/3 should land near 0.83, not near 0.4 (the giveaway for the "add denominators" mistake). If the sum's numerator exceeds its denominator, expect a mixed number with a whole-number part of at least 1.

Applications

Adding fractions comes up when combining measurements given in fractional units — inches on a tape measure, cups in a recipe, or hours recorded as fractions of a shift — and in algebra or homework problems that require an answer in lowest terms. Keep the numerator and denominator together as a pair when you record or share a fraction result, since either number alone is meaningless.

Frequently Asked Questions

How do I add two fractions with different denominators?
Find a common denominator (the least common denominator, or LCD, is simplest), rewrite each fraction over that denominator, then add the numerators. For example, 1/2 + 1/3 uses LCD 6: 1/2 = 3/6 and 1/3 = 2/6, so the sum is 3/6 + 2/6 = 5/6.
Why do I need a common denominator to add fractions?
A denominator tells you the size of each piece of the whole. You can only add pieces that are the same size, so 1/2 and 1/3 must both be rewritten in equal-sized pieces (sixths) before their numerators can be combined. Adding numerators and denominators directly, like 1/2 + 1/3 = 2/5, is a common mistake and gives the wrong answer.
How do I simplify a fraction after adding?
Divide the numerator and denominator by their greatest common divisor (GCD). For example, 4/8 has a GCD of 4, so it simplifies to 1/2. This calculator automatically reduces every sum to lowest terms.
How do I convert an improper fraction sum into a mixed number?
Divide the numerator by the denominator. The whole-number quotient becomes the whole part, and the remainder over the original denominator becomes the fractional part. For example, 11/4 divided is 2 remainder 3, so it is 2 3/4.

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