To add fractions with different denominators, find a common denominator, rewrite both fractions, add only the numerators, and reduce. For example, 1/3 + 1/4 = 4/12 + 3/12 = 7/12. In general, a/b + c/d = (a × d + c × b)/(b × d), with nonzero denominators; using the least common multiple can keep the intermediate numbers smaller. Never add the denominators directly: they name the size of the parts, so the parts must first use the same unit.
Find a denominator both fractions can use
Any common multiple of the denominators works, but their least common multiple usually keeps the intermediate numbers smaller. For 1/2 and 3/4, the least common multiple of 2 and 4 is 4. Multiply 1/2 by 2/2 to obtain 2/4; multiplying numerator and denominator by the same nonzero integer preserves the value. The second operand is already 3/4. FractionCalc shows this equivalence before combining anything, so the common denominator is a visible mathematical step rather than a hidden formatting choice.
Combine only the signed numerators
Once both fractions use fourths, 2/4 + 3/4 becomes (2 + 3)/4 = 5/4. The denominator does not become 8: the answer still counts quarter-sized parts. Subtraction follows the same structure, with the second signed numerator subtracted instead of added. Negative operands are handled by keeping their sign in the numerator while the denominator remains positive. This convention gives one normalized direction for every fraction and avoids equivalent but visually conflicting forms such as 1/−2 and −1/2.
Reduce, then check against the original scale
The greatest common divisor of 5 and 4 is 1, so 5/4 is already reduced. It may also be written as the mixed number 1 1/4 or the exact decimal 1.25; all three forms name the same rational value. A quick magnitude check supports the result: 1/2 is 0.5 and 3/4 is 0.75, so their sum must be 1.25, greater than one but less than two. The check does not replace exact arithmetic, yet it catches common mistakes such as adding denominators or losing the sign of a numerator.