About

Fractions represent parts of a whole, but adding them requires a common linguistic framework: the common denominator. In carpentry, culinary arts, and algebra, precision is lost when converting to decimals. For example, 13 is exactly one-third, whereas 0.33 is an approximation. This tool preserves that precision.

This calculator performs the complete algebraic workflow: finding the Least Common Denominator (LCD), scaling the numerators, adding them, and finally reducing the result to its simplest form. It also converts improper fractions (where the top is larger than the bottom) into mixed numbers, providing a comprehensive solution for students and professionals checking their work.

Formulas

To add two fractions ab and cd, we first find the LCD (Least Common Denominator) of b and d.

ab + cd = ad + cbbd

Simplification relies on the Greatest Common Divisor (GCD):

Reduced = Num ÷ GCDDen ÷ GCD

Reference Data

Operation	Formula/Logic	Example
Fraction	ab	12
Common Denominator	LCM(b, d)	LCD of 2, 4 is 4
Renaming	a × kb × k	1 × 22 × 2 = 24
Addition	A + CLCD	2 + 14
Improper	Num > Den	54
Mixed Number	W nd	1 14
Reciprocal	ba	Flip fraction

Frequently Asked Questions

The LCD is the smallest number that both denominators can divide into evenly. It is required to make the "slice sizes" of the fractions equal so they can be added together.

If the result is an improper fraction (the top number is larger than the bottom), it means the value is greater than 1. We convert this into a whole number plus a remaining fraction for readability.

Yes. If a numerator is negative, the tool treats it as subtraction. The logic for finding the common denominator remains exactly the same.

Always. After performing the addition, the tool calculates the Greatest Common Divisor (GCD) of the result to reduce the fraction to its lowest terms (e.g., 2/4 becomes 1/2).