Add, subtract, multiply, and divide fractions with automatic simplification.
The Arithmetic Fractions Calculator is a specialized math tool designed to perform addition, subtraction, multiplication, and division on fractions. Fractions represent rational numbers expressed as a ratio of two integers: the numerator (representing the parts we have) and the denominator (representing the total parts in a whole). Operating with fractions manually is a multistep process that requires strict adherence to arithmetic rules, making a dedicated calculator highly beneficial.
To add or subtract fractions, they must first share a common denominator. This requires finding the Least Common Multiple (LCM) of the denominators, converting the fractions, performing the addition or subtraction on the numerators, and then reducing the result to its lowest terms. For multiplication, you multiply the numerators together and the denominators together, then simplify. For division, you multiply the first fraction by the reciprocal (the flipped version) of the second fraction.
Fractions can be proper (numerator smaller than denominator), improper (numerator larger than denominator), or mixed numbers (combining a whole number and a fraction). A robust fractions calculator handles all these types, converting improper fractions into mixed numbers automatically and simplifying the final output by dividing the numerator and denominator by their Greatest Common Divisor (GCD).
Fractions are used extensively in cooking, carpentry, design, and sewing, where measurements are expressed in halves, quarters, eighths, or sixteenths. By automating fraction arithmetic and simplifying the output, this calculator prevents conversion errors, ensures precise measurements, and saves time during design and cooking tasks.
How it Works & Formula
After performing the operation, the result is reduced to lowest terms by dividing both numerator and denominator by their Greatest Common Divisor (GCD).
Practical Examples
Half of 3/4 cup is 1/2 × 3/4 = 3/8 cup.
Frequently Asked Questions
How do I divide fractions?
Multiply the first fraction by the reciprocal (flip) of the second fraction.