About

Fraction multiplication is unique among arithmetic operations because it does not require a common denominator. However, the complexity lies in simplification (reduction) and converting between mixed numbers and improper fractions. This tool automates these steps, providing a clear breakdown of the algebraic process.

It handles inputs of any form-Integers (5), Proper Fractions (1/2), or Mixed Numbers (2 3/4). The engine uses the Euclidean Algorithm to find the Greatest Common Divisor (GCD), ensuring that the final output is always in its simplest terms, matching standard academic requirements.

Formulas

Given two fractions ab and cd:

Product = a × cb × d

If mixed numbers are involved (W nd), convert to improper form first:

Improper = (W × d) + nd

The final result is simplified by calculating the GCD:

Simplified = Numerator / GCDDenominator / GCD

Reference Data

Type	Equation	Rule	Result
Simple Fractions	12 × 13	Top×Top, Bot×Bot	16
With Integer	5 × 23	Treat 5 as 5/1	103 = 313
Mixed Numbers	112 × 212	Convert to improper first	32 × 52 = 154
Simplification	24 × 23	412 → Divide by 4	13
Inverse	23 × 32	Product of reciprocals	1
Zero Rule	45 × 0	Multiply by zero	0

Frequently Asked Questions

No. Common denominators are only required for addition and subtraction. For multiplication, you simply multiply straight across (numerator × numerator and denominator × denominator).

Write the whole number as a fraction over 1. For example, 5 becomes 5/1. Then multiply as usual.

A simplified fraction is one where the top and bottom numbers share no common factors other than 1. For example, 4/8 can be simplified to 1/2 by dividing both by 4.

The tool automatically converts mixed numbers (like 1 1/2) into improper fractions (3/2) before performing the multiplication, then converts the result back if necessary.