About

Comparing fractions like 37 and 49 is counter-intuitive because the parts (denominators) are different sizes. You cannot simply compare the top numbers until the bottom numbers are identical.

This tool automates the process of finding the Least Common Denominator (LCD). It calculates the Least Common Multiple (LCM) of the denominators, scales both fractions proportionally, and compares the resulting numerators. The visual mode renders proportional pie charts to provide an immediate intuitive check of the result.

Formulas

To compare ab and cd, we find the Least Common Multiple (LCM) of b and d.

LCM(b, d) = |b × d|GCD(b, d)

We then convert both fractions to share this denominator and compare their numerators:

if a × d > c × b &implies; ab > cd

Reference Data

Fraction A	Fraction B	LCD	Scaled A	Scaled B	Larger
12	13	6	36	26	A
34	56	12	912	1012	B
25	410	10	410	410	Equal
78	67	56	4956	4856	A
13	39	9	39	39	Equal
512	38	24	1024	924	A
910	1920	20	1820	1920	B
1115	34	60	4460	4560	B

Frequently Asked Questions

LCD stands for Least Common Denominator. It is the smallest number that can be exactly divided by all the denominators in the set. It allows you to rename fractions so they are "like" fractions and can be compared directly.

Yes. The best approach is to convert mixed numbers (e.g., 1 1/2) into improper fractions (3/2) before using the tool. This avoids errors in the integer comparison step.

Cross-multiplication is a shortcut. Checking if a*d > c*b is mathematically equivalent to finding a common denominator (b*d) and comparing numerators. This tool shows the full LCD method for educational clarity.

This tool is optimized for binary comparison (two inputs) to provide detailed visual steps. For sorting lists of fractions, repeated pairwise comparison is the standard algorithmic approach.