What is the Ratio Simplifier Calculator?
This tool reduces any ratio A : B to its simplest whole-number form. Each term can be a whole number, integer, decimal, simple fraction, or mixed number — and the two terms can even be different types. The calculator converts every value to an exact fraction, scales both sides to integers, and divides by the greatest common factor (GCF).
How to use it
Enter a value for A and a value for B using any of these formats: a whole number like 5, a negative integer like -12, a decimal like 2.5, a simple fraction like 3/4, or a mixed number like 3 1/8 (whole, space, then numerator/denominator). Press calculate to see the reduced ratio plus the worked steps.
The formula
Each term becomes a fraction num/den. Both terms are placed over the least common denominator \(L = \operatorname{lcm}(d_A, d_B)\), where \(\operatorname{lcm}(x, y) = x \cdot y / \gcd(x, y)\). Multiplying both sides of a ratio by the same nonzero number \(L\) leaves the ratio unchanged but clears the fractions, giving integers \(a : b\). Finally divide both by \(g = \gcd(|a|, |b|)\) computed with the Euclidean algorithm.
$$\begin{gathered} \text{A} : \text{B} \;=\; \frac{a}{g} : \frac{b}{g} \\[1.5em] \text{where}\quad \left\{ \begin{aligned} L &= \operatorname{lcm}(d_A,\, d_B) \\ a &= \text{A} \cdot \tfrac{L}{d_A} \\ b &= \text{B} \cdot \tfrac{L}{d_B} \\ g &= \gcd(a,\, b) \end{aligned} \right. \end{gathered}$$
Worked example
For A = 5 and B = 3 1/8: A parses to \(5/1\); B parses to \((3 \times 8 + 1)/8 = 25/8\). The LCM of 1 and 8 is 8, so \(a = 5 \times 8 = 40\) and \(b = 25\). \(\gcd(40, 25) = 5\), giving $$\frac{40}{5} : \frac{25}{5} = \textbf{8 : 5}.$$
FAQ
Can I mix decimals and fractions? Yes. A = 2.5 and B = 0.75 reduce to 10 : 3.
Are negative ratios supported? Yes — the sign is preserved on each term, so -4 : 6 reduces to -2 : 3.
What about zero? 0 : 6 reduces to 0 : 1; 0 : 0 cannot be reduced and stays 0 : 0.
