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Mathematics

Ratio Simplifier

Simplify ratios. Free online Ratio Simplifier. Calculate ratio simplifier online — fast, accurate, mobile-friendly, no signup needed.

Simplified
2:3

Derivation

  1. ├── 01Givena = 12, b = 18
  2. ├── 02Formula{let t=e.a,a=e.b;const n=Us(round(t),round(a));return"".concat(t / n,":").concat(a / n)}
  3. ├── 03Substitute{let t=e.12,12=e.18;const n=Us(round(t),round(12));return"".concat(t / n,":").concat(12 / n)}
  4. └── 04Compute Simplified—
Did you know?

Ratios appear in the earliest Greek mathematics (Eudoxus, 4th century BCE) as a way to compare incommensurable lengths without a concept of irrational numbers.

§01What is

Understanding the Ratio Simplifier

The Ratio Simplifier computes Simplified from 2 inputs: a, b. Simplify ratios.

Mathematics shows up in every corner of daily life — budgeting, cooking, construction, engineering, even reading a bus schedule. A calculator like this lets you skip the scratch-paper step and move straight to the answer, without the arithmetic mistakes that creep in when the numbers get messy. The Ratio Simplifier sits in that toolkit — it simplify ratios. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

{let t=e.a,a=e.b;const n=Us(round(t),round(a));return"".concat(t / n,":").concat(a / n)}

Where

a
A
b
B
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: A = 12, B = 18.

  1. 01Start by noting the input — A: 12.
  2. 02Start by noting the input — B: 18.
  3. 03Substitute these values into the formula: {let t=e.a,a=e.b;const n=Us(round(t),round(a));return"".concat(t / n,":").concat(a / n)}
  4. 04Compute Simplified: the calculator returns 2:3.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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