Reduce rational expressions and polynomial ratios easily.
Quick, accurate, and educational. Designed for students, professionals, and everyday math.
See exactly how the simplified ratio is calculated using the Greatest Common Factor (GCF) method.
Convert any ratio to 1 : n or n : 1 form. Useful for unit rates, price comparisons, and proportional reasoning.
Multiply or divide all terms by a factor k. Keep the same proportion at a different magnitude.
Solve for a missing value in a proportion. Enter three known values and find the fourth using cross-multiplication.
Simplify ratios with 2, 3, or even 4 numbers at once. Perfect for complex mixing or scaling.
Automatically converts decimals and fractions into whole numbers before simplifying.
A polynomial ratio (rational expression) has polynomials in both the numerator and denominator. To simplify, factor both and cancel common factors.
Several methods can help factor polynomials for simplification.
Practice with these common polynomial ratio simplifications.
Understanding the math behind the simplification.
We determine the Greatest Common Factor (GCF) for all the numbers in your ratio.
We divide each number in the ratio by the GCF.
The new values form the fully simplified, co-prime ratio.
A ratio compares two or more quantities. Simplifying means reducing it to its smallest form — where the numbers share no common factor other than 1.
This calculator shows every step. It finds the Greatest Common Factor (GCF) and divides each term by it. You see exactly how the answer was reached.
Every result includes a step-by-step breakdown so you can follow the math yourself.
A ratio is fully simplified when no number greater than 1 divides evenly into all terms. The terms are called co-prime.
It's easy to partially simplify — for example, 12 : 18 → 6 : 9 (dividing by 2). But 6 : 9 is not fully simplified because both are still divisible by 3. The correct answer is 2 : 3.
This tool finds the GCF — not just any common factor — so the result is always fully simplified in one step.
A ratio expresses how much of one thing there is compared to another. It's written as A : B, A/B, or "A to B".
For example, a recipe uses 2 cups of flour for every 1 cup of sugar. The ratio is 2 : 1. Doubling the recipe gives 4 : 2 — same proportion, different scale.
A simplified ratio makes comparisons easier. 16 : 24 is harder to read than 2 : 3, even though they're the same proportion.
The formula to simplify A : B is:
For three or more numbers: find GCF of the first two, then take GCF of that result with the next number, and so on.
Simplifying a ratio is the same process as simplifying a fraction. The goal is numbers that represent the same relationship but are as small as possible.
Think of it this way: 10 : 15 and 2 : 3 describe the same proportion. But 2 : 3 is simpler to say, write, and compare.
Two numbers in a simplified ratio are always co-prime — GCF = 1. You can check this quickly to confirm.
When A and B are whole numbers, the steps are straightforward: list factors, find the GCF, divide.
If you can't spot the GCF directly, divide by any shared factor first, then repeat until no common factors remain.
When A or B is a decimal or fraction, convert to whole numbers first, then simplify.
The most common case: two numbers A and B. Enter them, choose "simplify the ratio," and click Calculate.
Common uses: cooking, screen aspect ratios, speed comparisons, probability and odds.
To calculate the ratio of A to B: write A : B, find the GCF, and divide both by it.
Three-part ratios appear in mixing, allocation, and any situation where a total is split three ways. Find the GCF of all three numbers, then divide each by it.
12 : 18 : 24 simplifies to 2 : 3 : 4 (GCF = 6)
Real examples: concrete mix (cement : sand : gravel), paint mixing, budget splits.
Four-part ratios work the same way. Find the GCF of all four values and divide each by it.
Use cases: chemistry compound formulas, colour mixing, resource allocation split four ways.
Sometimes simplifying gives a result with decimals — like 1 : 2.5. Multiply all terms by the smallest number that clears the decimal to get whole numbers.
Simplifying complex polynomial and rational expressions.