Ratio of 3 Numbers
Easily simplify any A:B:C ratio to its lowest whole-number terms using the GCD. Free online ratio simplifier for math students, chefs, and construction pros.
About This Calculator
The Ratio of 3 Numbers calculator simplifies any three-number ratio expressed as A:B:C to its lowest terms. It computes the greatest common divisor of all three numbers -- first finding GCD(A, B), then GCD of that result with C -- and divides each term to give you the simplest whole-number representation.
For example, the ratio 6:9:15 has a GCD of 3, so it simplifies to 2:3:5. This makes it much easier to understand and work with the proportional relationship. The calculator also displays the original ratio and the GCD value used for simplification.
Three-number ratios are commonly used in construction (concrete mix ratios like 1:2:4 for cement:sand:aggregate), cooking (ingredient proportions), chemistry (mole ratios), and financial analysis (debt:equity:asset ratios). This tool helps professionals and students quickly reduce any three-number ratio to its simplest form.
Regional Notes
India: Used in Class 6-10 mathematics for ratio and proportion problems involving three quantities, and in construction for cement mortar mixing ratios.
United States: Common in high school algebra, culinary arts for recipe scaling, and construction trade calculations.
United Kingdom: Featured in GCSE Mathematics and vocational courses for construction and food technology.
Frequently Asked Questions
How do you simplify a ratio of 3 numbers?
To simplify a ratio of three numbers A:B:C, find the GCD of all three numbers using the formula GCD(A, B, C) = GCD(GCD(A, B), C). Then divide each term by this GCD to get the simplified ratio in lowest terms.
What is an example of a 3-number ratio?
A common example is a mortar mix ratio of 1:3:6 (cement:sand:aggregate) or a recipe ratio of 2:3:1 (flour:sugar:butter). The calculator simplifies these to their lowest whole-number terms.
Can I use decimal numbers in a three-number ratio?
Yes, the calculator accepts decimal values and simplifies them by finding the GCD of all three numbers, returning the simplest possible representation.
Why do I need to simplify a ratio of 3 numbers?
Simplifying a three-number ratio makes it easier to understand the proportional relationship, scale recipes or mixtures, and compare different ratios. For example, the ratio 6:9:15 simplifies to 2:3:5, which is much clearer.
Is this tool free to use?
Yes, all calculators on Calculy are completely free to use with no registration required.
How do I divide an amount in a ratio of 3 numbers?
Add the three ratio numbers to find the total parts, divide the amount by this total to find one part's value, then multiply each ratio number by that value. For example, divide $50 in ratio 2:3:5 gives 10 total parts, $5 per part, so $10, $15, $25 respectively.
What happens if one of the numbers in the ratio is zero?
A zero in a three-number ratio is valid and simply means that term represents zero quantity. For example, 0:5:10 simplifies to 0:1:2. The calculator handles this correctly as long as not all three numbers are zero.
What does it mean if the ratio is already in simplest form?
If the GCD of the three numbers is 1, the numbers are setwise coprime and the ratio cannot be simplified further. The calculator will display the same numbers as the simplified ratio, confirming the ratio is already in its lowest terms.