Ratio of 3 Numbers Calculator

Understanding Ratios of Three Numbers ($A : B : C$)

A ratio of three numbers expresses the comparative relationship between three quantities simultaneously. Written as $A : B : C$, it tells us how much of each component is present relative to the others. Three-part ratios are widely used in cooking recipes, chemical solutions, concrete and mortar mixing, financial division of profits, and geometric scaling.

For instance, a concrete mix recipe of $1 : 2 : 3$ indicates 1 part cement, 2 parts sand, and 3 parts aggregate by volume. Unlike a standard two-number ratio or fraction, three-part ratios cannot be simplified simply as a single fraction $A / B$, but require finding the greatest common factor across all three terms. If you are comparing two values, check our Ratio Calculator or Ratio Simplifier.

How to Simplify a 3-Part Ratio Step-by-Step

Simplifying a ratio of three integers $A : B : C$ means dividing all three numbers by their Greatest Common Factor (GCF):

1. Convert Decimals to Integers: If any term has decimal digits, multiply all three terms by 10, 100, or 1000 until all terms become whole numbers.
2. Find the GCF: Calculate $\text{GCF}(A, B, C) = \text{GCF}(\text{GCF}(A, B), C)$.
3. Divide Each Term: Divide $A$, $B$, and $C$ by the common divisor to produce the simplest integer form.

For example, to simplify $12 : 18 : 30$:

• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 18: 1, 2, 3, 6, 9, 18
• Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
• $\text{GCF}(12, 18, 30) = 6$
• Divide by 6: $(12/6) : (18/6) : (30/6) = 2 : 3 : 5$

How to Divide a Total Amount in a Given Ratio

When dividing a sum of money, inheritance, or material weight into ratio shares $A : B : C$:

1. Add the ratio numbers together: $\text{Total Parts} = A + B + C$.
2. Determine the value of one part: $\text{One Part} = \frac{\text{Total Amount}}{\text{Total Parts}}$.
3. Multiply each term by the unit value:
   • $\text{Share } A = A \times \text{One Part}$
   • $\text{Share } B = B \times \text{One Part}$
   • $\text{Share } C = C \times \text{One Part}$

For example, dividing $300 among three partners in the ratio $2 : 3 : 5$: total parts equal $2 + 3 + 5 = 10$. Each part is worth $\$300 / 10 = \$30$. The shares are $\$60$, $\$90$, and $\$150$. To explore other ratio conversions, you can also use our Equivalent Ratio Calculator and Ratio to Fraction Calculator.