Proportion & Simplification

Ratio Calculator

Simplify two-part ratios to simplest integers, generate equivalent fractions, and solve for missing proportion variables instantly.

Guide & Overview

About the Ratio Calculator

The Ratio Calculator enables you to simplify ratios to their lowest whole number terms, convert decimal ratios to clean integer proportions, and solve equivalent proportion equations of the form A : B = C : D.

Ratios express the relative size of two or more quantities. They are ubiquitous in recipe scaling, graphic design aspect ratios (such as 16:9 and 4:3), financial balance sheet metrics (current ratio, debt-to-equity), and chemistry solution mixtures.

Step-by-Step Instructions

How to Calculate Ratio

To simplify a ratio, input numbers A and B and view the irreducible integer proportion.

To solve a proportion A:B = C:D, enter any three known values and leave the target field empty.

The calculator executes cross-multiplication and reduces terms instantaneously.

Mathematical Precision

Ratio Simplification & Proportion Formulas

Formula Definition

Simplified Ratio = (A / GCD(A, B)) : (B / GCD(A, B))
Proportion Equation: A / B = C / D  ⟹  A × D = B × C

To simplify a ratio, divide both terms by their Greatest Common Divisor (GCD). In proportions, cross-multiplication allows solving for any single missing variable.

Variable Descriptions

A & B: First antecedent and consequent of the ratio
C & D: Second antecedent and consequent of the equivalent proportion
GCD: Greatest Common Divisor between the numbers

Practical Walkthrough

Worked Example

Scenario: Simplify the ratio 24 : 36, and solve for X in 4 : 5 = X : 25.

Step 1 (Simplification): Find GCD(24, 36) = 12.

Step 2: 24 ÷ 12 = 2, and 36 ÷ 12 = 3. Simplified ratio is 2 : 3.

Step 3 (Proportion): 4 / 5 = X / 25 ⟹ 5 × X = 4 × 25 = 100 ⟹ X = 100 ÷ 5 = 20.

Result:24:36 reduces to 2:3. In 4:5 = X:25, X equals 20.

Important Considerations & Tips

Both sides of a ratio can be multiplied or divided by the same non-zero number without changing its value.
Decimal ratios are automatically multiplied by powers of 10 prior to reduction to guarantee integer outputs.
Ratios represent comparative relationships, not absolute amounts. A 2:3 ratio could describe 2 and 3 items or 200 and 300 items.

Search Questions Answered

Frequently Asked Questions

How do you simplify a ratio to lowest terms?

Find the Greatest Common Divisor (GCD) of both numbers, then divide both numbers by that GCD. For example, in 15:25, the GCD is 5, so dividing both by 5 gives 3:5.

How do you solve a proportion when one number is unknown?

Use cross-multiplication: if A/B = C/D, then A × D = B × C. Multiply the diagonal numbers and divide by the remaining number opposite the unknown.

Can ratios contain decimals or fractions?

While ratios can initially be written with decimals (e.g., 1.5 : 2.5), standard convention is to express them with positive integers by scaling both terms.

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