Math & EverydayVerified: 2026-10-05
Ratio Calculator
Simplify ratios to lowest terms, solve proportions (A : B = C : X), scale aspect ratios, and divide quantities or money into proportional shares.
Direct Answer:To simplify a ratio A : B, divide both numbers by their Greatest Common Divisor (GCD). For example, 12 : 18 simplifies to 2 : 3 (dividing both by 6). To solve a proportion A : B = C : X, cross-multiply: X = (B × C) ÷ A.
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Adjust Parameters
Common Ratios:
Simplified Ratio
2 : 3
GCD: 6 | Decimal: 0.6667
Decimal Value (A ÷ B)
0.6667
Unit Ratio (1 : N)
1 : 1.5
Percentage Breakdown
40% : 60%
Greatest Common Divisor (GCD)
6
Step-by-Step Solution
- Given ratio: 12 : 18
- Find Greatest Common Divisor (GCD): GCD = 6
- Divide both terms by 6: (12 ÷ 6) : (18 ÷ 6) = 2 : 3
- Decimal fraction: 12 ÷ 18 = 0.6667
- Percentage breakdown: Term A is 40% of total, Term B is 60% of total.
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How Ratio Calculator is Calculated
Transparent mathematical formulas and assumptions used across our financial engines.
Mathematical Formula
\text{Simplify: } \frac{A}{\gcd(A,B)} : \frac{B}{\gcd(A,B)} \quad | \quad \text{Proportion: } X = \frac{B \times C}{A} \quad | \quad \text{Share } A = \text{Total} \times \frac{A}{A + B}
Variables & Legend
A
Term A
B
Term B
C
Term C
X
Unknown X
\text{Total}
Total Amount
Step-by-Step Calculation
- Find GCD:
\gcd(A, B)Identify greatest common divisor of both terms.
- Simplify:
A/\gcd : B/\gcdDivide both terms by GCD to obtain simplest integer ratio.
- Solve Unknown:
X = (B * C) / ACross-multiply to find missing proportion value.
- Divide Total:
Share_A = Total * (A / (A+B))Multiply total by each term's fractional share.
Conventions & Assumptions
- Ratio terms can be whole numbers or decimals; decimals are converted to integer equivalents automatically.
- In aspect ratios, 16:9 and 4:3 are standard video and display formats.
Frequently Asked Questions
To simplify a ratio, find the Greatest Common Divisor (GCD) of both numbers and divide each number by that GCD. For instance, in 24 : 36, the GCD is 12, so dividing both by 12 yields 2 : 3.