Fraction Calculator
Add, subtract, multiply, divide, and simplify proper, improper, and negative fractions with step-by-step GCD reduction and decimal conversion.
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Ratio Calculator
Simplify ratios to lowest terms, generate equivalent ratios, divide any total amount according to a ratio, and solve for a missing value x in a proportion.
Simplify Ratio & Find Equivalent Ratio
Simplified Ratio
2 : 3
Equivalent Ratio
4 : 6 (×2)
Divide Amount According to Ratio
Share 1
Share 2
Find Missing Value in Proportion (A : B = C : x)
Missing Value (x)
x = 12
2 : 3 = 8 : 12 → x = (3 × 8) ÷ 2
Ratio & Proportion Formulas
1. Simplify A : B → (A ÷ GCD(A,B)) : (B ÷ GCD(A,B))
2. Divide Amount M in Ratio p : q → Share₁ = M × p / (p + q), Share₂ = M × q / (p + q)
3. Proportion A : B = C : x → x = (B × C) ÷ A
2. Divide Amount M in Ratio p : q → Share₁ = M × p / (p + q), Share₂ = M × q / (p + q)
3. Proportion A : B = C : x → x = (B × C) ÷ A
Frequently Asked Questions
Find the Greatest Common Divisor (GCD) of both numbers. For 12 and 18, the GCD is 6. Divide both terms by 6 to get the simplified ratio 2:3.
First add the ratio parts: 2 + 3 = 5 total parts. The first share is (1000 × 2) / 5 = 400, and the second share is (1000 × 3) / 5 = 600.
Write the proportion as a fraction equality: 2/3 = 8/x. Cross-multiply to get 2x = 24, then divide by 2 to find x = 12.
An equivalent ratio is formed by multiplying or dividing both terms of a ratio by the same non-zero number. For example, multiplying 2:3 by 2 produces 4:6.
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