Ratio Calculator
How do you simplify 4:6 — or find x in 3:4 = 9:x? Reduce any ratio to lowest terms or solve a proportion for its missing value, with the cross-multiplication shown step by step.
Simplified ratio
2:3
lowest terms
Decimal
0.6667
A ÷ B
Percentage split
40% / 60%
of the total
Steps
GCD(4, 6) = 2 4 ÷ 2 : 6 ÷ 2 = 2:3 split: 4/(4 + 6) = 40%, 6/(4 + 6) = 60%
Ratios compare part to part, fractions compare part to whole — in a 2:3 ratio the first quantity is 2/5 of the total, not 2/3. Cross-multiplication works because multiplying both sides of A/B = C/D by B × D clears both denominators at once.
Simplifying and Cross-Multiplying
A ratio simplifies exactly like a fraction: divide both sides by their GCD, so 4:6 becomes 2:3 (GCD 2). The same pair as a decimal is 4 ÷ 6 ≈ 0.6667, and as a share of the whole it splits 40% / 60%, since 4 out of every 10 parts go to the first quantity. Proportions solve by cross-multiplying: 3/4 = 9/x means 3x = 4 × 9 = 36, so x = 12 — the products across the equals sign must match.
Ratio toolkit
Simplify: divide both sides by GCD 4:6 → ÷2 → 2:3 Decimal: A ÷ B 4 ÷ 6 ≈ 0.6667 % split: A/(A+B) and B/(A+B) 4:6 → 40% / 60% Proportion: A/B = C/D → A·D = B·C 3/4 = 9/x → 3x = 36 → x = 12
Frequently Asked Questions
How do I simplify a ratio to lowest terms?
Divide both sides by their greatest common divisor, exactly like reducing a fraction: 4:6 has GCD 2, so it simplifies to 2:3. Ratios with more than two parts work the same way — 6:9:12 divides by 3 to give 2:3:4.
How do I solve a proportion like 3/4 = 9/x?
Cross-multiply: the products across the equals sign must match, so 3 × x = 4 × 9 = 36, which gives x = 36 ÷ 3 = 12. It works for whichever position is missing — cross-multiplication turns any proportion into a one-step equation.
How do I split an amount in a given ratio?
Add the parts to find the total number of shares, then divide. Splitting $100 in a 2:3 ratio means 5 shares of $20, so the split is $40 and $60 — the same 40%/60% the calculator shows for any ratio that simplifies to 2:3.
Are ratios and fractions the same thing?
Close cousins, but they compare different things: a ratio is part-to-part, a fraction is part-to-whole. In a class with a 2:3 ratio of boys to girls, boys are 2/5 of the class — not 2/3. That's why a 4:6 ratio shows a 40%/60% percentage split rather than 67%.