Ratio Calculator

To simplify a ratio, divide both values by their Greatest Common Divisor (GCD). GCD is the largest number that divides both values without a remainder. Example: simplify 24:16. GCD(24, 16) = 8. Divide both: 24 / 8 = 3, 16 / 8 = 2. Simplified ratio = 3:2. This reads 'for every 3 of A, there are 2 of B.' Ratios can also have three parts - 2:3:5 means the parts are in proportion 2, 3, and 5. To simplify a three-part ratio, find the GCD of all three numbers and divide each. Simplified ratios make proportional reasoning clearer by removing unnecessary common factors.

A proportion states two ratios are equal: A:B = C:D, or equivalently A/B = C/D. When three of four values are known, find the fourth by cross-multiplication: A x D = B x C, so D = (B x C) / A. Example: a car travels 60 km in 1 hour. How far in 2.5 hours? Set up: 60:1 = x:2.5. Cross-multiply: 60 x 2.5 = 1 x x, so x = 150 km. Proportions are used in cooking (scaling recipes), construction (mixing concrete), map reading (scale distances), and currency conversion. Whenever two quantities change at the same rate, their relationship is proportional.

GCD (Greatest Common Divisor), also called HCF (Highest Common Factor), is the largest positive integer that divides two or more numbers exactly with no remainder. The most efficient method is the Euclidean algorithm: GCD(a, b) = GCD(b, a mod b), repeating until the remainder is 0. Example: GCD(48, 36). 48 mod 36 = 12. GCD(36, 12). 36 mod 12 = 0. GCD = 12. So 48:36 simplifies to 4:3 (divide both by 12). When GCD equals 1, the numbers are coprime - they share no common factors and the ratio is already in its simplest form. GCD(7, 11) = 1, so 7:11 cannot be simplified further.

For ratio A:B, compute (A / (A + B)) x 100 for each part's share of the whole, or (A / B) x 100 to express A as a percentage of B specifically. Example: ratio 3:7. A's share of total = (3/10) x 100 = 30%, B's share = 70%. Alternatively, A as a percentage of B = (3/7) x 100 = 42.9%. The choice depends on context: in a profit-split scenario, percentage-of-total (30% and 70%) is usually more meaningful. In a comparison context like speed ratio, A as a percentage of B is more natural.

Ratios are fundamental to investing. P/E ratio (Price-to-Earnings) = Stock Price / EPS - tells you how much you pay per rupee of earnings; under 20 is generally reasonable for Indian stocks. Debt-to-equity ratio = Total Debt / Shareholder Equity - under 1 is considered healthy. Current ratio = Current Assets / Current Liabilities - should be above 1.5. For personal finance, the 50/30/20 rule (50% needs, 30% wants, 20% savings) is itself a ratio-based budgeting framework.

To divide a quantity in ratio A:B:C, sum all parts (A + B + C) to get total shares. Each party's amount = their share x (Total quantity / Total shares). Example: divide Rs. 1,80,000 among three partners in ratio 2:3:5. Total shares = 10. Each share = Rs. 18,000. Partner A = 2 x Rs. 18,000 = Rs. 36,000. Partner B = Rs. 54,000. Partner C = Rs. 90,000. Check: all three sum to Rs. 1,80,000. This method works for any number of parties and applies directly to partnership profit splits, inheritance distributions, and concrete mix proportions (cement:sand:aggregate).

Two quantities are inversely proportional when one increases as the other decreases at the same rate - their product stays constant. If A and B are inversely proportional: A x B = constant. Example: 8 workers complete a job in 15 days. How many days for 12 workers? Workers x Days = 8 x 15 = 120. Days for 12 workers = 120 / 12 = 10 days. More workers, fewer days - inverse proportion. Other examples: speed and travel time for a fixed distance (double the speed = half the time); gas pressure versus volume at constant temperature (Boyle's Law). Recognising inverse proportion prevents the common error of applying direct proportion when the relationship is actually inverse.