Simplify any ratio to its lowest terms or solve for the missing value in an equivalent ratio. Works for recipes, map scales, screen resolutions, mixing paint and every proportional problem in between.
GCD of 48 and 36 is 12 → 48÷12 : 36÷12 = 4 : 3
Method: Euclid's algorithm for the greatest common divisor and the cross-multiplication rule for proportions — the standard approach taught in NCERT mathematics.
A ratio compares quantities of the same kind. "4 : 3" says that for every 4 units of the first quantity there are 3 of the second — nothing more, nothing less. It carries no information about absolute size: a 4 : 3 photograph can be a thumbnail or a billboard. That scale-independence is exactly what makes ratios useful, because it lets you carry a relationship from one situation to another of a completely different size.
48 : 36 and 4 : 3 describe the identical relationship; the second is just easier to grasp and compare. Simplification divides both sides by their greatest common divisor. When you simplify 1920 : 1080 to 16 : 9, you've discovered why every full-HD screen is described as "16 by 9" — the resolution is just that ratio scaled up by a factor of 120.
Most real ratio problems are scaling problems. A recipe for 4 people uses 3 cups of rice to 4 cups of water; for 6 people, solve 3 : 4 = 4.5 : X to keep the proportion. A map scale of 1 : 50,000 means 1 cm on paper is 50,000 cm (500 m) on the ground. Cement mortar mixed 1 : 4 keeps the same strength whether you're mixing one bucket or one truckload — as long as the ratio holds.
The ratio 4 : 3 can be written as the fraction 4/3 (comparing part to part) or as percentages of the whole: 4 parts out of 7 total is 57.1%, and 3 parts is 42.9%. Switching between these forms is often the fastest way to solve a problem — percentages for communicating, ratios for mixing, fractions for calculating. Our percentage calculator handles the percentage side of the same coin.
Ratios extend naturally to three or more parts. Sharing ₹9,000 among three people in the ratio 2 : 3 : 4 means the money is split into 2+3+4 = 9 equal parts of ₹1,000, giving ₹2,000, ₹3,000 and ₹4,000. The rule is always the same: add the parts, divide the total by that sum, then multiply back — a technique used for splitting profits between business partners, dividing inheritance, or allocating a budget.
If class A has a boy : girl ratio of 2 : 1 and class B has 1 : 2, the combined school ratio is not 3 : 3. It depends entirely on the class sizes. To combine ratios you must return to the actual quantities first — one of the most frequent errors in exam problems and real reporting alike.