A ratio compares two quantities — A to B, written A:B. Two everyday tasks come up: simplifying a ratio to its lowest terms by dividing both numbers by their greatest common divisor, and solving a proportion, where two ratios are set equal and one term is unknown. The key fact is that multiplying or dividing both terms by the same number leaves the ratio unchanged, so 3:4, 6:8 and 9:12 are all the same ratio. That invariance is what lets you scale recipes, mixes and drawings.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: GCD reduction and cross-multiplication.
The ratio equations
Simplifying a ratio is identical to reducing a fraction: find the greatest common divisor of both terms and divide through. Solving a proportion uses cross-multiplication — because A/B = C/D, the cross products A·D and B·C are equal, so any single unknown is found by rearranging. The decimal value A ÷ B gives a single comparable number, and dividing each term by the total A + B converts the part-to-part ratio into part-to-whole percentages.
Worked example — simplify and solve
Simplify: reduce 18 : 24.
Solve a proportion: find x in 3 : 4 = 9 : x.
So 18:24 reduces to 3:4, with a decimal value of 0.75 and a percentage split of about 42.86% to 57.14%. The proportion 3:4 = 9:12 confirms that 9:12 is just 3:4 scaled up by three — an equivalent ratio. This is exactly how scaling works in practice: to keep a 3:4 mix while using 9 units of the first ingredient, you need 12 of the second. Whether you are resizing an image to a 16:9 frame or tripling a recipe, the same two operations — reduce and cross-multiply — cover almost every ratio problem.
Frequently Asked Questions
Divide both terms by their GCD. 18:24 ÷ 6 = 3:4.
Cross-multiply. 3:4 = 9:x → 3x = 36 → x = 12.
Same ratio at different scales: 3:4, 6:8, 9:12 all reduce to 3:4.
A ÷ B. 18:24 = 0.75, and 3:4 = 0.75 too — equal ratios share a decimal.
Divide each term by the total. 18:24 → 18/42 ≈ 42.86% and 57.14%.