Ratio Calculator

In the proportion a:b = c:x, the cross products are equal: a×x = b×c, so x = (b×c)÷a. Why it works: a ratio is a fraction, equal fractions have equal cross products, and solving for the unknown is one division. The calculator shows exactly this arithmetic so it can be copied as homework work. The practical shortcut it produces: the scale factor c÷a, which converts *any* quantity in the original ratio, not just the one you asked about.

Two moves. Decimals: multiply both sides by 10 until whole — 2.5:1.5 → 25:15 → 5:3 (the simplifier here works on whole numbers, because GCD does). Mixed units: convert to the same unit first — 30 minutes : 2 hours is 30:120 = 1:4, not 30:2. Forgetting the unit conversion is the single most common ratio error in word problems, and it produces answers that are confidently, cleanly wrong.

Mechanically nothing — 3:4 and 3/4 simplify identically, which is why GCD works on both. Conceptually, the reading differs: 3:4 usually compares part to part (3 cups flour to 4 eggs), while 3/4 usually reads part of whole. The trap: a class with a 3:4 boy-girl ratio is 3/7 boys, not 3/4. When a word problem feels off by a suspicious amount, check whether you've mixed part-to-part with part-to-whole.

Set up the proportion with what you know: the recipe serves 4 and you need 10, so the scale factor is 10÷4 = 2.5 — multiply every ingredient by it. Or per-ingredient: 2 cups rice : 3 cups water = 5 cups rice : x → x = 7.5. Kitchen honesty: scale spices and salt by less than the factor (start at ~75% and adjust), and baking is chemistry — scaling beyond about double gets unreliable for leavening.