Three ratio jobs in one place: solve A : B = C : X for the missing value, reduce a ratio to lowest terms, and divide a total into parts according to a ratio. Useful for recipes, scale drawings, mixing ratios and splitting anything proportionally.
In a : b = c : d the cross products are equal, so a x d = b x c. Rearranging for whichever value is unknown solves it. That one identity handles scaling recipes, reading map distances, converting currencies at a fixed rate and mixing anything to a specification.
Add the parts to get the number of shares, divide the total by that, then multiply by each part. Splitting 1000 in a 2:3:5 ratio gives 10 shares of 100, so 200, 300 and 500. The parts do not need to be whole numbers, but they do all need to be positive.
A ratio compares quantities: 3 : 4 means three of one for every four of the other. A proportion is a statement that two ratios are equal. A fraction is a ratio of a part to the whole - so 3 : 4 corresponds to the fraction 3/7 of the total, not 3/4. Conflating those two is the most common mistake in ratio problems.
In a : b = c : d the cross products are equal, so a x d = b x c. Rearranging for whichever value is missing solves it. That single identity is behind almost every scaling problem, from recipes to map distances.
Add the parts to get the total number of shares, divide the amount by that, then multiply by each part. Splitting 250 in a 2:3 ratio gives 5 shares of 50, so 100 and 150.
Steuervergleich Kanton Zürich — Gemeindesteuern vergleichen (Deutsch)