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 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.