ratio

A ratio compares two quantities by division. Three to four, 3:4 and 3/4 all say the same thing: for every 3 of the first quantity there are 4 of the second. Ratios are used whenever a question describes a mix rather than a count — paint mixed 2 parts red to 1 part white, a class with 5 boys for every 7 girls, a recipe scaled up or down.

The trap is that a ratio does not give you the totals. A 3:4 ratio says nothing on its own about how many there are; 3 and 4, 30 and 40, and 300 and 400 all satisfy it. When a question supplies a total, the ratio parts plus a multiplier are the way in: add the parts (3 + 4 = 7), divide the total by that sum to find the value of one part, then multiply each part by it.

Keep the order straight as well. "The ratio of a to b" is a/b, and reversing the two is the most common way to lose an otherwise correct answer. Simplify only when you want to compare ratios to each other.