Smart Numbers

Definition

Smart Numbers in plain English

Use Smart Numbers when variables cancel and a friendly number reveals the relationship. Clues include in terms of, what is the ratio, or independent of n. Pick a convenient value that respects constraints (often a LCM or 100), compute, read the invariant. Full symbolic algebra is correct but slower when the stem only wants a ratio or a percent. Choose numbers that keep fractions clean so arithmetic noise does not hide the relationship. Micro-example: a recipe uses flour:sugar = 2:3 and asks the fraction that is sugar. Pick 2+3 = 5 cups total; sugar is 3/5. No variables required once the smart total is chosen.

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