Ratio & Proportion

Read, simplify, and split quantities by a ratio. Ratios appear in arithmetic, geometry, and data questions alike.

Tell the two kinds of proportion apart and solve speed, work, and price problems without setting up heavy algebra.

Reduce any rate to "per one" and you can compare prices, speeds, and productivity instantly.

Use a scale factor to move between a drawing and reality, and between two similar shapes.

Track a part of a whole through mixing, and chain two ratios into one three-term ratio.

Treat every percent question as part / whole = percent / 100 — one set-up solves all three question types.

Use multipliers to apply, chain, and reverse percentage changes without slips.

Split a quantity three ways and solve age/ratio word problems with the "parts" method and a single variable.

Add rates, not times, to solve "how long together" problems — the single rule that cracks work questions.

Chain conversion factors so the unwanted units cancel — the safe way to convert anything.