Ratio and Proportion

GRE Quantitative · Axiom Academy

Comparing two quantities, scaling them together, and solving for an unknown by cross-multiplication. 1. A Ratio Is a Relationship, Not a Number The ratio of 3 to 4 is written 3:4 or . It doesn't say there are exactly 3 and 4 of anything — it says that for every 3 of the first quantity, there are 4 of the second . Scale both quantities by the same factor and the ratio never changes. Scaling both sides by the same factor k Scaling means multiplying both parts of a ratio by the same number. The relationship stays identical — only the actual sizes change. This is the move the GRE tests most: give you the ratio and one real value, and ask you to find the scale factor first. The ratio 2:5, scaled by 3, becomes 6:15. Same relationship, bigger numbers. 6:9 shares a common factor of 3, so it reduces to 2:3 — the same relationship in lowest terms. If A:B = 2:5 and A = 8, then is the scale factor — apply it to B too. . The scale factor found from one side always applies to the other. Ratios simplify to lowest terms, and the GRE writes them in whichever form is convenient. Always check: is 6:9 the same relationship as 2:3? Yes — divide both parts by their greatest common factor to confirm. 3. Solving a Proportion by Cross-Multiplying A proportion is an equation stating that two ratios are equal. Picture it as a balance beam: one ratio's cross-product sits on the left, the other's on the right. The beam only balances — the equation only holds — when those two cross-products are equal.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.