M02 | Lesson 1: Fractions, Decimals & Signed Numbers

The Core Idea

Fractions, decimals, and signed numbers are the foundation the GRE builds every other math concept on top of. The errors here almost never come from forgetting a rule entirely — they come from applying a half-remembered rule at speed, with unfamiliar numbers, under pressure. That's what this lesson fixes.

How It Shows Up

This material appears directly in roughly 3–5 Quant questions per section, but it feeds into almost everything else — fractions live inside exponent problems, decimals show up in rate and percent questions, signed number behavior hides inside inequalities. Difficulty ranges from basic simplification to hard Quantitative Comparison questions where the answer hinges entirely on knowing what happens to a fraction when the variable sits between 0 and 1.

The Rule

Fractions. A fraction c/d has numerator c and denominator d (d can never equal zero). Every integer is a fraction: n = n/1. Multiplying both parts by the same nonzero integer gives an equivalent fraction: 40/72 = 5/9. The three sign forms are identical: −c/d = c/(−d) = −(c/d) — the GRE uses all three interchangeably.

Operations. Adding with different denominators: find a common denominator, convert each fraction, then add numerators. Multiplying: multiply numerators together, denominators together — cross-cancel first to keep numbers manageable. Dividing: invert the second fraction and multiply.

(a/b) ÷ (c/d) = ad/bc

Mixed numbers. 3⅖ = (3×5 + 2)/5 = 17/5. A mixed number with a whole part of 1 — like 1⅞ — is always