Fractions & Decimals
Fractions are where careful GRE test-takers separate from careless ones. The basic on-screen calculator handles decimals, but it will happily give you 0.6666666667 for 2/3 and then you have lost the exactness the question wanted — so the smart move is to stay in fractions as long as possible and convert only at the end. A fraction is just a division waiting to happen, and every fraction, decimal and percent is the same value in three outfits. This chapter drills the fluency the test assumes: simplifying, comparing without a calculator, the four operations, decimal place value, and the conversions that let you switch outfits instantly. Get comfortable here and ratios, percents and even algebra stop feeling like new topics.
Topics
⚡ GRE shortcuts & speed methods
The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.
- Stay in fractions for exact answers; convert to a decimal only at the very end. The basic calculator rounds and can hide ties.
- Memorise the benchmark table (1/8 = 12.5%, 3/8 = 37.5%, 1/3 ≈ 33.3%, …). It turns "37.5% of 64" into (3/8)×64 = 24 instantly.
- Compare two positive fractions by cross-multiplying: bigger cross-product sits over the bigger fraction.
- Cancel common factors BEFORE multiplying fractions — you work with far smaller numbers and rarely need to simplify at the end.
- A fraction terminates as a decimal only if, in lowest terms, its denominator is 2^a·5^b. Otherwise it repeats.
- To multiply decimals, multiply as whole numbers and place the point using the total count of decimal places.
⚠️ Common mistakes & traps
GRE is designed so that careless errors here cost you marks. Internalise each trap before the exam.
- Adding fractions straight across (2/3 + 1/4 ≠ 3/7). You must find a common denominator first.
- Trusting a rounded calculator decimal on a "which is greater?" call — 0.6667 vs 2/3 can flip the answer.
- Forgetting to invert the second fraction when dividing (multiply by the reciprocal, not the fraction).
- Misplacing the decimal point when multiplying decimals — miscounting the total decimal places.
- Leaving an answer unreduced when the choices are in lowest terms, then failing to find the match.
- Comparing decimals digit-count first (thinking 0.089 > 0.1 because it has more digits).
📈 GRE exam insight & question patterns
Quantitative Comparison — Quantity A: 5/9. Quantity B: 0.55. Which is greater?
5/9 ≈ 0.5556 > 0.55, so Quantity A is greater. Repeating decimals just past a benchmark are a classic trap.
Numeric Entry (fraction box) — 3/4 of a class of 32 study Spanish. Enter the number of students as a fraction of the whole reduced, then the count.
(3/4)×32 = 24 students; as a fraction of the class that is 24/32 = 3/4.
A recipe uses 2/3 cup of sugar; you make 1½ batches. How much sugar as a fraction?
(2/3)×(3/2) = 1 cup exactly — the fractions cancel cleanly, which is why staying in fractions beats decimals here.
Multiple-answer — which equal 0.375? Select all: 3/8, 37.5%, 15/40, 0.38.
3/8, 37.5% and 15/40 (= 3/8) all equal 0.375; 0.38 does not.
🎴 Flashcards — instant recall
Tap a card to reveal the answer. Drill these until they are automatic.
📌 Quick revision
- A fraction is a division and a decimal is a fraction over a power of 10 — the same value in different outfits.
- Simplify with the GCD; a fraction is fully reduced when numerator and denominator are coprime.
- Compare positive fractions by cross-multiplying or by benchmarking against 1/2 and 1.
- Add/subtract need a common denominator; multiply straight across (cancel first); divide by the reciprocal.
- Place value governs rounding and decimal multiplication — count total decimal places for products.
- Convert fluently: fraction→decimal by dividing, decimal→percent by ×100, percent→fraction over 100.
- Memorise the benchmark table so common values are recognised on sight.
- Stay in fractions for exactness; the basic calculator rounds and can flip close comparisons.
Chapter test
🏆 Vidaara GRE success checklist
You have truly mastered Fractions & Decimals when you can tick every box below.
- Recall every formula in this chapter without looking them up
- Solve each topic’s practice set with at least 80% accuracy
- Use the chapter shortcuts to cut your solving time in half
- Spot and avoid every common trap listed above
- Score 80%+ on the timed chapter test
📋 Chapter mastery scorecard
Track where you stand. Aim for the target before moving to the next chapter.
| Skill checkpoint | Target |
|---|---|
| Concept theory & formulas understood | 100% |
| Topic practice sets attempted (5 topics) | 5/5 |
| Best topic-test score | — → 80%+ |
| Chapter test score | — → 80%+ |
| Flashcards drilled to instant recall | 8 cards |
Formula Reference Sheet
Fraction operations
| Add / subtract | common denominator, then add numerators |
|---|---|
| Multiply | (a/b)(c/d) = ac/bd |
| Divide | (a/b) ÷ (c/d) = (a/b)(d/c) |
| Simplify | divide top and bottom by their GCD |
Conversions & benchmarks
| Fraction → decimal | divide numerator by denominator |
|---|---|
| Decimal → percent | multiply by 100 (shift 2 places right) |
| 1/8 = 0.125 | = 12.5% |
| 1/3 ≈ 0.333 | ≈ 33.3% |
| Cross-multiply to compare | a/b vs c/d ⇒ compare ad vs bc |