Study Guide to Fractions, Decimals and Percentages: 75 Flashcards from Numerators to Repeating Decimals

Most people who "can't do fractions" actually stumble on three separate skills: reading what the two numbers mean, moving between fraction, decimal and percent notation, and knowing which operation rule applies. The Fractions, Decimals & Percentages deck (code WN2143 on Flip It) splits those skills into 75 cards that mix definitions with worked mini-problems, so you drill the rule and the calculation side by side.

Sample cards

Everything the deck drills

• Vocabulary and etymology: fraction from Latin fractus (broken), numerator, denominator, the "invisible denominator" 1, per centum, permille (parts per thousand).
• Types of fractions: proper, improper, unit, dyadic, mixed number, decimal fraction, complex, compound, Egyptian, equivalent fractions, reciprocal (multiplicative inverse).
• Conversions: mixed ↔ improper, fraction ↔ decimal ↔ percent, repeating decimals (0.333… = 1/3, 0.5̄ = 5/9), 0%, 100% and 150% as fractions.
• Simplifying and comparing: lowest terms, greatest common divisor, common denominators, cross-multiplication, least common denominator.
• Four operations: adding and subtracting with like and unlike denominators, multiplying (with cancellation), multiplying by a whole number, dividing by the reciprocal, halving and doubling fractions.

Two tips specific to this deck

Memorise the "nines trick" as a pattern, not a fact. Three cards cover repeating decimals, and they share one rule: put the repeating block over as many 9s as it has digits. 0.5̄ → 5/9, 0.6̄2̄ → 62/99, and by extension 0.3̄ → 3/9 = 1/3. Once you see the pattern, the three cards become one, and you can generate the answer for any repeating decimal the deck (or a test) throws at you.

Build a mental "benchmark table" from the conversion cards. The deck repeatedly returns to 1/2, 1/4, 1/5, 2/5, 3/4 and 1/8 with their decimals (0.5, 0.25, 0.2, 0.4, 0.75, 0.125) and percentages (50%, 25%, 20%, 40%, 75%, 12.5%). Learn these six as a block. Almost every other conversion in the deck is a multiple or a half of one of them — 3/8 is three eighths, so 37.5%; 60% is three fifths — and comparing fractions like 3/4 vs 5/6 becomes trivial when you can read both as decimals instantly.

How to sequence the 75 cards

Take the deck in the order it is written: definitions, then simplifying and comparing, then the four operations, then decimal and percent conversions. Each block assumes the previous one — you cannot add 1/3 + 1/4 without a least common denominator. Ten to fifteen cards a day puts the whole deck in rotation within a week; keep the worked-problem cards (Reduce 63/462, Divide 2/3 ÷ 3/4) in daily review longest, since they test the rules under time pressure.

Open Flip It, find WN2143 — Fractions, Decimals & Percentages in the library, and start with the first ten definition cards.

Related reading: the Mathematical Constants, Squares, Cubes and Roots guide pairs well with this deck for building number sense.