One idea, three costumes
A fraction, a decimal and a percent are three ways of wearing the same number. One-half, 0.5 and 50% are identical quantities in different outfits. Once you truly believe that, conversions stop being magic tricks and become obvious moves.
The bridge between all three is place value and powers of ten. Fraction to decimal: divide the top by the bottom (1 ÷ 4 = 0.25). Decimal to percent: multiply by 100, or just slide the decimal point two places right (0.25 → 25%). Percent back to decimal: slide two places left (7% → 0.07).
- 1/2 = 0.5 = 50% — same number, three costumes
- Fraction → decimal: divide numerator by denominator
- Decimal → percent: move the decimal point 2 places right
- Percent → decimal: move the decimal point 2 places left
- Decimal → fraction: use place value (0.7 = 7/10)
Working with fractions without fear
Fractions only follow two big rules. Rule one: you can only add or subtract when the denominators (bottoms) match — find a common denominator first. Rule two: you can always multiply straight across, top times top, bottom times bottom, no matching needed.
Division uses the famous 'keep, change, flip': keep the first fraction, change ÷ to ×, flip the second fraction upside down. It works because dividing by a fraction means asking 'how many of these fit in that?' And always simplify your final answer by dividing out common factors — 8/12 isn't finished until it's 2/3.
- Adding: common denominator first, then add tops only
- Multiplying: straight across, then simplify
- Dividing: keep, change, flip — then multiply
- Simplify by dividing top and bottom by the same number
- Mixed numbers: convert to improper fractions before computing
Common denominator is 12. Rewrite: 2/3 = 8/12 and 1/4 = 3/12. Add the tops: 8/12 + 3/12 = 11/12. No simplification needed — 11 and 12 share no factors.
Percents: the real-world champion
Percents show up everywhere money goes: tips, discounts, tax, interest, test scores. The key insight is that 'percent' literally means 'per hundred,' so 25% is just 25/100 = 0.25. Finding 25% of 80 becomes 0.25 × 80 = 20.
Learn your benchmark fractions cold and mental math transforms: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/10 = 10%, 1/3 ≈ 33.3%. To tip 20%, move the decimal on the bill one place left and double it. To take 10% off, move the decimal one left and subtract. Percent power is estimation power.
- Percent means 'per hundred' — 25% = 25/100 = 0.25
- Find percent OF a number: convert to decimal, multiply
- 20% tip trick: 10% (move decimal left) × 2
- Discount: original × (1 − percent as decimal)
- Memorize: 1/2=50%, 1/4=25%, 1/5=20%, 1/10=10%
Key concepts to memorize
🎯 Study tips for this topic
- Memorize the benchmark conversions (1/2, 1/3, 1/4, 1/5, 1/8, 1/10) — they power all mental math.
- When a fraction problem confuses you, convert everything to decimals; often it becomes obvious.
- Draw a rectangle and shade it — visual fraction sense beats rules for beginners.
- Drill conversions with the flashcard deck until 3-second recall, then let spaced repetition maintain it.
