Fractions without fear: a 10-minute guide
Fractions are division written down: 3/4 means 3 ÷ 4. To add or subtract, force a common denominator; to multiply, go straight across; to divide, flip the second fraction and multiply.
They matter wherever precision beats decimals: recipes, construction, music, finance ratios. A third is 0.333… forever — 1/3 stays exact while decimals must round.
Mistakes: adding numerators and denominators separately (1/2 + 1/3 is not 2/5), forgetting to simplify (4/8 = 1/2), and mixing units inside one fraction.
Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. As a proportion: 3:4 = 6:x → x = 8.
Try: Fraction Calculator · Ratio & Proportion Solver
Unit conversion: exact factors vs approximations
Unit conversion is multiplication by 1 in disguise: 1 m = 3.28084 ft, so multiplying by 3.28084 changes the label, not the length. Chain factors and units cancel like algebra.
Exact vs approximate matters: 1 in = 2.54 cm exactly (by definition), but 1 L ≈ 4.23 cups is a rounded cooking convention. Engineering needs the exact factor; dinner needs the convenient one.
Mistakes: converting °C↔°F with a pure ratio (it has an offset: °F = °C×9/5+32), squaring the factor for areas (m²→ft² uses 3.28084²), and mixing US cups (236.6 mL) with metric cups (250 mL).
Example: 5 km → miles: 5 × 0.621371 = 3.107 mi. 2 cups → mL (US): 2 × 236.588 = 473 mL.
Try: Length Converter · Cooking Converter
Ohm's law in practice
Ohm's law is one triangle: V = I × R. Cover the letter you want — voltage equals current times resistance, current equals voltage over resistance, resistance equals voltage over current. Power rides along: P = V × I.
It matters for sizing fuses, resistors, LED current-limiting, and answering 'why does my cable get warm'. Every circuit question starts here before anything fancier.
Mistakes: mixing milliamps with amps (220 mA = 0.22 A), applying DC law to AC reactive loads, and forgetting that P = V×I with household 230 V turns small currents into serious watts.
Example: 12 V across 4 Ω → I = 3 A, P = 36 W. A 1500 W heater at 230 V draws ~6.5 A — that decides the fuse.
Try: Ohm's Law Calculator · Electric Power & Cost