On a 1:50,000 map, 3 cm represents 3 × 50,000 = 150,000 cm, or 1.5 km. Keep both units in view while converting; scale means map distance to real distance, not a percentage reduction.

Four values: 6, 8, 9, 13. Mean = 36/4 = 9; median = (8+9)/2 = 8.5. Add one very high outlier and the mean can move more than the median. They describe different things, so choose the measure that fits the question.

A triangle with an 8-ft base and a 5-ft perpendicular height has area (8 × 5) ÷ 2 = 20 sq ft. Use the perpendicular height, not a slanted side. For an irregular garden bed, split it into triangles and add the areas.

A 90-mile trip takes 1.5 hours at 60 mph and 2 hours at 45 mph—30 minutes longer, even though the speed is 25% lower. Travel time changes inversely with speed, so compare trip time, not just the speed difference.

A 3:2 recipe ratio has 5 total parts. If the batch is 750 mL, one part is 750 ÷ 5 = 150 mL: use 450 mL of the first ingredient and 300 mL of the second. Scale every part together to keep the ratio.

With a 6% nominal APR compounded monthly, $1,000 becomes $1,061.68 after a year: $1,000 × (1 + 0.06/12)^12. That’s a 6.17% effective annual yield before fees or taxes. Compounding changes the annual result; APR alone doesn’t show it.

At 1.25× speed, an 80-minute recording takes 80 ÷ 1.25 = 64 minutes. That saves 16 minutes, not 25: playback time is inversely related to speed. Multiply by the rate to estimate duration.

Mix 1 cup of concentrate with 4 cups of water: the finished drink has 5 cups total, so concentrate is 1/5 = 20%. The recipe ratio is 1:4; the percentage uses all five parts in the finished mixture.

A 12 ft × 9 ft room has 108 sq ft of floor area. A 10% tile buffer brings the estimate to 118.8 sq ft, so round up to at least 119 sq ft (then to full-box coverage). That allowance covers cuts and breakage; complex layouts can need more.

Scaling a 3:2 recipe? If 3 cups of flour becomes 12 cups, the scale factor is 4. Multiply both parts: 2 cups of the second ingredient becomes 8 cups. Ratios scale by multiplication; adding the same amount to both sides changes the relationship.

Buy for $80, sell for $100. The $20 profit is a 25% markup on cost, but a 20% margin on selling price. Same dollars; different denominator. When you set a target margin, calculate from the sale price—not the purchase cost.

A 20% increase followed by a 20% decrease doesn’t get you back to the start:

100 → 120 → 96

Same percentage. Different starting value.

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