Everyday Maths
The mental arithmetic that saves you money in a shop, a showroom or a meeting.
Every speed conversion is the same move — multiply by how many of the target unit fit in one of the source unit. Three constants cover almost every real case.
Every volume unit is a fixed multiple of one liter — once you know the multiple, converting any amount is a single multiplication or division.
Most tools and specs give angles in degrees, but the math behind CAD, trigonometry and many calculators runs in radians — the conversion is one multiplication by a fixed constant.
Estimating how much dirt a trench or grading job moves comes down to two cross-section areas, a distance, and a swell allowance — here's the formula and a worked run.
Every length conversion is one multiplication once you know a unit's factor in meters — the trick is picking exact factors, not rounded ones, so the answer doesn't quietly drift.
n! multiplies every whole number from n down to 1, and it answers a simple question — how many ways can these things be arranged — that shows up in probability, lottery odds and combinatorics.
A logarithm just asks “what power gets me here” — pH, decibel and bit-count problems all reduce to that one question, and the change-of-base rule handles any base a calculator doesn't have a button for.
Slope is just rise over run — but from two points you also get the angle and the y-intercept for free, and a wheelchair ramp, a roof pitch and a road survey all use the same three numbers.
Every volume formula here reduces to the same idea — base area times height, adjusted for the shape — and a shipping box worked two ways is the fastest way to see why the adjustment matters.
An exponent says multiply a number by itself repeatedly; a root undoes that — and a fractional exponent is both operations at once, which is worth being able to do on paper before trusting a calculator's display.
Both count ways to pick r items from n, but one counts arrangements and the other counts selections — and mixing them up is the most common mistake in a probability class.
Density is mass divided by volume, and it needs nothing but a scale and a way to measure volume to check what something is made of, whether it floats, or how concentrated a mix really is.