Everyday Maths
The mental arithmetic that saves you money in a shop, a showroom or a meeting.
A gradient is one multiplication per channel repeated across a line. Why a gradient between two channel-opposite colours always passes through grey, and what moving a stop really changes.
How many days from Monday to Friday depends entirely on whether you count both ends. Both answers are correct arithmetic, and the ambiguity is worth naming out loud.
An age in years depends on whether the birthday has already happened this year, and one month after 31 January has no single correct answer. Here is how the calculation actually proceeds.
Counting weekdays between two dates is exact arithmetic. Deciding which days are the weekend, and which holidays you observe, is not something any date can tell you.
The best-known number in fitness was never a precise result, and people of the same age genuinely differ. What the arithmetic gives you, and what no arithmetic can.
Two standard formulas agree exactly at ten reps and then pull apart fast. The arithmetic, and why an estimate from a high-rep set is worth much less than one from a low-rep set.
Minutes per kilometer, kilometers per hour and total time are the same fact rearranged. The conversions worth carrying in your head, and why small pace changes compound over distance.
The number comes from a MET value, a population average for an activity, multiplied by your weight and your minutes. What each part means, and why the output is a scale rather than a measurement.
A diagonal measurement tells you almost nothing about how much surface you get, because the answer depends on the shape as well as the length. The formula, worked through at one fixed diagonal.
Pixels per inch comes from Pythagoras on the pixel grid, and it is exact arithmetic. What it cannot do on its own is describe what reaches a viewer, because that depends on distance.
Area grows with the square of the radius, which makes the difference between two round things much larger than their diameters suggest. Worked through with real numbers, including the two-small-versus-one-large comparison.
The right-triangle relationship earns its keep away from the classroom: sizing a diagonal brace, checking whether something fits through an opening, and proving a corner is square before you fix it.