Everyday Maths
The mental arithmetic that saves you money in a shop, a showroom or a meeting.
Every line is right, the total is right, and they disagree by a penny. That is rounding doing exactly what it does — plus why half-up and half-even give different answers.
Two discounts applied one after the other multiply, they do not add. “50% off, then an extra 20% off” is 60% off, and here is the arithmetic that shows why — plus the one case where the order really does matter.
Move the decimal point one place and you have 10%; everything else is halves and doubles of that. Then the harder part — splitting a bill where people ordered very differently, and the pre-tax question, both put to you as choices rather than rules.
The common error is multiplying the gross figure by the rate. Divide by 1 plus the rate instead — and the wrong method is always too high by exactly the rate, which is why it survives so long unnoticed.
Miles per gallon measures distance per fuel, so equal steps up the mpg number are not equal savings. Over the same distance, going from 15 to 20 mpg saves more than three times the fuel that going from 40 to 50 does.
The ratio comes out of 1830s social statistics and picked up its modern name over a century later. Here is the arithmetic and what it contains.
Devine and its successors exist to estimate lean mass so a medication dose can be calculated. They were never validated as targets for a person.
A tape measure and a logarithm produce a percentage to six decimal places. Here is the method, and why the precision is not the accuracy.
One division, no constants, no reference table, no population fit. The simplest measure in the set is also the most portable, and that is not a coincidence.
Contrast ratio is a defined calculation over relative luminance, not a judgement call. The gamma correction, the channel weights, and one worked example from two hex codes to a number.
A hex colour is three bytes written in base 16, and once you can read it #1a2b3c stops being opaque. Including why the shorthand #abc expands to #aabbcc and not #0a0b0c.
A tint and shade ramp built by mixing toward white and black in sRGB takes equal steps in the numbers and very unequal steps in perceived lightness. The measurements, on a real nine-step ramp.