Everyday Maths
The mental arithmetic that saves you money in a shop, a showroom or a meeting.
Converting money at a rate you already have is one multiplication — the skill worth learning is which direction the rate points.
Four shapes, four formulas — width × height, half base × height, πr², and (a+b)/2 × height cover nearly every flat surface you'll ever need to measure.
A ratio simplifies to its lowest terms the same way a fraction does — divide both sides by their greatest common divisor. One division rule, endless uses.
Two coordinates and one formula — the straight-line distance between any two points is just the Pythagorean theorem applied to their x and y gaps.
Time = distance ÷ speed. The division is the easy half — the half people get wrong is turning the decimal answer into hours and minutes.
A fraction is a division that hasn't been done yet — 3/8 means 3 ÷ 8. Doing it is what makes two fractions comparable at a glance.
Resistance = V ÷ I and power = V × I. Between them they answer most hobby wiring questions — provided you feed in the voltage across the part, not the supply.
The greatest common divisor reduces a fraction to its simplest form; the least common multiple tells you when two repeating cycles next coincide.
One formula solves every quadratic. The part under the square root answers a question first: how many real solutions are there at all?
Testing whether a number is prime looks like it needs a lot of division. It needs far less than people expect — and the reason why is a neat piece of logic.
Not every loan compounds. Here's the formula behind flat-rate interest, a real worked example, and exactly how many dollars compounding would have added to the same loan.
A percent is just “per hundred.” Learn the one rule and three shortcuts, and most percentage problems become mental math.