All in One Calculator guide
Six Calculators That Cover Most of School Maths
Six calculators cover the majority of school and early university maths: fractions for arithmetic, quadratics for algebra, the rule of Sarrus for linear algebra, base conversion for computing, area and perimeter for geometry, and the rule of three for proportions.
Fractions — arithmetic
Where it turns up: roughly ages 9 to 14, and then constantly afterwards as a component of harder problems.
Fractions are the point where a lot of students first decide they are "bad at maths", usually because the rules for adding and multiplying look contradictory. You need a common denominator to add, but not to multiply, and there is no obvious reason why.
It is worth working through the reasons rather than memorising both rules, because fractions never stop appearing. Algebra is largely fractions with letters in.
Quadratic equations — algebra
Where it turns up: ages 14 to 18, and in every subsequent maths course.
The quadratic formula is one of the few things from school maths that almost everyone remembers decades later, partly because it gets drilled so hard and partly because it genuinely works on everything.
The sticking points are consistent: keeping the sign of b, and understanding what the discriminant is telling you before you finish the calculation.
Rule of Sarrus — linear algebra
Where it turns up: final year of school or first year of university.
Determinants come up in linear algebra, and the rule of Sarrus is the fastest way to handle the 3×3 case by hand. Most students meet it alongside matrix inverses and Cramer's rule.
It is the most specialised of the six, and the one where good explanations are hardest to find — which is why it has the most detailed guides on this site.
Base conversion — computing
Where it turns up: computer science courses at any level, and any programming work.
Binary, hexadecimal and octal are unavoidable once you touch computing. Colour codes, memory addresses, file permissions and network masks all assume you can move between bases.
The good news is that it is mechanical. Once the method is clear there is nothing conceptually hard left, unlike most of the other topics here.
Area and perimeter — geometry
Where it turns up: ages 8 to 16, and then whenever you own or decorate anything.
This is the topic with the longest practical life. Flooring, paint, turf, fencing and fabric are all area or perimeter problems, and getting them wrong costs money.
The recurring mistake at every level is the same: using a slanted side where the formula wants a perpendicular height.
Rule of three — proportions
Where it turns up: ages 10 to 14 formally, and then constantly in everyday life without being named.
Recipe scaling, currency conversion, unit pricing, map scales, percentages and aspect ratios are all the same calculation wearing different clothes.
The part worth learning properly is telling a direct proportion from an inverse one. The arithmetic is easy; choosing the wrong type is what produces confident wrong answers.
