16 explainers

Knowledge base

The reasoning behind every calculator, written out. Each article names what you need to know first, works through the method, and says where it usually goes wrong — so you can get unstuck without asking anyone.

Method AlgebraHow to Factor a Trinomial: Step by StepFactoring a trinomial means finding the two binomials that multiply to give it. There is one method that always works, and one shortcut worth knowing.7 min read Method FractionsHow to Add Fractions With Different DenominatorsAdding fractions is only hard when the denominators differ. Once you know why they have to match, the method stops being a rule to memorise.6 min read Method Basic MathHow to Simplify a Square Root Step by Step√72 and 6√2 are the same number. The second is the finished answer, and getting there is a search for one thing: the largest square factor.6 min read Method Pre-AlgebraHow to Solve a Proportion by Cross-MultiplyingA proportion says two ratios are equal. Cross-multiplying is not a trick — it is one multiplication applied to both sides.6 min read Concept GeometryThe Pythagorean Theorem Explained Simplya² + b² = c² is a statement about areas, not just a formula. Once you see the squares, the theorem stops needing to be memorised.7 min read Method TrigonometryHow to Convert Degrees to Radians (and Back)Every conversion is one multiplication. The part worth understanding is why the factor is π/180, and why the answer should stay in terms of π.5 min read Concept CalculusWhat Is a Derivative? A Plain ExplanationA derivative measures how fast something is changing at a single instant. Every rule in differentiation is a shortcut for that one idea.7 min read Distinction StatisticsMean, Median and Mode: Which Average to UseThree numbers all called the average, answering three different questions. Choosing wrongly is how statistics ends up misleading.6 min read Method GraphingHow to Find Slope-Intercept Form From Two Pointsy = mx + b is the form that tells you what the line looks like. Two numbers, and each one is visible on the graph.6 min read Method ConvertersHow to Convert Celsius to Fahrenheit (and Back)The formula does two separate things: it changes the size of a degree, then it moves the zero. Missing the second is why manual conversions go wrong.5 min read Concept FractionsWhat Is a Fraction? Numerator and DenominatorA fraction is two numbers doing two different jobs. Once you know which job is which, most of the rules stop needing to be memorised.6 min read Formula FractionsFraction Rules: All Four Operations in One PlaceFour operations, four rules, and one idea underneath all of them: you can only combine parts that are the same size.6 min read Examples FractionsFraction Examples: 10 Worked Problems With AnswersTen problems, worked in full. They are ordered so each one adds exactly one new difficulty to the last.7 min read Mistakes Fractions5 Common Fraction Mistakes and How to Catch ThemEvery one of these has a ten-second check. Learning the checks is faster than learning to never make the mistake.6 min read Distinction FractionsMixed Number vs Improper Fraction: Which to UseTwo ways of writing the same quantity. One is easier to picture, the other is easier to calculate with — and questions expect you to move between them.5 min read Application FractionsFractions in Real Life: Where They Actually Turn UpFractions did not survive because schools like them. They survive because for halving, sharing and measuring, they are simply better than decimals.5 min read