78 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 Simplify an Expression: Step by StepTwo moves, always in the same order: distribute what is in parentheses, then add up the coefficients of every matching power of x.7 min read Concept AlgebraWhat Does It Mean to Simplify an Expression?Simplifying does not change what an expression equals — it rewrites it in a form with fewer, cleaner terms that means exactly the same thing for every value of x.6 min read Mistakes Fractions5 Common Ratio MistakesFour of the five are caught the same way: add the parts back up, or reduce the answer again, and compare with where you started.6 min read Examples FractionsRatio Examples: 7 Worked ProblemsSeven ratios, ordered so each one adds exactly one new idea to the last — every answer here is checked by adding the parts back or reducing them again.6 min read Method FractionsHow to Simplify a Ratio (and Split a Total by It)Simplifying a ratio and splitting a total are two sides of the same idea: keeping the relationship between the parts intact while the numbers change.7 min read Concept FractionsWhat Is a Ratio? A Plain ExplanationA ratio is a comparison, not a count. 2:3 says nothing about the actual sizes involved — only that the second is always one and a half times the first.6 min read