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Knowledge base
More explainers from the knowledge base. Each one names what you need to know first, works through the method, and says where it usually goes wrong.
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.
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.
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.
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.
Mistakes Basic Math5 Common Nth Root MistakesFour of the five are caught the same way: raise your answer back to the original index and confirm it reproduces the radicand.
Examples Basic MathNth Root Examples: 8 Worked ProblemsEight roots, ordered so each one adds exactly one new idea to the last — every simplification here is checked by raising it back to the original number.