Mathematical rules

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Order of operations Exponent rules Divisibility rules

Does the distributive law still hold once you leave the real numbers? Multiplying two negatives into a positive is the rule that trips up almost everyone What actually justifies moving a term across the equals sign with a flipped sign? Why does subtracting a negative number give a larger result? Why dividing by a fraction means multiplying by its reciprocal Where the convention that 0! equals 1 actually comes from Cancelling terms across an addition sign is the mistake teachers warn about most Logarithm rules and the base change formula in practice Exponent rules that quietly fail when the base is zero or negative Flipping the inequality sign when you multiply both sides by a negative Order of operations: why 2 + 3 × 4 is 14 and not 20 What changes about the rules of arithmetic when you work modulo n? Is a rule that works for every case you can test really a rule?

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