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The distributive law of algebra gives multiplication a natural higher precedence in notation
The convention that multiplication is performed before addition—memorably encoded in PEMDAS—grew out of the needs of algebraic notation in the 1600s and was later formalized in school textbooks as par...
The standard long-multiplication algorithm is not a mysterious new rule but a compact, place-value–aware shorthand for computing the same set of partial products that arise when numbers are expanded a...
PEMDAS is a shorthand to resolve ambiguity in multi-operation expressions: do Parentheses, then Exponents, then Multiplication/Division (left-to-right), then Addition/Subtraction (left-to-right) — whi...