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Partial Products Method

The partial products method is a conceptual alternative to the traditional long algorithm for multiplication, using the distributive property to break down factors into place-value parts and multiply every pair of parts.

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Jan 14, 2026
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How does the standard long-multiplication algorithm relate to partial products and the distributive law?

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...