Use commutative, associative, and distributive structure to rewrite and simplify numerical expressions efficiently.
Translate a shortcut into symbols
Problem
Use the shortcut: “Rewrite \(16\) as \(4~\times~4\), then multiply \(4~\times~25\) first.” Start with \(16~\times~25\). Write an equivalent symbolic rewrite that shows this strategy, and then find the value.
Big Picture
What this problem is really about
The shortcut works by breaking one factor into smaller factors and regrouping them. We’ll replace sixteen with four times four, use the associative property to pair one four with twenty-five, and then multiply by the remaining four. The factors and product stay unchanged while the arithmetic becomes friendlier.
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