Use commutative, associative, and distributive structure to rewrite and simplify numerical expressions efficiently.
Rewrite a contextual calculation efficiently
Problem
A classroom buys \(8~\text{packs}\) of pencils, and each pack has \(25~\text{pencils}\). Rewrite the total in an efficient way using a property of operations, then find how many pencils the class bought altogether.
Big Picture
What this problem is really about
The story is about equal groups, and the product becomes easier if we pair the packs. We’ll rewrite eight as four times two, regroup so two multiplies twenty-five first, and then multiply the four equal pair totals. The associative property changes only which factors we combine first, so every pack is still counted.
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