Use commutative, associative, and distributive structure to rewrite and simplify numerical expressions efficiently.
Use a common factor in context
Problem
The art club buys \(18\) sketchbooks, and the science club buys \(27\) sketchbooks. Each sketchbook costs \(\$4\). Which complete response correctly represents the total cost?
Big Picture
What this problem is really about
Both clubs pay the same price for every sketchbook, so that unit price is a common factor. We’ll write each club’s cost as quantity times price, factor the shared price outside a sum, and combine the sketchbook counts before multiplying. This reverse-distributive form preserves both club purchases.
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