# Why do we want the distributive property?

I think that you can get motivation for our arithmetic rules from geometry, interpreting multiplication as finding the area of rectangles. Suppose we want to compute $4(2+3)$. On one hand, this is $4\cdot 5$, finding the area of a $4\times 5$ rectangle. On the other hand, we can break it up into a $4\times 2$ and $4\times 3$ rectangle. We should expect the two values to be the same, because we simply took a figure and cut it into two parts.