The distributive property explains that a factor multiplied by a sum can be found by multiplying it by each addend and combining the partial products, such as . Arrays, area models, and equations show why decomposing a factor preserves the product and supports efficient multi-digit multiplication; the focus is on whole-number computation rather than formal algebraic generalization or more advanced number systems.
To use the distributive property, break apart one factor into easier parts. Multiply the other factor by each part, then add the partial products.
Example: Find .
So,
The distributive property works because you are finding all the groups in and all the groups in , then combining them.
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