The distributive property explains that multiplying a whole number by a sum or difference gives the same result as multiplying each part and then combining the partial products, as in . Decomposing factors by place value supports efficient computation and reveals the connection between arrays, area, and multiplication; the scope is limited to numerical whole-number expressions, not negative or rational numbers or symbolic polynomial expansion.
To use the distributive property, break apart a number into friendly parts, multiply each part, and then add the partial products.
For example, find:
Break into tens and ones:
Rewrite the multiplication:
Multiply by each part:
Find the partial products:
Combine them:
Therefore,
The distributive property lets you multiply by each place-value part and combine the results.
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