The Distributive Property, Part 1
Student Summary
When we need to do mental calculations, we often come up with ways to make the calculation easier to do mentally.
Suppose we are grocery shopping and need to know how much it will cost to buy 5 cans of beans at 79 cents a can. We may calculate mentally in this way:
5⋅795⋅(70+9)5⋅70+5⋅9350+45395
When we think, “79 is the same as 70+9. I can just multiply 5⋅70 and 5⋅9 and add the products together” we are using the distributive property.
In general, when we multiply two factors, we can break up one of the factors into parts, multiply each part by the other factor, and then add the products. The result will be the same as the product of the two original factors. When we break up one of the factors and multiply the parts we are using the distributive property of multiplication.
The distributive property also works with subtraction. Here is another way to find 5⋅79:
5⋅795⋅(80−1)5⋅80−5⋅1400−5395
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