When you use the distributive property do you use multiplication or addition?

Answer 1

The distributive property uses both operations. As usual with this sort of thing, it's best to start with an example. Let's say you are asked to multiply in your head the numbers 6 and 17. Very few of us have memorized our multiplication tables up to 17, so we're stuck doing a mental calculation. One easy way of doing it is to use the distributive law. Here's how. If you wish to multiply 17 by 6, first think of 17 as the sum of 10 and 7. That is to say, 17 = 10 + 7. Now, just multiply the 10 by 6 (to get 60) and the 7 by 6 (to get 42). Now add those two products to get 102 (60 + 42). In mathematical terms, 6 x 17 = 6 x (10 + 7) = 6 x 10 + 6 x 7 = 102. You have "distributed" the 6 over the 10 and 7. So the distributive property uses both addition and multiplication, because it is a law that addresses both operations to begin with.