What is the distributive property of 45+90?

Question

I dont understand im in middle school i need help .

Answer 1

The distributive property is where you have a number that can be multiplied into the other numbers for the same result.

Let's take a look at 45 + 90. 45 and 90 both have a 3 in common, and a 5 in common, which means they have a 15 in common (because 3 times 5 equals 15):

45 ÷ 15 = 3

90 ÷ 15 = 6

so our expression now looks like:

15(3 + 6)

But wait, there's more! 3 and 6 have a three in common as well, so that can get factored out, too:

45(1 + 2)

Now just to show that each of these expressions equate, I'm going to solve them to demonstrate:

45 + 90 = 135

15(3 + 6) ⇒ 15 * 9 = 135

45(1 + 2) ⇒ 45 * 3 = 135

 

And that's what the distributive property is: You factor out a common multiple from the other numbers which can be later multiplied back in, or divided out in equations.