Question

Explain how you can mentally find 8 times 45 by using Distributive property.AND PLEASE EXPLAIN

Answer 1

Very handy question. Don't use a calculator. That's "cheating" when you do problems like this.

Most people would break up 45 into something more easily handled but I think there is an easier way to do it. All you have to know is what 2 * 45 is.

Do you know that 2 * 45 = 90?

If you do then here's a much easier way to do the problem.

45 ( 10 - 2)

45* 10 = 450

45 * 2 = 90

450 - 90 = 360

Answer 2

Well, look at this. 45, 4 is in the tens place and 5 is in the ones place so we have
$(40 + 5)$
because 4 is a ten, so basically 4 times 10, and 5 a one so 5 times 1.

Now we just place our 8 on the outside of the parentheses
$8(40 + 5)$
Now first mentality we know 8 times 4 is 32 and carry over the zero that's 320. And 8 times 5 is easy, that's simply 40 so now we have to add 320 + 40
$8(40 + 5) \\ 8(40) + 8(5) \\ 320 + 40 \\ 360$
So, now try
$4 \times 25$
Which is broken into
$4(20 + 5)$
4 times 2 equals 8 carry over 0 that's 80 and 4 times 5 equals 20, and 80 +20 equals 100