Explain how you can mentally find 8 times 45 by using distributive property. and explain

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

ab: 2 n83b8eb7ebi. 8e yen in

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4