Fun With 5's 1

I have always been relatively good at dealing with numbers. Awhile back I noticed a pattern when multiplying numbers that end with “5”. I would like to share that pattern with you so that, hopefully, it will help you to figure out some computations in your head.
No, this method is not always faster than a calculator, but for some of the solutions, it is. I believe that we live in a world that is way too dependent on calculators. I think if you don’t use your brain to figure out things like this, you're losing something. This keeps your brain active, thus keeps it alive.
This method assumes that you already know how to add and subtract and that you also know your multiplication tables through at least 10x10.
I hope you enjoy learning these methods. I know they were fun to figure out.
Good luck and happy learning.
 
These first sets of computations are not very difficult. We will be multiplying 2 digit numbers that are the same number. There are 2 ways to achieve the right answer here. Just do it with the one that you are the most comfortable with.

The first thing you should know is that any number that ends in “5”, when you multiply it by itself, the answer always ends with “25”. You will see what I mean as we go along.

Let’s say you have the problem 25x25. For this one, the answer is 625. I got that mostly by just straight multiplying. As I said earlier, it ends with “25”. To get the “6” I just did 2x2+2. If the problem is 45x45 then you do 4x4+4, then add the “25. So 45x45 is 2025. If it’s 85x85 then it’s 8x8+8 (72), then add the “25” and you get 7225.

Try a few on your own before we get into the second method of achieving this. Believe it or not, you might possibly think that the second method is even easier than the first one.

For the second method, all you need to do is manipulate one of the first numbers. In our 25x25 example, you would change one of the 2’s to the next higher number, a 3. Then you just multiply straight down. With 25x25 it would be 35x25 and multiplying straight down is 3x2=6 and 5x5 is 25, so 25x25=625. If you have 65x65, then you convert it to 75x65, the answer, 4225. 95x95 = 9025. Simple, right?

In my next post, I will explain how to do these calculations if the numbers are not the same.