While browsing v/new I came across and old Schoolhouse Rock video about figure 8. I watched about a minute and a half of the video and noticed a pattern I never picked up on before. Paused the video to test it out in my head. this may be completely obvious to you but for me this is something I just noticed and thought was interesting. If we take any 2 part multiplication problem such as 8x2=16 half the first number and double the second and the answer will always be the same 4x4=16 2x8=16 1x16=16 .5x32=16 .25x64=16 ... I can't believe I never notice this before. I do often see patterns in math and know there are different ways to solve problems but this seems so obvious I can't believe it just dawned on me now.

I know there are other probably lots of other cool things like this some I have noticed and others I haven't. I am happy that these little light bulb moments still happen to me. I feel like no matter how small or large the connection it sparks an interest and makes learning fun.
Sometimes I come across these odd little posts and suddenly something I knew about just clicks and makes more sense or I get a different perspective. It makes me wish I were back in school.

Just thought I would share :) you can now laugh at how silly it this post is.

Off to bed now. Goodnight.

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[–] chrimata 0 points 5 points 5 points (+5|-0) ago

It's because you are multiplying the expression by 1 which is the identity operation and because multiplication is commutative so it doesn't matter the order you do it right?

You could do it with any number, try multiplying the first number by 35/3 and the second number by 3/35.

Or take a three part multiplication problem and multiply the first number by 4 and the second two by 1/2

[–] Opieswife [S] 0 points 0 points 0 points (+0|-0) ago (edited ago)

Thank you. There are so many cool thing I learn about math as time goes by and it suprises me that this didn't all make more sense when I was younger. I typically think of multiplication as a shortcut or shorthand for addition. It can be a short way of writing or figuring out an addition problem. It may sound silly to you but seems to work for me.

I find visual tools help me understand math concepts better. One day I toured a school and noticed some educational toys for kids to help them count. All of a sudden a bunch of math concepts suddenly made sense. Yes I could previously have figured them out using pencil and paper but to visualize what they represented helped me actually understand what I had been doing. Parroting back an answer or figuring out an answer just because I used a specified process is one thing but actually understanding why it worked was a completely different thing. That's what I hope for is an understanding of why and of various relationships.

For some reason I kicked ass at binary and subnetting computer networks. Once I figured out how this worked I aced the class and loved it. Heck at one point we did some work with hex and some of that still sticks with me but we only did basics problems with it. I think if I ever meet the right teacher math can work out to be very interesting. Doors will open and I feel like I will be able to solve problems beyond just base 10 because finally I will understand.

I think I will play with some three part problems as you suggested, it sounds I interesting. Thank you.

[–] chrimata 0 points 1 points 1 points (+1|-0) ago

Hey happy to help! Glad you liked my comment. I think in a lot of ways the educational system is broken with math. Each topic builds on the one before it and if you don't have a comfortable grip on the foundation topics that next section is confusing. I think a lot of times the system says "passed the test" and moves onto the next thing when the student isn't ready. Learning math I think requires students to be honest about what they don't know or are confused about because otherwise the next topics will never be learned. Those insights about the true nature of the problem will never come.

Multiplication being a shorthand for addition does not sound silly to me, if you start having only defined the rules for addition you can derive multiplication :)

[–] [deleted] 0 points 5 points 5 points (+5|-0) ago

[–] Apathy 0 points 2 points 2 points (+2|-0) ago

Time to hit up wikipedia and let the world know all about the inventor of the algorithm. Make sure to put your birthday (year included) and your height in there, that shit's vital.

[–] Opieswife [S] 0 points 0 points 0 points (+0|-0) ago

Seriously I get you are being a wise ass and this is simple for you. For me I have never studied algorithms so really didn't know what this was, I just thought it was interesting.

Yes I am a grown adult who can't pass algebra, seriously I have no need to hide this or be ashamed. I have many other skills and have managed to compensate for my shortcomings in math through the years. The cool thing is just because I haven't passed yet doesn't mean I won't eventually. I still love to learn and focus on things that interest me. This one area has not held me back from being a successful and happy adult with a good career.

So cool, now I know this interesting pattern I happened on is an algorithm. When I get to that in class I will remember this and it will help me understand it better, hopefully enough to pass and move on to the next skill.

[–] Seventh_Jim 0 points 5 points 5 points (+5|-0) ago

Check out prime-factorization OP. Basically what you're observing is just multiple expressions of 2^4. This gets pretty important as you move into intermediate level algebra.

[–] Opieswife [S] 0 points 0 points 0 points (+0|-0) ago

Thanks I will. Algebra is something I have difficulty with. Somehow I come up with the right answers but not usually with the method I am supposed to use. I find it frustrating because there seems to be something that just doesn't click in my head when it comes to math which is why little discoveries like this are exciting to me.

[–] Seventh_Jim 0 points 1 points 1 points (+1|-0) ago

I hear this on a pretty regular basis as a tutor. Part of the reason for math homework is that the brain takes time to flip the intuitive "ah-ha" switch. You have enthusiasm and are looking under-the-hood so to speak, so you're actually farther along than most people. Keep at it if you want to improve!

[–] Norm85 0 points 1 points 1 points (+1|-0) ago

Here is some nice visual beauty of multiplication tables.

[–] Opieswife [S] 0 points 1 points 1 points (+1|-0) ago

This is really cool. Thank you for sharing. Guess I am not getting any more work done today :)

[–] bikergang_accountant 0 points 1 points 1 points (+1|-0) ago

So all numbers are just smaller numbers multiplied, unless they're prime.

4 * 4 is really just (2

2) * (22). You just move one of the twos over so (2) * (222).You can do it with any number. 8*9

(2

22) * (33) = (2(223)3) = 89 = 12*6. Really the parenthes don't exist at all. It's just 22233 no matter how you order them.[–] Holonomic 0 points 1 points 1 points (+1|-0) ago (edited ago)

So, half of 8 is 4, double 2 is 4, and 4x4 is 16, right.

But if you look at it this way you will see why it works:

original: 8x2 = 16 yours: 4x4 = 6

If we start with the original and follow along:

(8/2)(2x2) = (4)x(4) = 16

=> but (8/2)(2

2) is (1/2)(8)(2)(2) = (1/2)(2)(82) = (1)(8x2) = 8x2All you're actually doing is multiplying it by 1

You first divide by 2, and then you multiply it back in, which is just 1.

[–] Opieswife [S] 0 points 0 points 0 points (+0|-0) ago

I this pretty neet. I think they are essentially different ways of writing or expressing the same number. It would have been so much more interesting if I had realized this when I was young. I think I could have learned so much more.

A good thing about this is I am now interested in going back to college. It really is math keeping me from graduating as I have all the other requirements complete and then some. Thinking about starting with the basics to be sure I have the fundamentals down and I get some practice then I will take another shot at Algebra.