Trouble with Mathematics?

[Pop]

Basic math made easy to wrestle with, because everyone deserves to understand mathematics, the language of the universe.

Many people struggle with math, and I dont mean advanced stuff, but basic stuff, things like percentage conversion to angle-partitions and multiplication.
So here are a few tips to help ease that entry into low-level algebra, and hopefully make math less scary for those intimidated by it, because once you know the rules, math really is very simple(until you wanna be an engineer and it gets a bit tricky again)


A calculation such as 17,983 x 21,973 can be a mouthful, so what you wanna do is break it up into digestible bits like so:

17,983 turns into:

10,000
7,000
900
80
3

and 21,973 turns into:

20,000
1,000
900
70
3


Take each number from the first row and multiply them one by one with each number from the second row.

10,000 x 20,000 = 200,000,000
10,000 x 1,000 = 10,000,000
10,000 x 900 = 9,000,000
10,000 x 80 = 800,000
10,000 x 3 = 30,000
7,000 x 20,000 = 140.000.000
etc. etc. etc.

But wait, that many zeros might be confusing, so simply take away ALL the zeros and multiply the 2 numbers you have left, using 7k x 20k as the example:
Removing all 7 zeros and simply do 7 x 2 = 14, add back in the zeros after the fact giving you 140,000,000.
If you need a visual aid you can use a standard XY diagram to keep track of the numbers.

The key "trick" to learn here is that you can move the decimal marker forward, jumping over and ignoring any and all 0s reducing the number in size to something manageable, then simply slap them on the end of whatever number you get from your "easy" calculations.
This trick can be applied to conversion maths, simply break everything into percentage pieces by "moving the decimal marker", this way you can quickly do angles as each 1% is equal to 3,6 degrees of a full circle, and this method can be applied across multiple problems you might face in math.

[galled]

It's all making my head hurt!!

[Pop]

Curse me for trying to keep a short form.
Please, if you struggle with this, ask away!

I will gladly elaborate on any and all parts in excrutiating detail, because if there is one thing I feel strongly about, its math being an important skill to have.


For starters lets break it down using a set of much smaller numbers.

76 x 93 should be tricky enough for most to do on the fly to serve as an example:

Broken down the numbers would become:
70 x 90
70 x 3
6 x 90
6 x 3
Take any 0s and set them aside like so:
7 x 9 (00)
7 x 3 (0)
6 x 9 (0)
6 x 3
Once these simple multiplications are done, you simply add the 0s back on the end and add up all your results:
7 x 9 = 63 (add the 2 00s to get 6300)
7 x 3 = 21 (add the single 0 on the end to get 210)
6 x 9 = 54 (again add that 0 back on the end of it and you sit on 540)
6 x 3 = 18 (no 0s to add here so its just 18)
6300 + 210 + 540 + 18 = 7068

[galled]

Ok, that's much easier. I'll have to study it a bit, but it makes more sense as I think I'm starting to understand what you're doing there. Very cool!

[Pop]

It is a bit counter intuitive at first, but once you get the hang of it all multiplications become alot easier.
Since I always did math like this since I was a little kid, I always wondered why my classmates were struggling, and not untill many years later, after a punk-rock concert while I was hanging out at the afterparty, some college kids were talking about how they had to go early because they had some math projects that needed finishing the following Monday, I offered to take a look (they had the papers with them as they went to the concert straight from class) and after realizing that all of it was simple conversions, I asked why they didnt simply "move the commas?", they looked at me like I was speaking greek, so I elaborated and an hour later, they had finished their projects and were back to drinking beer and smoking blunts as all students should be doing on a Friday night
They both passed with decent grades(despite one of them claiming that he had never passed a math test before), so figured its the way to get the "math resistant" onboard the "physics ship" so-to-speak.

[Akuyi]

I bestow upon you the title Grand Multipoplier!

[Pop]

hehe, that might be a bit much, but I am honored none-the-less

[Vivianne]

This is the logic behind a lot of very useful mental math tricks.

For example, squaring any number ending in 5. I'll use a two digit number as an example, but I think the rule holds for more.

To multiply 65 x65 quickly, you take the non 5 digit and multiply it by (itself + 1).[note: Order of operations matters!] Then you put 25 at the end.

4225

This works because the last digit is always 5. Picture writing out multiplication 'traditionally.'

The second to last digit is always 2. This is because that digit is calculated by 6 x 5 plus 6 x5 plus the carried over 2. (for odd numbers ending in five, the same thing happens because you are effectively multiplying the original tens digit by ten then adding 2.)

The leading number(s) are 6 x(6+1) [again, order of operations. Parentheses first!] because 'traditionally', you'd multiply 6 by 6 and add the carryover, which in this case is 6 and will always be whatever y is in your 'y5' number.

I willingly spent years of my life doing this competitively. Ah, middle school.

[galled]

Wait a minute, what?? I'm slow at this. Can you actually layout an example--maybe your 65x65 example? I'm not seeing it. Isn't 6x6=36+1=37? I get 3725.

Competitive math genius were ya? You continue to amaze me! Well, I think anyone who has met you too!

[Vivianne]

6 x (6+1) = 6 x 7 = 42, the answer to everything

Does it make sense? Let me edit my original post. C:

[Akuyi]

That's clever. I feel like people who are good at doing math in their head use lots of tricks like this.

[Vivianne]

One of the contest forms I participated in was a ten minute 80 question mental math only test. No scratch work allowed and you had to write in pen. Inkblots were grounds for disqualification, and negative scores were possible. Slashing out an answer made that question automatically wrong.

This was my idea of fun. Well, at least for the first year.

[Pop]

That sounds like a lot of fun, wish I had the opportunity to try something like that back in school, but "competetive" is a no-no word in danish education sadly.

[Vivianne]

Here in the US, in middle school we had Mathcounts, which was a bunch of super fun word problems. I think artofproblemsolving.com has a free random question generator you can try. there are even leaderboards and statistics.

[galled]

6 x (6+1) = 6 x 7 = 42, the answer to everything

Does it make sense? Let me edit my original post. C:

Yes it does! I feel smarter already!

OK, one that always amazed me and you probably know how it's done.

What's the trick (if there is one) to adding a bunch of numbers together in your head? I've seen people on shows solve things like this faster than several people with calculator. Very impressive, but there must be a trick to it, right?