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A BUNCH MORE IS ON THE WAY! Feel free to add stuff, but everyone, just keep in mind that more is coming!

I (Drewblet) was looking around through some of my old algebra textbooks, and I realized how much people struggle with math. So I decided to write a page that would have some crap that would help with math. Yeah, so here it is.

NOTE: I'm soon moving on to vaguely more complicated things like polynomials. Note the vaguely. It's gonna get more algebraic; I'm just starting with the simple schidnit.

Funny, I opened my notebook and the first page is completely full of these numbers:
25, 52, 73, 78, 81, 62, 90, 72, 21, 52, 34, 28, 65, 23, 24, 30, 45, 01, 12, 84, 71, 42, 19, 66,49, 75, 22, 05, 39, 27, 95, 87, 76, 83, 44, 14, 20, 59, 82, 44, 48, 98, 77, 57, 86, 17, 02, 276, 863, 832, 824, 012, 952, 735, 424, 335, 735, 128, 489, 902, 362, 270, 645, 735, 424, 225, 735, 128, 489, 902, 362, 270, 645, 735, 725, 725, 724, 875, 324, 012, 634, 735, 424, 225, 735, 128, 489, 902, 362, 270, 645, 735, and 725, and I have no recollection of writing this. Any of you recognize these numbers? Message me if you do.

Rules on Division

These are some rules to help you find out if y is divisible by x. This table is fairly screwy, so could somebody help me (I have no time)? Post your name at the bottom of the page, and get acknowledgment. Thanks.

If the number is divisible by...	...then...
2	The number ends in 0, 2, 4, 6, or 8
3	The sum of all the digits in the number equal a number that is divisible by 3. eg. 1,890 is divisible by 3, because the digits equal 18, when added.
4	The last two digits in the number are divisible by 4. eg. 76,824 is divisible by 4, because the last two digits in the number are 24.
5	The number ends in 0 or 5.
6	The number is divisible by both 2 and 3.
7	No rule.
8	The last three digits in the number are divisible by 8. eg. 1,480 is divisible by 8, because the last three digits are 480.
9	The sum of all the digits in the number equal a number that is divisible by 9. See the example for #3.
10	The number ends in 0.
11	The sum of the alternating digits have a difference of 0, 11, 22, 33. . . This requires explaining. Okay, 39,919,100 is divisible by 11, because 3+9+9+0=22, and 9+1+1+0=11, and 22-11=11. So, with the 39, you start with the 3, and once you've done that alteration, you start with the 9.
12	The number is divisible by both 3 and 4.
13	No rule.
14	No rule.
15	The number is divisible by both 3 and 5.

Was that helpful? I hope so.

The way mentioned above works, but it takes a while. Best option is to learn your tables by heart, of keep a table with you.(example below)

X	1	2	3	4	5	6	7	8	9	10	11	12
1	1	2	3	4	5	6	7	8	9	10	11	12
2	2	4	6	8	10	12	14	16	18	20	22	24
3	3	6	9	12	15	18	21	24	27	30	33	36
4	4	8	12	16	20	24	28	32	36	40	44	48
5	5	10	15	20	25	30	35	40	45	50	55	60
6	6	12	18	24	30	36	42	48	54	60	66	72
7	7	14	21	28	35	42	49	56	63	70	77	84
8	8	16	24	32	40	48	56	64	72	80	88	96
9	9	18	27	36	45	54	63	72	81	90	99	108
10	10	20	30	40	50	60	70	80	90	100	110	120
11	11	22	33	44	55	66	77	88	99	110	121	131
12	12	24	36	48	60	72	84	96	108	120	131	144

Lemme Just Tell you my Favorite way of Doing Division:
...................____
Let’s use 3| 64 here, okay? You know how, normally, you would see how many times 3 goes into 6, subtract, drop the 4, yadda yadda? Well, here’s my favorite way.

What’s 3×10? 30. How many times does 30 go into 60? Twice. So, you’ve got 3×20= 60 so far, right? Now, how many other times will 3 go into 64 after 60? 1 time, which equals 63.
.........................................._21 R1
This makes the answer 3| 64 , get it? A nice little rule to remember is, when dividing 3 into something, a remainder of 1 equals .333…, so the answer is 21.333…

This is also handy for larger numbers, like 640÷30. 30×20= 600, and 30 goes into 640 once after 600, so 640÷30= 21.333...

“But I always do it this way!” you might be saying. I’m quite confident you don’t, actually. REMEMBER, though, that there are times (very rarely) that it would, in fact, be easier to do long division, I think, than this method, you know. Anyhoo, onward!

Speedily Doing Elementary Processes:

Here's a section on quickly doing the things that you learned in 3rd grade.

Left to Right Addition:

I like this, cuz you can get the answer quite quickly. So, for this example, I’ll use
123
226
121
214, a’ite?

So, it’s basically the same as right to left addition, except you keep a running total in your head, and don’t write anything down until you’ve got everything figured out.

Let’s start, and remember, it’s LEFT TO RIGHT! So, the first column is 1+2+1+2= ? It’s 6, but you knew that, right?

So, now the running total in your head is 600, cuz you just added the 100’s column. On to the 10’s column, which is 2+2+2+1= ? Why, 7, of course!

What’s the running total in your head? 670. Now for the 1’s column. 3+6+1+4= ? Good lord, you’re stupid, it’s 14! If you were doing this normally, you would carry the 10 in 14 into the 10’s section, but, seeing as we’re doing it in a better fashion, you just add 10 to the running total, and then put the 4 after, so 670, 680, and then 684.

I’ve gotten used to doing addition in this fashion, so I could tell you in about 5 seconds that
123
226
121
214
684. This can be done with everything from 2 digit numbers to ∞ digit numbers, but I recommend using scientific notation for particularly high numbers.

Left to Right Subtraction:

Same basic idea. Let me use
/124
-112

So, starting in the 100’s column leaves you with 0, so there’s no running total yet.

The 10’s column is 2-1=1, so the running total is 10.

The 1’s column is 4-2=2, so the running total and answer is 12.
/124
-112
////12

Now, let me talk about borrowing during subtraction.
/346
-137

So, 3-1= 2, so the running total is 200. 4-3= 1, so the current running total is 210. Okay, now 6-7= -1, so that won’t work in this context. To fix it, take 1 out of the 10’s column, which makes the running total 200 again, and add it to the 6 in the 1’s column, which makes it 16-7= 9, making the running total and answer 209, so
/346
-112
/209. Again, this is a very good way of doing this. It saves quite a bit of time. I like it. Hoorah!

Right to Left Cross Multiplication:

This is also very good; much nicer than the normal multiplication method. Let’s multiply
//12
×14

Mkay, so multiply the 2 times the 4, which is 8. Now put it in the 1’s section of the equation.
//12
×14
/////8

So now you cross multiply and add the results together. 1×4= 4, and 1×2= 2. 2+4= 6. You now put the 6 in the 10’s column.
//12
×14
///68
The last operation is multiplying the two numbers in the 10’s section. 1×1= 1. Put the 1 in the 100’s column.
./12
×14
168

Let’s talk about carrying, shall we?
//32
×14
////8

Right? Now, for the cross multiplication. 1×2= 2, and 3×4= 12. Add them together: 2+12= 14.
////1
//32
×14
///48

Get it? Carrying is the same as normal, just put it above the next number to be multiplied. Now, 3×1= 3. Add in the one being carried, 3+1= 4, and stick that in to complete the solution.
////1
//32
×14
448

If you’re gonna be equating logistics, however, methinks ye should be able to almost immediately know what 12×14 is.

Complimentary Multiplication:

Here’s way of multiplying if you’re multiplying two numbers between 91 and 99. Let’s use
//96
×94

Figure out how far from 100 each of the numbers is, and write it beside the actual equation.
//96 4
×94 6

Super job! Boy, you’re neat! Okay, now you subtract the 6 from the 96. 96-6= 90. Write the 90 down as the first two digits in the equation.
//96 4
×94 6
90

To get the rest of the solution, multiply the 4 and the 6. 4×6= 28. Stick the 28 into the equation.
//96 4
×94 6
9028. There’s your answer.

For a number between 101 and 109, figure out how far the numbers are from 100 and then, rather than subtracting the lower distance from the top number, add.

Really, this is purdy useless, seeing as it requires such particular numbers. Alas! It's still worth knowing, though.
(red numbers are indices)

Indices
An indice is how many times a number is multiplied by itself. example is 5 to the power 4 is 5x5x5x5. normaly powers are applied to unknowns represented by a letter, most frequently a, b, c, x, y and z. In this form X2 stays in that form because X could be any number, positive or negative.
Squares

IF I WRITE [2] NEXT TO A NUMBER, IT MEANS THAT THE NUMBER IS SQUARED. Curse Wetpaint for not allowing superscripts!

I freaking HATE square roots, so I found this quite helpful. These are the first 15 squares. A square is a number times itself, like 6×6=36. 36 is the square of 6. Square roots are 'what times itself equals this number'. 6 is the square root of 36. The square root sign looks like √. It's called a radical, in case you didn't know.

Squares

1=1	2=4	3=9	4=16	5=25
6=36	7=49	8=64	9=81	10=100
11=121	12=144	13=169	14=196	15=225

Extra Squaring Thingy:

If the number being cubed ends in 5, then the solution always ends in 25. Let’s use 35 squared here. So, 35[2]= ?25. To get the first part of the answer, take the number in the 10’s section (3) and add 1 to it (4) and multiply the two, so 3×4= 12. Now stick it in there. 35[2]= 1,225. Get it?

It also works with higher numbers, like 625. 625[2]= ?25. Now, take the 62, and 1 to it, and multiply. 62×63= 3906. So, 625[2]= 390,625.

It works on every possible square. Even 2,093,140,195,782,109,535.

Cubes

I hate cube roots even more. these are the first 10 cubes A cube is a number times itself twice, like 6×6×6=216. 216 is the cube of 6, and the cube root of 216 is 6.

Cubes

1=1	2=8	3=27	4=64	5=25
6=216	7=343	8=512	9=729	10=1,000

Extracting Cube Roots:

I always use this for factoring. First, let me give you the list of cubes again:
1=1
2=8
3=27
4=64
5=125
6=216
7=343
8=512
9=729
10=1000
Let me rewrite these in a different order:
10=1000
1=1
8=512
7=343
4=64
5=125
6=216
3=27
2=8
9=9

Look at the bold, and you’ll see what I did, here. Let’s call them List 1 and List 2, a’ite?

195,112 is what you’ll be extracting the cube from.

First, divide at the comma, so 195|112, okay?

All you need to look at are two things, the last digit on the right side, namely 2, and the whole number on the left side, namely 195.

Look at List 2. Which number cubed ends in a 2 (the last digit of the cube you're extracting the root from)? Why, 8 does! This means that the last digit in the cube root of 195,112 is 8.

Now look at List 1. What two numbers does 195 go between on that list? 125 and 216, so 5 cubed and 6 cubed. Take the smaller of the two cubed numbers, that being 5, and stick it in the 10’s column of your answer.

That means the number cubed that makes 195,112 is 58. Get it? Lemme use another example.

12,167. What cube on List 2 ends in a 7? 3. What cubes on List 1 does 12 go between? 8 and 27, or 2 cubed and 3 cubed. Stick the 2 in before the 3, and you find out that 12,167’s cube root is 23.

This method also works on high numbers like 13,265,902, and I can tell you right now that the last digit in 13,265,902’s cube root is 8, but I would have to know what two perfect cubes 13,265 goes between to get the full solution. I don’t.

Primes

Figuring out if a number is a prime is often a pain in the ass. These are the first 32 primes. A prime number is a number that is divisible only by 1 and itself, like 61. 61 is only divisible by 1 and 61. Some rules to remember are that a number that ends in 7 is almost always prime, there's no such thing as an even prime number (except for 2), most (but NOT all) numbers that end in 1 are prime, and most (but NOT all) numbers that end in 3 are prime.

The first 32 primes are: 2; 3; 5; 7; 11; 13; 17; 19; 23; 29; 31;
37; 41; 43; 47; 53; 59; 61; 67; 71; 73; 79; 83; 89; 97; 101;
103; 107; 109; 113; 127, and 131.

Decimals

Almost every fraction can be rewritten as a decimal, and here are a few. I skip obvious numbers (like 3/6). Please note that numbers like .333. . . are infinite repeating numbers, which means that the number(s) that repeats continue on forever. like, in .8333. . ., only 3 repeats, not 8. To figure out what the decimal of a fraction is, do what it says. For example, 1/2 is 1 divided by 2. 158/1000 is 158 divided by 1000. Get it? Got it? Good.

Fractions to Decimals

1/2=.5	3/2=1.5
1/3=.333. . .	2/3=.666. . .	4/3=1.333. . .	53=1.666. . .
1/4=.25	3/4=.75	5/4=1.25	7/4=1.75
1/5=.2	2/5=.4	3/5=.4	4/5=.8
1/6=.1666. . .	5/6=.8333. . .	7/6=1.1666. . .	11/6=1.8333. . .

Novelty Operations:

Didn’t I promise that I’d give you some operations to entertain yourself? Maybe it’s the dementia, but I think so. . .

Today’s addition is:

The Calendar Formula:

Here’s it:


Yeah. So, you take the year, add it to the year’s number divided by 4, add the day of the month (e.g. Feb. 12. 12 is the day of the month.), add the significant values, and divide it all by 7. Okay?

The Significant Values:

January =0
February =3
March =3
April =6
May =1
June =4
July =6
August =2
September =5
October =0
November =3
December =5

A’ite? Now, let’s take Dec. 22, ’75. You only use the last two digits of the year. So, 2008 is ’08. Copasetic?



Drop the decimal off of 18.75.



Okay, so 7 goes into 120 17 times, with a remainder of 142857. . . Use the first number of this remainder, namely 1.

The Other Significant Values:

Sunday =0
Monday =1
Tuesday =2
Wednesday =3
Thursday =4
Friday =5
Saturday =6

Now, with that remainder being 1, what day of the week was December 22, 1975? Monday. Get it?

****. Know what I just figured out? I need to figure out the significant values for the days at and above year 2000. Hang on, this’ll take a while.

Sunday =0
Monday =1
Tuesday =3
Wednesday =4
Thursday =5
Friday =7
Saturday =8

Almost the same. So, this formula, come to find out, was designed for the 1900’s, so when you get to 2000, the year becomes 100. 2008 is 108. Okay? Same, otherwise. I WILL NOT go to the trouble of redesigning this formula to fit the 2000’s, so you’re out of luck if you want me to.

Enjoy.

I want no criticism about how ‘irrelevant’ this is. Take note that this is in the Novelty section, and only give constructive criticism, praise, or advise, just no flaming, friends and neighbors.

There's that. Next time, I'll add to the little novelty things you can use to freak out your friends (math can be fun!), talk about factoring, talk a bit about polynomials, and maybe give a few more shortcut operations. I'll be updating super duper soon! Time to go watch Designing Women!

Drewblet likes him his math!!!!11!!!!11111!!!!!!oneoneeleven!

Quickrace89: Well, I'd like to add some stuff about triangles. God **** those triangles. For most of these, you'll need a scientific calculator. Indeed, for most logistical issues you will.
.....................................^ 3DayAsylum recommends a TI-84.

• Triangles have three sides, and therefore, three angles. All these angles add up to 180.
• A triangle is the strongest shape.
• The squares of the two shorter sides added together will give the square of the longer side. This is called Pythagoras's Theorem.

Trigonometry

• Trigonometry allows you to calculate the lengths of each side, given one side and an angle. Or, you can calculate an angle, given two sides.
• The Hypotenuse is the side opposite the right angle in a right-angled triangle.
• The Opposite is the side opposite the angle. It can change depending on which angle is specified.
• The Adjacent is the side next to the angle. It can change depending on which angle is specified.

(more coming later)

3DayAsylum's Triangles, Letters, Numbers, and ****
Hey, I could write a BOOK on this...*writes down this notion for future reference*

Alright, now that we're out of 3rd grade, lets start with the basics.

1) Every triangle has exactly 3 sides, and 3 angles.
2) The sum of all of those angles = 180 degrees.
3) And whatever the hell Quickrace said...

Pythagorean Theorem Example

NOTE: When I write ^2 next to a number, it means that number's squared.

ALSO: Only works with right-angled triangles

So, you have three cities: Brownstone, Boulder, and Roanoke.
You know that the distance between Brownstone and Boulder is 5 miles.
You know that the distance between Boulder and Roanoke is 7 miles.
How do you know the distance between Roanoke and Brownstone?
Simple. a^2 + b^2 = c^2





Brownstone to Boulder = a = 5 miles
Boulder to Roanoke = b = 7 miles
Brownstone to Roanoke = c = x


5^2 = 25 = a
7^2 = 49 = b
25 + 49 = c^2
74 = c^2
..____
\/ 74 = 8.60232527

x = roughly 8.6 miles
c = roughly 8.6 miles
Brownstone to Roanoke = roughly 8.6 miles

And that's your daily Algebra 1 lesson from 3DayAsylum.

P.S. **** YOU ANTI ASCII EASYEDIT PAGES!!!! DREWBLET: Agreed!