Personal development for brains - Daretravels.com

To accomplish anything in life you have to have willpower, you have to want to reach your goals. You have to be so damn extremely focused you know everything there is to know about your subject, or about yourself for that matter.

Today people are sourounded by shit all day long; commercials all over the place, TV in the background, phones ringing, drinking coffee, having fun etc.

You have to learn to forget about all that shit. Ignoring it like hell. Yeah, it might be hard, but I promise you, the less need you have for it, the better you will feel, the better life you will have. And the more you will accomplish.

People always talk about how they don’t have time for this and that. That’s one big fat lie. What they actually mean is that they don’t have time to do anything that really make them grow as a person, because they are drinking coffee, watching TV, bragging or partying etc. Get a grip. Stop complaining! NOW!

If you really want to accomplish something, being good at anything or travel around the world or whatever, you have to work for it. That’s the number one reason 90% don’t reach there goals according to me. They never want to fight for it. They rather hang with friends or go out partying. Here’s where the “being pissed” part comes in. If you are pissed you always want to improve something, you always want to change stuff, including yourself and your goals. This will help you to move forward and fast.

So, stop feeding those rich companies living on you watching shit on TV, eating burgers or whatever, and take control of your life and start working on what you really want to do. Change your habits today and you’ll be happier from that moment.

Okey, now it’s time to learn the Trachtenberg system. It is a system very close to vedic mathematics I explained before.

Let’s begin by looking at multiplications. When you multiply two different numbers you always have to place as many numbers of zeros in front of the multiplicant as there a digits in the multiplier. So, if you should multiply 123 with 34 you have to look at 123 as 00123. 1234 * 4 then it’s 01234. Ok?

Each number has a “neighbour” to the right, except the last digit. 1234, where 2 is the neighbour to 1, 3 is the neighbour to 2, 4 is the neigbour to 3 and no one is the neighbour to 4.

Ok, we begin with multiplication by 12. Double each digit, starting from the right, and add the neighbour.

379 * 12 = ?

00379 * 12

9 has no neighbour. 9*2 = 18

(7*2) + 9 = 14 + 9 = 23 (and then the 1 from 18) = 24

(3*2) + 7 = 6 + 7 = 13 (and then the 2 from 24) = 15

(0*2) + 3 = 3 (and then the 1 from 15) = 4

(0*0) + 0 = 0

379 * 12 = 4 548

Multiplication by 11.

First recopy the last digit, then add the number with the one before on the rest.

4 862 * 11 = ?

004862 * 11

2 = 2

6 + 2 = 8

8 + 6 = 14

8 + 4 = 12 (and add the 1 from 14) = 13

4 + 0 = 4 (and then add the 1 from 13) = 5

0 + 0 = 0

4 862 * 11 = 53 482

Multiplication by 3.

Rules:

1. Take ten minus the first number and double this. Add on 5 if the number is odd.

2. Take each successive number from 9 and double this. Add half the neighbour. Add on 5 if the number is odd. (rule: “half”)

3. Write down a zero next to the last number. Subtract two from half its neighbour. (rule: “half”)

4 932 * 3 = ?

04932 * 3

(10 - 2) * 2 = 16

((9 - 3) * 2) + (2/2) + 5 = 12 + 1 + 5 = 18 (add the 1 from 16) = 19

((9 - 9) * 2) + (3/2) + 5 = 0 + 1 + 5 = 6 (add the 1 from 19) = 7

((9 - 4) * 2) + (9/2) = 10 + 4 = 14

(4/2) - 2 = 0 (add the 1 from 14) = 1

4 932 * 3 = 14 796

Multiplication by 4.

Rules:

1. Take ten minus the first number. Add on 5 if the number is odd.

2. Take each successive number from 9 and add half the neighbour. Add on 5 if the number is odd. (rule: “half”)

3. Write down a zero next to the last number. Subtract one from half its neighbour.

4 932 * 4 = ?

04932 * 4

10 - 2 = 8

(9 - 3) + (2/2) + 5 = 6 + 1 + 5 = 12

(9 - 9) + (3/2) + 5 = 0 + 1 + 5 = 6 (add the 1 from 12) = 7

(9 - 4) + (9/2) = 5 + 4 = 9

4 - 3 = 1

4 932 * 4 = 19 728

Multiplication by 5.

Rules:

1. Take half of each numbers neighbour. (rule: “half”)

2. Add on another 5 if the number is odd.

3. Write down a zero to the last (left) number.

4 932 * 5 = ?

04932 * 5

0/2 = 0 (has no neighbour)

(2/2) + 5 = 6

(3/2) + 5 = 6

9/2 = 4

4/2 = 2

0/2 = 0

4 932 * 5 = 24 660

Multiplication by 6.

In this case you have to think about a rule called “half”. Half is the number divided by another minus the rest. For example 7/2 = 3 and not 3,5.

This is what you do:

1. Add half the neighbour to each number.

2. Add on another 5 if the number is odd.

3. Write down a zero next to the last (left) number and repeat the above.

4 932 * 6 = ?

04932 * 6

2 (has no neighbour)

3 + 1 + 5 = 9

9 + 1 + 5 = 15

4 + 4 = 8 (and add the 1 from 15) = 9

0 + 2 = 2

4 932 * 6 = 29 592

Multiplication by 7.

3 steps:

1. Double each number and add half its neighbour. (rule: “half”)

2. Add on another 5 if the number is odd.

3. Write down a zero next to the last (left) number.

4 932 * 7 = ?

04932 * 7

2 * 2 = 4 (has no neighbour)

(3 * 2) + 1 + 5 = 12

(9 * 2) + 1 + 5 = 24 (add the first 1 from 12) = 25

(4 * 2) + 4 = 12 (add the first 2 from 25) = 14

(0 * 2) + 2 = 2 (add the first 1 from 14) = 3

4 932 * 7 = 34 524

Multiplication by 8.

Rules:

1. Take ten minus the first number and double this.

2. Take each successive number from 9 and double this. Then add its neighbour.

3. Write down a zero next to the last number and subtract two from its neighbour.

4 932 * 8 = ?

04932 * 8

(10 - 2) * 2 = 16

((9 - 3) * 2) + 2 = 12 + 2 = 14 (add the 1 from 16) = 15

((9 - 9) * 2) + 3 = 0 + 3 = 3 (add the 1 from 15) = 4

((9 - 4) * 2) + 9 = 10 + 9 = 19

4 - 2 = 2 (add the 1 from 19) = 3

4 932 * 8 = 39 456

Multiplication by 9.

Rules:

1. Write down ten minus the first number.

2. Take each successive number from 9 and add its neighbour.

3. Write down a zero next to the last number and subtract one from its neighbour.

4 932 * 9 = ?

04932 * 9

10 - 2 = 8

(9 - 3) + 2 = 8

(9 - 9) + 3 = 3

(9 - 4) + 9 = 14

4 - 1 = 3 (and add 1 from 14) = 4

4 932 * 9 = 44 388

Multiplication by 10, 2, 1 and 0.

Well, I’m not sure if I have to go thru this one but here it is.

To multiply by two, double each number.

To multiply by ten, write down a zero at the end of the number.

Any number multiplied by 1 is itself and multiplied by zero is zero.

So, that was it for now. I hope you have learned something and start to use your head more when calculating.

Related links:

Practice Trachtenberg multiplications

Trachtenberg system on Wikipedia

Vedic mathematics is mental calculation. It is you doing flawless calculations in your head fast. So, get rid of your calculator and start using your head more efficiently. I’d like to think that being fast with calculations also increase your mind in other areas and make you do fast conclusions on alot of stuff.

Vedic mathematics consist of 16 main sutras (sanskrit). Learn these and you are off with a good start.

1. By one more than the one before

2. All from 9 and the last from 10

3. Vertically and Cross-wise

4. Transpose and Apply

5. If the Samuccaya is the Same it is Zero

6. If One is in Ratio the Other is Zero

7. By Addition and by Subtraction

8. By the Completion or Non-Completion

9. Differential Calculus

10. By the Deficiency

11. Specific and General

12. The Remainders by the Last Digit

13. The Ultimate and Twice the Penultimate

14. By One Less than the One Before

15. The Product of the Sum

16. All the Multipliers

Okey, there are sub sutras too but I will mainly focus on a few of the above, the most handy to know, to show you how this works.

Let’s start with the first sutra, by one more than the one before.

This sutra helps you figure out how to square numbers that ends with a 5; like 45², 25², 55² etc.

Okey, let’s look at 45². Start by squaring 5²=25. Then you take the 4 and multiply by one more, 5, and you get 20.

So, 45²=2025

25²= 2*3 and 25=625

55²=3025

Easy right?

Okey let’s move one to the next sutra, all from 9 and the last from 10.

This sutra is used for subtractions. It works for subtractions when you subtrack from numbers starting with a 1 followed by zeros, like 100, 1 000, 10 000 etc.

100-69= (9-6) and (10-9) = 31

So, all the numbers before the last number you subtrack from 9 and the last number from 10.

1 000-594= (9-5) and (9-9) and (10-4) = 406

10 000-6 437= (9-6), (9-4), (9-3), (10-7) = 3 563

10 000-489 = 10 000-0 489 = (9-0), (9-4), (9-8), (10-9) = 9 511

How hard was that?

Vertically and Crosswise is mainly used for multiplication and fractions.

Okey, let’s start with an example, 9*6.

9 1 = (10)
*

6 4 = (10)

——

5 4

You start by subtracking from 10 to get the right digits. Then you subtract crosswise to get the first figure, so either you go with (6-1) or (9-4), wich is 5. To get the last digit you just multiply 4 with 1 and gets 4.

7*8 = ?

7 3 = (10)
*

8 2 = (10)

——

5 6

(8-3) or (7-2) = 5

(3*2) = 6

Vertically and crosswise can also be used for numbers close to 100.

80*96 = ?

80 + 20 = (100)
*

96 + 4 = (100)

——-

76 80

(80-4) and (20*4)

Multiplying with numbers just over 100.

103 * 105 = (103+5) and (5*3) = 10815

101 * 123 = (101+23) and (1*23) = 12423

Let’s look at another example when you can use vertically and crosswise, fractions.

2/3 + 1/6

Here you multiply crosswise, 2*6 and 3*1 and then add them together, and then you multiply the lowest figures vertically, 3*6. So the result is (12+3)/18 = 15/18

5/7 + 3/4

((5*4) + (7*3))/(7*4) = (20+21)/28 = 41/28

You can use vertically and crosswise on all multiplications:

23*56 = ?

23
*

56

————

(2*5) and (6*2)+(5*3) and (6*3) = 10; 27; 18 = 1288

You add the 2 from 27 to the 10 and you add the 1 from 18 to the 7. Easy as hell.

56*78 = ?

56

*

78

————–

(5*7) and (5*8)+(7*6) and (8*6) = 35; 82; 48 = 4368

Multiplying by 11.

This is really a piece of cake. You just add the number together in the middle, like this:

45 * 11 = 4, the first digit. 4+5=9. 5, the last digit. = 495

79 * 11 = 869

234 * 11 = 2574

Dividing by 9.

This is not exactly the correct answers as you can see but very close. Can be used for assumptions.

34/9 = 3,7

3*9=27 and 4*9=36, so the only possible figure is 3. And the 7 you simply get from adding 3 and 4 together.

46/9 = 4 + 10 = 5 (you move over the 1 from 10 as I have showed before)

139/9 = 1 + 4 + 13 = 15,3 (the 1 comes from the first figure, the 4 from adding 1 and 3, 13 from adding 1,3 and 9.

That was easy wasn’t it? I hope you learn these simple tricks and use them in real life to keep your brain in shape.

To learn more about vedic mathematics and more simple tricks you can visit following websites:

All the vedic sutras

Vedic mathematics on Wikipedia

Vedic tutorials