.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 45

^{2}, 25^{2}, 55^{2}etc.
Okey, let’s look at 45

^{2}. Start by squaring 5^{2}=25. Then you take the 4 and multiply by one more, 5, and you get 20.
So, 45

^{2}=2025
25

^{2}= 2*3 and 25=625
55

^{2}=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.