**Adding big numbers :**

Eg: 500

+995

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A: 1495

Tip : 50/0

99/5

crack the numbers (0+5)=5 , add the rest (50+99)=149. thus the answer will be 1495.

Another example : 6789

+4622

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A: 11411

Tip : 67/89

46/22

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114/11

add 89+22=111 . key in the last 2 digits and carry forward 1 . add 67+46=113

and add the 1 which was carry fwd.

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Mutiplying Big nos :

Eg: 254* 50

Tip 25/4

X 50

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12700

Crack the 1st no . Multiply each by the second no. Ie. 50 *4 = 200 , 50 *25= 12500.

Add the two [12500 + 200 ].

So answer is 12700

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Multiplying by 5

suppose the no is 300 . divide the no by 2 = 150 and add a "zero". So the ans= 1500

another example: 244 * 5 = 1220

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mutiplying a number by 11

Tip : for 2 digit nos Simply add the first and second digits and place the result between them.

Eg. 24 * 11 = 264

another eg : 79*11 = units place =9 , here 7+9= 16 so write 6 in middle..

carry fwd 1 and add to 7 so the ans will be 869

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Cube root trick (works only for ans of cube roots from 1-99)

Eg. Find cube root of 148877 ( Needs memorsing last digits of cubes from 1-9)

here is the list :

1-------->1

2-------->8

3-------->7

4-------->4

5-------->5

6-------->6

7-------->3

8-------->2

9-------->9

Can be memorised as These are easily memorized. 1 and 9 (at the extremes) are

"self-enders", as are the 4, 5, and 6 (in the center).

The others involve "a sum of 10": 2 ends in 8, 8 ends in 2, 3 ends in 7, and 7 ends in 3.

To instantly determine his original number, do the following:

1. Drop the last three digits and find the largest cube contained in 148. This is 5^3 = 125, so the tens-digit is 5.

(This is why you had to memorize the cubes of the digits 1 through 9)

2. Now go back to the last three digits. Look at the last digit, 7. That's the same ending as 33, so your units-digit is 3.

(This is why you had to memorize the "endings" of the cubes for digits 1 through 9)

so cube root of 148877 is 53 .

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Sq root trick with nos above 100

Needs memorising of last digits of squares from 1-9

Here is the list

1---------->1

2---------->4

3---------->9

4---------->6

5---------->5

6---------->6

7---------->9

8---------->4

9---------->1

suppose the no is 169, then take the hundreds value (over here 100 and key in its sq rt ie 10)

now observe the last digit . Thats the same ending for 3 and 7 . so the no is either 10+3=13

Or 10+7= 17 . To determine the correct answer , take average of the sq of extreme digits ie

over here (10'2 + 20'2) /2 = 250. In our case 169<250 . Therefore the answer will be 13 .

If here the problem number was greater than 250 then the answer would have been 17 .

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Method for multiplying numbers where the first figures are same

and the last figures add to 10

Method for multiplying numbers where the first figures are same

and the last figures add to 10

Eg: 42 x 48 = ???

Both numbers here start with 4 and the last

figures (2 and 8) add up to 10.

just multiply 4 by 5 (the next number up)

to get 20 for the first part of the answer.

And we multiply the last figures: 2 x 8 = 16 to

get the last part of the answer

So the answer is 2016.

another eg : 33 * 37 = 1221

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Method for multiplying numbers where the first figures add up 10

and the last figures are same

Eg : 44X64

Here first figures are 4 and 6 and their add up 10 and unit figures of both number are same

Just multiplying the last figures 4x4=16 Put it at right hand side

Again multiplying the first figures and add common digit

(4x6 )+4=24+4=28 ,

put it at left hand side

Now we get required answer 2816

Similarly 36x76 , 6X6 =36 right hand side , (3x7)+6= 21+6=27 left hand side

Required answer is 2736

NOTE If multiplication of last figures is less than 10 add zero before unit digit

Ex 81x21 , 1x1=01,( 8x2)+1= 16+1=17 Required answer 1701

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Method for multiplying numbers where the first number"s add upto 10 and and the second

number's digits are same

Eg : 46X55

Here first number's add up is 10 and second number "s digits are common i.e 5

Just multiplying last figures of both numbers 6x5 =30 put it at right hand side

Again multiplying first figures of both numbers and add common digit of second number

(4x5)+5 =20+5 =25 put it left hand side

Required answer is 2530 ( If multiplication is in unit in first step add zero before it)

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Multiplying numbers just over 100.

108 x 109 = 11772 14042

Similarly 107 x 106 = 11342

The answer is in two parts: 117 and 72,

117 is just 108 + 9 (or 109 + 8),

and 72 is just 8 x 9.

Another eg: 118 * 119 = [ 18 * 19 = 342,so key in the last 2 digits and c/f 3,

now, 118+19 =137.we add the c/f 3 to 137 = 140 ]

So ans is 14042

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If you know ne more methods then feel free to hit a reply to this !!. :wink: