Adding big numbers :
Eg: 500
+995
----
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
--------
A: 11411
Tip : 67/89
46/22
------
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
-----
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
__________________________________________________________________________________________-
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 .
----------------------------------------------------
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:
Eg: 500
+995
----
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
--------
A: 11411
Tip : 67/89
46/22
------
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.
---------------------------------------------------------------------------------------
Mutiplying Big nos :
Eg: 254* 50
Tip 25/4
X 50
-----
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
----------------------------------------------------------------------------------------
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
----------------------------------------------------------------------------------------
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
__________________________________________________________________________________________-
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 .
------------------------------------------------------------------------------------------
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 .
----------------------------------------------------
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
-------------------------------------------------------------------------------------------
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
--------------------------------------------------------------------------------------------
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)
--------------------------------------------------------------------------------------------
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: