How To Multiply Any number with 11
How To Multiply Any number with 11 in a Smarter way .... Friends i will explain this method with an example ....
Ex 1: Multiply 12 * 11 ? ( First Take a Simple Example )
Step 1 : Place 1 _ 2
Step 2 : now add 1 and 2 ===== >>>> 1+2 = 3 Place that 3
in between 1 and 2 thant is the answer . ie 132 is the answer .
now multiply 13 * 11 ?
1_ 3
1+3 = 4 ===== > 143 is the answer .
Exception : Multiply 19 * 11 ??
Step 1 is same as the above 1 _ 9
Step 2 : now add 1 and 9 ==== >>>> 9 + 1 = 10 here we
have two digits coming from right place take 1 as carry to the next
letter ie 1109 ====> now take one carry to the next letter then it
will become 209 ... that is the answer ....
How to find squares up to 50
Friends to use this method we should learn squares up to 25.
Ex : Find 36 ^ 2 ??
Step 1 : Make a Bench Mark on 25 . now subtract 25 from 25
===>>>> 36 - 25 = 9
Step 2 : multiply 9 with 100
====>>>> 9 * 100 = 900 Keep this a side .
step 3 : Now Subtract 9 from 25
=====>>>> 25 - 9 = 16 .
step 4 : we know 16 square is 256
step 5 ; add 900 with 256
900 + 256 = 1156 is the answer .....
Multiplication of numbers with a series of "9"
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So many people thinks that Multiplication of any number with digits
of "9" is difficult but this is the very easy .... i will explain some
methods by taking some examples ... ok ...
Ex : 568 * 999
Step 1 : subtract 1 from 568 .... then it will become 567 it is the right part of the answer ....
step 2 : and now subtract each number in "567" from the digit "9" ie
if we subtract 5 from 9 we get .... if we subtract 6 from "9" we get 3
..... if we subtract 7 from 9 we get 2 ...... 9 - 5 = 4
9 - 6 = 3
9 - 7 = 2
432 is the right part of the answer .....
step 3 : so our final answer is 567432
Ex 2: 6784 * 9999
Step 1 : subtract 1 from 6784 ... it will become 6783 it is right part of the answer ....
step 2 : and now subtract every number in 6783 from 9 ...we will get 3216 it is the right part of the answer ......
so our final answer is 97833216
Ex : 45 * 999 ?
Step 1 : we can one zero in front of 45 it will not affect the value
.... now subtract 1 from 45 .... it will become 44 .... it is the left
part of the answer ....
step 2 : subtract every number in 045 with 9 ... we will get 955 .... it is the right part of the answer ......
so our final answer is .... 44955
Numbers which are nearer to 10 , 100 , 1000 , 1000
numbers which are nearer to 10 , 100 , 1000 , 10000 ......etc
i will explain this method with an example
Ex: Find 98^2 ?
Step 1 : we know 98 is 2 less than 100
write 98 -------- 2
98----------2
------------------------------
Step 2 : we now 2 digit numbers square ( greater than 31 ) will have four digits
and now we know 2 square is 4 write it as "04" which is the right part of the answer
Step 3 : this is the very imp step subtract 2 from 98 we will get 96
which is the left part of the answer .... so the final answer is 9604
short cut for square of a no ends with 5
25 X 25 = 625
2x(2+1)=2x3 = 6
so left most digit is 6
and add 25 with that
95 X 95 = 9025
9x10=90 add 25 with that
105 X 105 = try step by step
add 1 to 10 i.e= 11
multiply 10 by 11 i.e= 110
5X5=25
now 11025 ans
try this 1005 X 1005 = 1010025
85 X 85 = 7225
Shortcuts for square (xy)²
Shortcuts for square (xy)²
=============
1st Step: Y²
2nd Step: (y+y) ×x or (x+x) ×y [Add carryover if any]
3rd step: (x) ² [Add carryover if any]
Note: consider from right to left
Example number 1 :
==============
12²
2² = 4
(2+2)×1 or (1+1)×2 = 4
1² = 1
12²= 144 (from right to left)
Example number 2 :
==============
28²
8²= 64 (take 4) = 4
(2+2)×8 = 32+6 =38 (take 8) =8 { because carryover was 6}
2²=4+3=7 =7 {because carryover was 3}
28²=784 (from right to left)
Example numer 3: 19
=================
19^2 = 361
9^2 = 81 (take 1) = 1
(1+1)x9 =18 + 8 = 26 = 6 (because carry was 8)
1^2 = 1 + 2 = 3 ( because carry was 2)
Hence ans is 19^2 = 361
square when the number has only 9 :
when the number has only 9 :
9²=81
99²=9801
999²=998001
9999²=99980001
99999²=9999800001
……………………............
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count the number of 9 s ...
put number of 9's one less than the count...
and put a digit 8 ...
and then put one less than count number of zeros - 0 s
and the digit 1 with that.
square when the number has only 1 :
1²=1
11²=121
111²=12321
1111²=1234321
11111²=123454321
111111²=12345654321
………………………...............
count the no of 1 's in the given number
put value of count in middle of the answer
add numbers from middle to left most and to right most by decresing value by one until you get the number one ..
ie...1
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