Off late, one of my friends shared this link about confidence in Facebook; I was going through other related searches and then I saw this video. Sadly, sometimes algebra makes people skeptical but simple tricks and practice can make everyone certain. So I wanted to share couple of tricks regarding timeses and divisions w.r.t number eleven.
The first one is about the timeses of 11. For example, if you want to find 11 times of 532
i) your answer consist of right most digit as it is (here it is 2) then
ii) add on its immediate left hand side (LHS) digit to it(i.e. 2+3= 5)
iii) and place it towards the LHS in result(i.e., 52) repeat the same process with all the remaining digits towards LHS, one by one, and at the end you will get the result as 532*11=5852
See it below in detail:
- First take the right most digit i.e., 2,
- Then immediate LHS digit is 3, sum it up with earlier digit i.e., 2, sum is 2+3 =5, place it to the LHS of previous result i.e., 52
- Next immediate LHS digit is 5, sum it up with earlier digit i.e., 3, sum is 3+5=8, place it to the LHS of previous result i.e., 852
- Repeat the same steps till you reach the extreme right digit of the given number and you get 5852 as final result.
- Key step in this trick is, if there is no carry-forwards, we will go ahead with simple addition of adjacent digits, if there is any carry-forward from previous addition (take an example of 11 times of 2365, when we are adding digits 5, 6 we get the total 11, then place the units digit value (here it is 1) to the LHS of previous result set (here it would be 15) and carry-forward the remaining digit to the next step. The end result of the example is thus 26015.
The second one is about whether a given number is divided by 11 or not. It’s very simple and indeed we can calculate it faster than the machine sometimes!!!
If the sum of the odd positioned digits is equivalent to sum of the even positioned digits of the given number, then it is divided by 11.
For example in the above result 26015, the even positioned digits are 6, and 1; their sum is 7. And the odd positioned digits are 2, 0, and 5; their sum (2+0+5=7) is 7, which is equivalent to the sum of the even positioned digits. So the given number is divided by 11.
We can imply the same trick with little modifications to the operations related to the numbers 22, 33, 44, so on and so forth.
