 So in yet another multiplication technique, let us try and understand how do we quickly multiply any number by 11 it is very easy technique and if you use it You'll be able to save a lot of time while doing calculations in your regular problem solving So let us take examples and understand and how this technique works So let us say I have to multiply a number 46 or rather let us start with us, you know easier number will go to Complex calculations as well. So let us start with a number 42 and Multiply this number by 11. So how does this technique work is simply this you take this to and write it here Okay, then add two to four. So what do you get six? Okay, right six here and then the four which is remaining put it back here So the answer is 462 you can try using a calculator and validate the answer Let us take another example Let us say we are multiplying 33 with 11 Okay, so what will happen? You have to write this three units place three first here Then add this three to this three. What do you get six and then the final three here? So 363 is the answer once again, let us take some Some more examples, so let us say 53 Into 11. Okay. Now again, what do you need to do? You take this units place number three here Then add three to five. What will you get eight and then what is left this five back here? So 583 Okay, another example. Let us say 62 into 11. What do you get? First this two here then two plus six is eight write that eight here and then six back Here 682 is the answer Now I started with an example 46 now. I'll take how to do multiplication of 46 by 11. There is a slight difference here Why because you will start as usual and write this six here Okay, but now when you add six plus four, what do you get ten? Obviously, you can't have two digits here So you will take zero of that ten and let's take carry one now In the usual process, you would have written four down here But then since it is a carry here one, so you add four to this one and hence you'll write Five so answer is five not six or five zero six. Okay. Let us take another such example So let us say 76 into 11 now Similar thing. So if you see this six comes here, no problem now six plus seven if you do you get 13 So obviously you have to take the units place of 13 here units digit And then what is the carry one write it here one now seven had to be written over here Now instead of writing seven here, you add this seven to one here and write eight So answer is eight thirty six one more example. Let us say we have 59 into 11 Okay, so again start with nine Right now add nine to five. What will you get 14? So four will be written over here One is carry now you have to write five down here But then you add five to one you'll get six and hence you write 649 now these were all two digit numbers Let us take some three digit number or four digit number like that. Let us say we have one 23 to be multiplied by 11 same process is Here also you have to just repeat one few steps more. So hence this is three here then add three to two. What do you get? Five so five here then add two to one. What do you get three? So right three here and what is left one? So one is back here So answer is one three five three, right? So so quickly even your mind if you have enough practice You'll be able to do these calculations in your mind itself. Let us take another example. So three 23 into 11 Right, so three and Then now three plus two five. So right five Two plus three is five again. So right five again, and then this three comes back So three five five three is the answer. Let us take one four one more two four Three one into eleven Okay, so what is it? So you start with one then add one two three you will get four then add three to four you'll get seven and Four to two you'll get six and finally two this two will come here So two six seven four one how quickly you are able to do just see now Let us take a little complicated one. So two forty seven into eleven Okay, I completely complicated because there will be Carry overs. So let us say we'll start with seven. Yes, seven now seven plus four is 11 So you write one carry one now four plus two was six. So six plus one is Seven and then two seven one seven once again. So I wrote seven first then Seven plus four was eleven. So I wrote one of that and then put one over as the carry on two Now four plus two if you do four plus two you'll get six, but you had carry also one. So six plus one Seven and then finally the last two will come down and it will be two seven one Seven you can you can try and calculate by dividing it So if you see if you divide two seven one seven by eleven, you will get two then four and yeah It's two forty seven. This is how the technique works, right? Let us take another example To understand it better one three five six seven into eleven. Okay, so hence first what? Seven then seven plus six is 13. So three here then one is here left over, right? Now six plus five is eleven plus one is 12 right and then again one now five plus three is eight and eight plus this one is nine and then three plus one is Four isn't it four and then finally this one will come here So the answer is one four nine two three seven Let us check whether we did correctly or not one four nine two three seven Let us try and divide it by eleven to see if we got the same or correct result or not So we see what is it eleven times one is eleven? So that is thirty nine then three times 33 so hence we have sixty two then five Fifty-five then seven seven is the remainder seventy three So this is six, which will give you sixty six Seven left and seven is the remainder again. So again seven times 77 and you get nearly here. So one three five six seven, right? So that means we have calculated here correctly. Can you see how easily you are able to multiply a number by eleven? Now let us take one more interesting problem two nine one zero four two into eleven. How do I do this? So hence again to start with two will be the first digit here then add two to four you'll get six right six four two zero is four Then zero two one is one Then one two nine is ten so zero will be here and then one will be written over here Now nine plus two is eleven and then plus one the above carry one. So eleven plus one is 12 but then you have to have one as carry and the last digit which was supposed to be written over here is two So ends but there was a carry. So two plus one is three two three. So hence the result is three two zero one four six two Again, I'll repeat this because it is little critical. So two nine one zero four two into eleven How do I do it? So take this two down add two to four you will get six four two zero no problem here four Zero two one you get one One two nine you get ten right ten now here is where you need to pay attention one plus nine is ten So carry one so write one here now complete this sum nine plus two is eleven Plus carry this one so eleven plus one is twelve now one again Carry is one now this two was to be supposed to be written down over here If there was no if it was a usual method, but usual case rather now in this case there was a carry one So this two plus this carry one will get you three. So the result is three two zero one four six two Now in the same line you can use the same Principle to solve or problems like 32 into 1.1. Let us say 1.1. So, you know how to do it. So you simply Ignore this decimal point and multiply by 11. So you'll get 352 Now since there was one decimal point after one digit. So hence the answer will be 35.2 exactly how many Digits are there after decimal in the result also same number of digits should be there after the decimal Let us say it is 421 into 1.1. So, how do I calculate? Ignore this decimal multiply by 11. So it is 1 364 Correct now what 4631 is the answer, but then there's a decimal and after decimal there's one digit So 463.1 will be the answer. Let us take another case 342 Into let us say you have to do point one one now same thing But there after decimal there are two digits, right? So ignore again this decimal has to be ignored Multiply by 11 you'll get two two plus four is six four plus three is seven and this three will come here So three three seven six two, but there were two digits after decimal So it will be thirty seven point six two Okay, this is how you can use this technique to multiply either by 11 or 1.1 or even for 0.11 or 11 into any 10 to the power n can be Done using this technique