 Welcome friends, so we are again here to discuss another calculation technique this time multiplication of any given number by two digit number from 12 to 19. Now this will be very handy tool while you are doing any other calculation in mathematics or physics or chemistry or any other subject. So hence if you practice a little bit more then this technique could be perfected and you will find this technique to be easier to calculate such multiplications. So what is this method and how to go about it? So let us first take some examples. So let us say I have to multiply 46 by 12. One way is that if you remember the table nothing like it then it becomes much easier but remembering table also requires a lot of practice. So similarly this technique also will require a lot of practice and if you are very comfortable with the technique then you can use this technique to calculate faster. So all depends on which technique do you practice more. Now how to start this process? So in this case we know that if there is a two digit number the multiplication by a two digit number is little bit more difficult. So if we got some number, some single digit number then multiplication becomes much easier. So assume that there is no one in this 12. So mind you we are discussing multiplication of any given number by number between 12 and 19 that is 12 to 19, 12, 13, 14, 15, 16 to 19. Now so hence assuming that one is not there now let us do the multiplication by two. So how do I multiply by two? So this is the process you first multiply these two numbers units to units. So two into six is nothing but 12 okay I am doing this process a little slowly but while you are practicing it you have to do it in your mind and it becomes then if you perfect it then you will be able to solve such calculations in a much faster way. So two into six is 12 so hence in this case what will we do? What we will just segregate this two out of one and two and let the one which is here as a carry and let us write this carry here okay then add to it what do you add to it? So this two will now get multiplied by this four so it becomes two into four and then also the next to the four that is six will be added to it so what is this value? So this value is nothing but if you see two into four eight plus six fourteen plus one fifteen isn't it? Now out of this fifteen again you write five adjacent to the previous two so fifty two is the new number and what is carry? Carry is that one which comes here again. So this one is what do you need to do is now after four there is no number isn't it? But then we can assume that there is something called zero right? So now again take two and multiply this zero so what will it be now two into zero and then add the adjacent number to zero that is four so again so this will be plus four which is nothing but five right? Now this five has to be written adjacent to the previous fifty two so the answer is five five two okay let us take another example and please understand it thoroughly and observe closely what all steps am I doing okay? So let us take another example so another example could be let us say I have sixty five to be multiplied by now thirteen okay again thirteen is between nineteen and twelve isn't it? This is between twelve and nineteen so I can apply this method so what do I need to do? First take this three and multiply by five so what is it fifteen right? So I will write three into five is fifteen out of this fifteen write five here okay what is carry one that one comes here okay then add to it what? You add to it three times six and then five add it to it so it is nothing but three into six plus five which is eighteen plus six is twenty four so hence it is twenty four this four will go and sit next to five so it is forty five and carry two this two will come here let us write two then plus again this three will multiply by something here which is nothing here so we can say this is zero and then add six to it okay then what is it? So this is nothing but three into zero plus six so six plus two is eight so this eight goes and sits next to forty five so eight forty five is the answer okay this is how it has to be done once again so what is the terminating point terminating point is the moment you get zero then you don't need to proceed further okay let us take one more example let us say I have to multiply fifty nine with seventeen okay so what to do again forget this one there is no one okay now you take this seven and multiply with this you will get seven into nine which is sixty three so what to do write three here six comes here six is carry then what take seven multiply by five and add nine to it so hence it is seven into five plus nine plus six that is thirty five plus nine is forty four plus six is fifty fifty right out of this fifty this zero will go and sit here so it becomes zero three and this five comes here and sits here five now next what take seven again and multiply by something which is not there zero so hence it is and then add to it five as well so hence what is it seven into zero plus five so five plus five is ten so hence if this this is nothing but ten this ten goes and sits there it is one zero zero three is the answer okay let us take three digit number and try this method once again so let us say I have to multiply one thirty seven by sixteen how to do this again you as I told you forget this one and now multiply six by seven so what is this this is six into seven what is it forty two right right to here okay and four here okay now add to it what this six goes and multiplies with three and then add to it seven so then it becomes six into three plus seven so eighteen plus seven twenty five plus four is twenty nine so right twenty nine so nine goes here and sits with two becomes ninety two this two comes here becomes twice to two here then add to it what then you take six multiply it by one and add to it three right so hence it is six into one plus three right so six point one plus three is nine plus two is eleven so this is eleven take this one and let it sit here so it becomes one ninety two this one goes here it becomes one and then again plus six into here nothing zero plus one right so right six into zero plus one that means two so it is two so this two goes here and sits becomes two one nine two two one nine two is the answer let us take one more example let us say I have two one nine one into I have to multiply this by 18 okay so what to do again so eight goes to one so eight into one is eight right eight here then what in carry is zero so zero plus eight goes to nine plus one eight into nine plus one is seventy three is it it so three goes here sits with eight seven comes here and then what eight goes and multiplies by one by one and added to nine so eight into one plus nine so eight plus nine is seventeen plus seven is twenty four so twenty four is it in here four goes here sits with thirty eight two comes here plus eight goes and multiply by two so eight into two and then added to one so plus one sixteen plus one seventeen plus two nineteen so nine so nine comes here nine four three eight what is remaining one plus now eight into zero plus two right so hence it is eight into zero plus two that is three so three goes here and sits with nine three nine four three eight is the answer