 Hello and welcome to another session on speed mathematics. So we are going to take up division today now for me Division was very hard process. So I never Loved the division process and I am sure most of you also Would be finding division a lengthy very mechanical and too boring and at times too erroneous as well so hence during any calculations in Exams any comparative exam when division comes in we try to evade that process So is there a way to simplify division process? We have learned the long division method where there's a dividend There's a divisor and we keep on devising dividing it till you get a quotient and remainder so we have observed that process and We have come up with or it's not that we have discovered this process. This is If you put a little bit of mathematics behind it, you will Understand how the process which we are going to discuss works So this division is what we are going to take up is first of all is division by a two-digit number so you can take any large number and And we are dividing them these numbers by Numbers which are closer to multiples of N's for example, if I have to divide 75213, let's say 75213 is a random number and let's say In a calculation, you are encountering this thing. So you have to divide it by 29 now. This is very ugly Division process if you go by the you know normal long division method and hence you have to remember or otherwise calculate the multiples of 29 is it so we will start like, you know two times So this is 58 and then you will do 27 and then to 72 and Blah blah blah blah like that you will continue to visit it But this process is tedious and at times You will do a lot of oil make a lot of errors as well So we have come up with a new process or as I told you this is not the process that we have discovered It's there in practice and you can also see the arithmetic behind it how it works So basically the underlying process is simply this so any dividend any dividend is equal to deviser Into quotient plus remainder you'd have encountered this relation Lot many times right so underlying philosophy is this only how it works will take another set So in this session what we are going to do is demonstrate how to divide it little You know quickly and not only with 29. Let's say the same number has to be divided by 39 59 and 68 27 like that. So what to do right so hence there is a process. Let's learn that process so the process you need to you know pay attention to and It will be little Demanding in terms of your understanding in the first few cases and then later on you will yourself Discover this process yourself right so hence. Let's say I'm dividing this by 29 This is the question. So first step is you segregate the last Digit why is that because that will be helpful in terminating the process what we are going to do Okay, so this is the first step, right? So what is step one step one is? segregate or isolate The last or units place Units place digit So when I say segregate you don't need to write it separately something just put a line just like this so that you know that this is the last process second thing is find out how Close the divisor. So what is divisor? This is divisor. So how close it is to the nearest multiple of ten So the nearest multiple of ten nearest You have to find out nearest multiple of ten ten for divisor now here it might Appear that it is taking a lot of time because I'm explaining the process once you are thorough with the process It will hardly take ten seconds maximum to solve this or lesser It's practice. Okay. So the nearest multiple of ten for divisor in this case is 30 So that means you have to add one to get that 30. So I'm writing this like this add one to get 30. Okay Now your divisor is Three now don't you think dividing by three is much easier than dividing by 29? But yes, it will not be the regular division process. There will be few modifications which you need to learn So hence what did we do? We found out a synthetic divisor Why synthetic because I am dividing with a new number which was not given in the In the question, let's say it was not demanded in the question synthetic divisor in this case is three Okay, and this plus one factor also you Remember or keep in mind. Okay now What to do now you can divide using three so treat this as the new dividend and Start dividing so hence. Let me put a bar over here So let's say three times two three times two is six. So that's what I'm writing just like the normal division So what is the remainder guys one? Now what you need to do is you need to take this one and put it here So one and five becomes 15. So keep the number 15 in mind So this you have to do in mind. So hence I'm giving you shortcuts. So one this remainder goes and Just for remembering purposes. I have written it here one And then five so 15 now to this add the previous quotient you got so two So the new dividend is now 15 plus two 17 Once again So this was the remainder In the first division process. I put this here And now one and five together. I am treating as 15 Add the previous quotient. So that is two 15 plus two 17 now go for the division again So now new quotient will be three fives of 15 Is it so 15 What is the remainder two the process repeats now this two You take it and make it sit here. So two two and two 22 Right. So this number is 22 add the previous quotient. So 22 plus five 27 Right, so this is the new Dividend okay now divide again three times nine is 27 so gone This is zero right Right now what you have to take this zero and Take it here And add what the previous Quotient so zero plus zero one that is one plus nine that is 10 So the new dividend is 10 now divide again three times three is nine So hence One is the remainder Okay, now you take this one And put it over here. So one and three 13. So you put one over here 13 add this number three to it So what will you get 13 plus three 16? So this is the last step you have to check if the last step whatever you get 16 is less than the divisor. So 29 it is true hence This will be the last step that mean we are not going to Divide it further. Let's say if the last step you would have got 33 okay last step you would have got 33 Then you can see that 33 is more than 29 then Whatever quotient you had got you have to just add one to it. Why because if you divide 33 33 is 29 times 1 plus 4 so whatever quotient you had got you had to add one there And the remainder would have been 4 but in this case 16 is less than 29. So I don't So I don't need to add anything So q will be simply 25 9 3 and remainder is 16 Now this process will take some time for you to digest But never mind. We will so show this with one more example Okay, so let's say we have another example. We have to divide 269143 big number 269143 Using or by divisor 49 Now during in physics calculation acceleration due to gravity is 98 9.8. Sorry. So 9.8 by 2 is 4.9. So usually we get such scenarios. We have to divide by 49 or something So 269143 has to be divided by 49 again. So what do you do first step is isolate the Last digit. So I have isolated the unit's place digit. Now Here is where I am going to calculate it Yeah, so this is the bar. I will write the quotient above it. Okay, nearest multiple of Nearest multiple of 10 is 50. So I'm adding So my synthetic divisor is 5 Now it will be easier to divide by 5 very very quick. So 5 times 5 is 25. So start like that Is it so what is the remainder one? What did I say put this one here treat it as 19 and add what 5 to it So 19 plus 5 is 24. So write 24. Now. This is a new dividend divide by 5. So 5 times 4 Is 20 Correct remainder is 4. So this 4 I will write here 41. I will treat it as 1 41 plus 4 45 So new dividend is 45. Now again divide by 5. So 555 9za 5 9za 45 isn't it 5 9za 45. So 0 Now put this 0 here. So 0 4 plus this 9 is 13. So new dividend is 13 Divide by 5 so 5 tools are 10. So remainder is 3 Put this remainder here. So it becomes 33 33 plus this 2 35 now 35 is the last Step why because 35 is less than 49. So I'll stop here. So remainder is 35 And your quotient is 5 4 9 2 as you can check that right. So hence if you see 2 6 9 1 4 3 is equal to 49 times 5 4 9 2 In plus 35 You can check that. So this is our quotient and this is the Reminder right. Let's take one more example. It will become much easier to understand now another example is I am dividing 7 1 3 4 5 2 3 4 5 2 by By 79 Divide by 79 now if you have gone with the regular division process It will take a lot of time and multiples of 79 as well. So see how quickly I'm going to divide it now So here is the first step now plus 1 makes it 80. So that is synthetic divisor is 80 So let me put a line over here Now how to go about it? Okay, so 8 uh 8 8 just 64. So to start 8 8 just 64. So 64. What is the difference? 7 7 has to be written here. So 73 73 plus 8 is 81. So this is the new divisor 8 times 10 Now here is a new thing 8 times 10 you are getting a Caution with two digits. So you write the unit's place here zero And the one here as a carry. Okay, so remember this so the moment you get two digits as a quotient So you have to write only the unit's place as the Uh, you know the number here and the one goes as a carry. Okay, good So 80 8 into time 10 is 80. So remainder is one. Sorry remainder is one now this one comes and sits here So this becomes 14 plus the previous quotient which was 10. So the new dividend is 24 Now what 8 times 3 is 24 Okay, remainder is 0 this remainder sits here becomes 5 5 plus 3 becomes 8 itself. So 8 So 5 plus this 3 becomes 8. So 8 times 1 8 times 1 is 8 And remainder is 0. So this remainder sits here 0 plus 2 0 2 is the new dividend plus 1 0 3 0 3 correct, but now we have You know arrive at the last step. So this is a remainder Since it is less than 79 and the quotient is very clearly you can see 8 and now here 8 plus 1 has to be added. So it becomes 9 0 3 1. So this is a quotient And 3 is the remainder. So I could do this within very small amount of time One more with slightly different uses. Okay, so let's take one more example to understand this. So 7 1 3 6 2 9 Let's say randomly you are taking 3 6 2 9 and let's say 5 and 4 Very weak number 7 1 3 6 2 9 5 4 and you have to divide it by let's say 89 Okay, so what do you need to do? You already know that you have to first isolate the last digit. So isolate it for termination, right now Let us now put a bar over here and start dividing but before that synthetic divisor has to be found out So this 0 goes 9 is the near 90 is the nearest multiple. So 9. Okay and start with 9 division with 9. So 9 7s are 63. No doubt remainder is 8 This remainder sits here becomes 83. So 83 plus 7 is new Uh dividend 90 But now 9 times 10. So as I told you in the previous example, if you have two digits In the quotient, write one here and the other one has carry Okay, so 9 times 10 is 90. So write 90 remainder is 0 0 goes here. It's here 0 6 is the new number plus the previous quotient that is 10. So 6 plus 10 is 16 Now 9 times 1 again divide you'll get 9 remainder is 7 7 comes and sits here 72 plus the 1 so 73 is the new dividend divide now. So 8 times 72 what do you get one as the remainder? This one comes here and sits here. So 19 plus 8 A previous 8 which will give you 27. Correct divide again. So 3 times 27 right so 0 0 comes and sits here. So 0 5 plus the previous that is 8 0 8 right is the new dividend, but 0 8 will go 0 times So you'll get 0 the remainder is 0 8 only. So this 8 comes and sits here 84 plus the previous quotient is 0. So 84 plus 0 remains 84. So this is the last step This is my remainder, which is less than 89 And my quotient is 7 0 no not 7 0 7 plus 1 will be The first digit why your carry has to be added. So 801830. So this is the 801830 is the quotient and remainder is 84. You can check with the calculator. This will be the Output