Division by 7 is AMAZING !!! Cyclicity of Recurring Decimals II How to Divide Numbers Orally #magic

Ajouté : 2026-06-01

[00:00:03]Hello friends.

[00:00:04]Welcome to Suresh Aggarwal's Mathematics Shortcuts. I hope you are watching all these short tricks and enjoying them and making maths joyful for yourself.

[00:00:15]Making maths joyful is really important because when you study something joyfully, you know, it really becomes quick also and it becomes accurate also and you feel like doing it. So, making it joyful is really really really important and that's what is the intention of this amazing channel Suresh Aggarwal's Mathematics Shortcuts.

[00:00:36]So, in this video I'm going to take up the division by seven.

[00:00:40]You know, whenever you divide a number by seven, you have an amazing cyclic pattern. When I tell you that pattern, you will be like, "What? Why didn't we observe this before?"

[00:00:50]And you are going to divide numbers by seven like this. You know, very very comfortably and joyfully. So, the topic is division by seven. Yes, it is unique.

[00:01:02]Yes, it is interesting and so easy to find. So, watch the complete video. You are going to learn something really useful and talking about useful things, let me tell you about the ultimate guide to speed maths. If you are a student studying in class 5 6 7 8 9 10 11 12 or getting into and some entrance exams of universities or trying for placement exams, SSC CGL, uh you know, railways, banking, LIC, CAT, MAT, UPSC.

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[00:02:32]I will take your query myself, okay? And I'm I'll be very happy if you can call me and ask me for this combo of speed maths, okay? So let's get into the trick first.

[00:02:45]The first thing is this important thing, NT R. What is NTR?

[00:02:51]You know, NTR is very important in decimals, especially when you have non-terminating decimals.

[00:02:58]NT stands for non-terminating.

[00:03:01]So something which does not end, non-terminating.

[00:03:06]And what is R? R stands for recurring.

[00:03:10]That means something which is repeating over and over again.

[00:03:14]Do you know what happens when you divide a number by seven?

[00:03:18]After dividing, that means obviously the number will have a decimal. There is something in front of the decimal, the whole number part.

[00:03:25]After decimal, we are going to have a NTR, non-terminating recurring decimal. And do you know how many digits are going to repeat over and over again?

[00:03:36]Just like when you do 10 upon three, what do you get?

[00:03:42]You get 3.33333.

[00:03:45]So three repeats itself. Now, when you divide a number by seven, there are one, two, three, four, five, six digits which are going to repeat over and over again.

[00:03:58]Six digits, yes. So, let's start with 1 upon 7.

[00:04:04]When you divide 1 by 7, if you remember 1 by 7, you can divide any number by 7.

[00:04:10]Yes, any number by 7. You know how?

[00:04:13]This starts with 0. because it is a proper fraction, 1 is smaller than 7, right? So, 0.

[00:04:19]Now, the six digits which repeat over and over again when you divide 1 by 7 starts with the double of 7.

[00:04:27]Double of 7 is 14.

[00:04:31]How about double of 14?

[00:04:33]28. So, next two digits are 28.

[00:04:37]How about taking the double of 28? It is 56, right? But, so sorry, it is not repeating. 56 is not repeating. One more than that, 57 is repeating. And therefore, when you divide 1 by 7, pick up the calculators and check.

[00:04:54]0.142857142857142857 and so on. It goes on and on. How do you remember it? You have a 7 as the divisor, right? 7 * 2 = 14, 14 * 2 = 28, 28 * 2 = 56. Just one more than that, 57.

[00:05:12]Got it?

[00:05:13]Now, the most interesting thing is coming up here.

[00:05:19]Now, suppose you have to do 2 by 7.

[00:05:22]Now, obviously it is a proper fraction, so 0. again, same thing, okay? Now, what is going to happen next is going to surprise you.

[00:05:30]2 by 7, when you do traditional division, you will write 0. and put a 0, right?

[00:05:36]So, 20 / 7 gives me first digit as 2, 7 * 2 = 14, right?

[00:05:42]This is how you will continue.

[00:05:44]So, first digit is 2. So, I am just bothered about the first digit. two So, 0. And now go back to 142857.

[00:05:53]Okay? Now, I have to start with what?

[00:05:56]two So, start with two.

[00:05:59]Go in front like this. 2 8 5 7 and then come back like this. 1 4 and pick up the calculators now and see the surprise yourself. Just press 2 / 7 = You will see that the calculator is going to say 0.285714285714 and as many digits as your calculator can allow.

[00:06:23]Okay? So, wonderful. See, the same digits in a different cyclic manner.

[00:06:29]I am going to tell you the most important thing in division by seven.

[00:06:33]Before that, I need to tell you the two books. Look at this. Volume one and volume two. They are in my hands now. In printed form, they are going to They are waiting for you to be delivered to you on your postal address, you know. And this is the WhatsApp number 9896369963.

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[00:07:37][laughter] Okay. So, the next thing. How about 3 / 7? Obviously, 0. right?

[00:07:43]Because it's a proper fraction. Now, when I divide 30 by 7, I will get 7 * 4 = 28, right? So, I have to start with 4.

[00:07:51]Now, what was the cyclic order? 1 4 2 8 5 7. Now, I have to start with a 4.

[00:07:58]So, start with a 4, go across like this, and come back. 4 2 8 5 7 1. And these six digits are going to repeat over and over again. See? So easy. Now, what would happen if I have an improper fraction? So, let's cover that also.

[00:08:14]Suppose I do 12/7.

[00:08:18]Now, convert it to a mixed number first.

[00:08:20]7 * 1 = 7. 12 - 7 is 5, so 5/7.

[00:08:24]So, the whole number part is 1, so 1.

[00:08:27]5/7. If you divide 50 by 7, you are going to start with 7, right? So, in this order, start with 7. And then come back. 1 4 2 8 5. And these six digits are going to repeat over and over again.

[00:08:43]Surprise?

[00:08:45]Yes, math is such a wonderful thing if you start understanding the things.

[00:08:49]Let's have one more question, and then we are going to conclude.

[00:08:52]Uh suppose I do uh 100 and uh 53/7.

[00:09:00]So, 7 * 2 = 14.

[00:09:03]13. 7 * 1 = 7.

[00:09:05]Uh 6. So, 6/7. So, 21. So, 21.

[00:09:10]6 / 7 means 60 / 7. And when I do 60 / 7, 7 * 8 = 56. So, I'll start with the 8.

[00:09:18]8 5 7. Then come back. 1 4 2.

[00:09:22]And these six digits are going to repeat over and over again, giving me the decimal representation of 153 / 7. See how wonderful it is.

[00:09:31]All these tricks are a part of the speed maths uh combo. And the links which are given in the description of this video you can click the links and purchase a copy of those speed maths books. Thanks for watching this video and let me know in the comments below is that trick working for you. All the best.