Transcript for:
Understanding Integer Operations and Rules

Hello everyone, good evening. Yes, sorry for the delay, there was some technical glitch. So we have our Tejaswini over here, Deepak, hi Riona, Yashvi, yes, Jimin.

Am I audible and visible to everyone? Quickly let me know. Yes, Nandita, good evening.

Hi, Santosh, Shriyanshi, Ankit. Hi, hello, Harsh. All right. Good evening, Akansha, Deepa, Vignesh. Hi, Rahul.

Hi, Sara. Alright, alright so there is no glitch at all so we can continue. My name is Khushboo and a very, very warm welcome to yet another wonderful session.

So today's session is basically about integers. So today we will be having our first concept. concept session on integers. So we have segregated this session in two parts basically.

Alright so let's not waste any more time here, let's first quickly discuss the flow of the session. So today I'll be starting this session with BODMAS followed by some we'll be learning learning about multiplication on number line. Then we will learn about how to do multiplication without a number line and finally we will end this session by division of integers. And before I start these topics, please subscribe the channel so that you do not miss any new updates from us.

Alright, alright so let's get started. Now just like you, this kid is also very excited that he has been promoted to grade 7. So in our last session, we did a quick recall. of what we have learnt in integers in the previous grade, right? Now let's move forward in our journey. Alright so as I said one by one I'll be discussing all these topics.

So let's first start off with the board mass. Now this kid is thinking why this tree is moving over there? Is there anything hidden inside it?

Oh yes, so basically board mass that's what we need to discuss now, right? So board mass is basically the short form right? So here every letter is telling about something, B stands for bracket, O stands for order of, D for division, M for multiplication, A for addition and S for subtraction. So in integers, like in the previous grade you learnt about there was basically let's say it's in two numbers you are doing addition or subtraction. Now there can be multiple operations with different different signs also.

So this board mass actually tells you the right order in which you have to use them, right? So keep this in mind, right? And I'm sure that these full forms are very easy to remember also.

Right Kasturi? Yes, thank you Aghrim. Monkey could be there but there was board mass because are you studying maths? Yes, alright, alright so just keep this in mind, we'll be using it in the questions. Alright so that was about BODMAS, so what do we have next?

Now we'll be learning about multiplication on number line. We all know how to do a normal multiplication but how to do multiplication on a number line? To learn that, now we'll be talking about multiplication of integers. By the way what this frog is doing here? Well we will see that this frog is actually going to help us.

us to learn multiplication of integers. Alright, so basically math is a very simple and interesting language, isn't it? Right?

So you can see here 2 plus 2 plus 2, you all say that ma'am we all know how to do it, right? 2 plus 2 plus 2, that's going to be 6 but another way to do it instead of adding 2 plus 2 plus 2, 3 times what mathematicians did, they introduced an effective manner to do it. So multiplication instead of doing this way, what we can simply times 3, right? That's going to be what?

That will actually give you 6, the same result that you would be getting by doing 2 plus 2 plus 2, right? Similarly, if I talk about 3 plus 3 plus 3 plus 3, so instead of adding it 4 times, I can simply say it's 3 times 4, this will also give me the same result, that's going to be 12, right? So n times the number, right?

We simply multiply n with that particular number, n is representing this 3 over here, similarly n is representing representing this 4 over here. How many times 3 is coming? How many times 4 is coming? Another way to do it, a simpler way, right?

Now let's take a look at the how to do multiplication on a number line. I'll be using the previous example which I just showed that to you in a previous slide, yes? So here you can see that this boy over here, is walking on the number line, right?

So let me just show that to you. When he walks on the number line, so you can see that it's a very slow process. So that's 2 plus 2, he comes to 4 and finally he stops at 6, right?

So this was a very slow process but what if we... take a frog over here instead of the boy. So here the frog comes and you can see that the frog is hopping and in every, in each time the frog hops, he takes a leaps of two points, right? Finally he also reaches six but but the process word a was a lot more faster, right?

So to do speed up, we used a frog here but in both the cases we are getting the same results, right? Yes, correct, easy topic, right? So that's how we can, we do multiplication on a number line. So here you can see that when we talk about multiplication of integers, basically on a number line if you see it, we move away from 0. Like let's say whenever, if I do 2 multiply by 3, you will be moving this side, a leaps of 2, 2, right?

3 times, right? You would reach here at this point. We are moving away from 0. But here I have got minus 2 times 3. So I will be moving towards the negative side of the number line this time and this is going to be what?

A leap of 2, 2, right? But on the negative side. I reach minus 6. Again I am moving away from 0 in both the cases, right? So when we talk about multiplication of integers on a number line, we move basically away from 0. Now let's try out some more questions to get a better understanding. Solve the following problem using a number line.

So here we have got 2 times 4. So just like the frog was hopping on this number line, let's use the same way. 2 times 4, both the numbers are positive. I will be moving towards the positive side of number line. So 2 times 4, so maybe you can do this way. basically we can make a group of two to four times second time third time four time we reach it one way to do is this right so for the first one I am getting the answer it another way to do it is basically we make a group of four four right four and we do it two times that also can be done still we will be getting the same answer right similarly if we talk about option B that's minus four times two right minus 4 times 2 so I'll be let's say if I move towards the negative side obviously we have a negative number over here so minus 4 times 2 so a leap basically a group of 4 on the negative side and 2 times I'll be doing it I'll reach where I'll reach minus 8 this time that's going to be my answer Yes, right.

Minus 3 times 3 in a similar manner. I'll be moving using the negative side of number line. So when I say minus 3 times 3, right, I'll make a group of 3, 3 on the negative side and 3 times, right, so that's going to be 3 leaps over here and that would be minus 9. I'll answer to your question, Sasmita. Everything will be covered.

Good question. We will do that. Minus 1 times 3. Yes, minus 1 times 3. Minus 1 times 3, I'll be using the negative side again. So, minus 1. I'll make a group of 1, 1, right?

times 3, I reach here. That's going to be minus 3. So, this is clear to everyone, right? No doubt still here? Quickly give me thumbs up in the comment section if this is clear to you. If you have understood this, yes, everyone is giving the right answer.

Yes, quickly tell me, thumbs up, smileys, if you have understood this. Gayatri says, okay, Atkarsh, Santosh, Anukriti, Gayatri, S. Nagendra, Biswarupa, Swamitha. This is clear to everyone.

Awesome. All right. Clear.

Great. Let's move ahead. So, this was about multiplication of a number line.

What if we have to do multiplication without number line? So, let's take a look at that. So, now we need to understand the signs first. Like, somebody just asked me this question.

What if we have these? signs both are negative or something. Now I will answer to your question. So you see here when we are multiplying two numbers and both of them are positive we get the result also positive. And let us say we are multiplying two numbers and both of them are are negative, right?

We are multiplying two numbers, both of them are negative, right? Again, we get the positive result. So, when the signs are, when the signs are same, like positive, positive, negative, negative, right? Every time you are getting a result, a positive result.

Now, what if the signs are different? We are multiplying two numbers which have got different signs. Every time you will be getting the answer as a, you will be getting a negative result, right? So, let me just give you a crux of this topic.

So, what we are doing here is when you have two negatives or you have two positives, they always make a positive, right? Same signs. They become, they give you a positive number.

But let's say if we have one negative or one positive, we will be getting a negative result. So in same signs, we get positive result. Different signs, we get negative result.

Yes? Thank you, Hrithi. I hope this is clear to everyone.

Right? Now using this, I'll be answering, we will be solving a few questions. Whomsoever had a doubt in this, what if we have these different signs? I hope your doubt is clear now. Alright, clear, great.

Let's move ahead, let's take a look at the next topic. So, multiplication without a number line when we are doing it, right? Take a look at this.

Let's use some examples. We have got positive 5 and minus 6. So, what we see here is that signs are different. So, what did I tell you? When the signs are different, we are going to get a negative result. Simply, we will do 5 times 6, that's what?

30 and signs are different, so result would be negative. Yes, whatever doubt you have, please write that in the comment section. Talking about this, minus 5 plus 6. Again, signs are different. Doesn't matter if it is negative, this is positive or this is negative, this is positive.

We just have to see that signs are different. So, 5 times 6 is 30. Since signs are different, answer would be negative. Yes, easy one. Let's take a look at this.

This time, we have minus 5 minus 6. Signs are same. What did I tell you? When signs are same, we get a positive result. So, 5 times 6 is 30. This time, we will be getting a positive result. You know why this happens?

Because negative and negative cancel out each other. That's the reason. Yes, Narendra? So, same signs. When we have same signs, we get a positive result.

When we have different signs, we get a negative result. I hope red is visible here on screen. Yes?

Thank you, Jimin. Thank you for such positive words. We will be learning everything, Arya. Don't worry. Whatever you have in your syllabus, everything will be covered.

Thank you, Harsh. Yes, same signs make positive. Different signs make negative. Yes? I hope this is clear now.

Just keep this thing in your mind. Thank you, Narendra. Alright, talking about the next thing, 5 times positive 6. So, there is nothing written with this 5. So, when nothing is, no sign is there, we always consider that as a positive number. Keep this thing in mind. This will be considered as a positive number.

So, both are positive. Same signs give you a positive result. So, I will say 5 times 6, we know that is 30. Since both of them are positive, signs are same, result will be positive.

No need to write plus over here. Since nothing is written with it, it will be considered positive only. Clear? Yes?

So, what is the crux here? Crux is multiplying same signs. When we are multiplying same signs, we get the positive result.

When we are multiplying, sorry, when we are multiplying different signs, we get a negative result. Yes? Alright, let's move ahead.

Let's take a look at the next question. Solve the following problem, minus 40 times minus 5. So, what do we see here? Simply, first we will multiply 40 with 5. What do we get?

40 with 5, that's going to be 200. Since both the signs are same, when signs are same, we get a positive result. And we know the reason also. Because negative, negative will cancel out each other. So, you get 200. Yes?

Wow! That's amazing, Ravinda. Congratulations.

It will be positive 200. Sriyanshi, not negative 200. When signs are same, positive result. Yes, this is clear to everyone. Great.

Now we have minus 15 times 6. Signs are different. 6 would be considered positive. So we get a negative result.

And 15 times 6 is nothing. That's 90. So minus 90 would be the answer. This is clear to everyone.

Thank you, Gayatri. Right. So, 200, yes, absolutely, minus 90. Great.

All right. So, we all have understood how to do multiplication on a number line, multiplication of integers on a number line or without a number line. So, now that we have understood this, so it is quiz time.

So, let us check your understanding now. So, here we go. Complete the number pyramid given below such that each pair of side by side numbers multiply to give the number above.

So when I multiply side by side numbers, I multiply them, I get the result which is written above. Similarly, when I multiply them, I get the result which is written above. I multiply these, I get the result which is written above. So this is what question is saying. Now you need to find out these missing values A, B and C.

So I will give you 30 seconds to answer this question. I am starting the timer now. Quickly. Quickly tell me what the values of ABC are going to be?

Yes. Okay, Avni says C would be minus 3. Wow, Avni, you are super fast, I must say. Yes, Sriyanshi says yes, C would be minus 3. Okay, I'll tell you the answers, you tell me the values of the other variables also.

B is 20, Anvi. okay minus 20 sorry okay minus 20 all right let's see what the value of each one of the variables is going to be when we are saying C times when we multiply side by side numbers that's going to give us 12 yes give us 12. So this is going to be what? In this case 12 by minus 4 you will get what?

You get minus 3, right? This is going to be minus 3 in this case. So the value of C is minus 3. I'm writing here, yes. Similarly, minus 4 times 5, minus 4 times 5 give us B.

That's going to be minus 20. So B over here is minus 20, right? And 12 times B give us A. So 12 times B, what is B?

B is minus 20 now. That gives you A, right? So that's going to be minus 240. That's the value of A.

So we have the value of all these variables. Not minus 250, that's minus 240. Thank you, Gayatri. So this is clear to everyone. Awesome, let's move ahead, let's take a look at the next question now.

So you will be answering this question on your own. So Ben gets rupees 20 every week as pocket money. How much money will he have after six weeks if he spends rupees five every week? So you have 30 seconds for this question, starting the timer now. Quickly, so how much money he will have after six weeks?

Wow, that's amazing Abhiraj. Congratulations. Yes, Sohini, you can ask whatever doubt you have.

You can post your doubts here in the comment section. Yes, quickly. Okay, 90. Wow, so fast you are.

Alright, yes, option C, that's the right answer. It is 90. So, let me just explain it to you for the ones who haven't understood this. Ben gets rupees 20 every week as pocket money. How many weeks we have? 6 weeks.

So, rupees 20 every... week so in total six weeks he will have rupees 120 right okay now he spends rupees five every week every week you are spending rupees five so since I'm spending it so obviously I'm losing money in that that case. So, I will take it as minus 5. So, in 6 weeks, I will be spending this much money, 30 rupees, right? So, 120 minus 30, what do I get?

I get 90 rupees at the end. This is what he will have at the end. Yes, that is going to be 90. Option C, that is the right answer. Yes. So, in the previous question, okay, let us take a look at the previous question.

So, here in the number pyramid, so basically it is saying, says each pair of side by side numbers multiply to give the number above. So, side by side numbers like say times minus 4, it will give us 12. So, what do I multiply minus 4 with to get 12? Right?

That would be minus 3. Because obviously 4 multiply by 3 give us 12. But this is positive. Minus 4 is negative here. I will be multiplying this with a negative number to get a positive 1. Because 2 negatives will make 1 positive.

Yes? Similarly, minus 4 times 5 gives me B. So, minus 4 times 5, that would be be minus 20. Right, Sohini? Yes.

Thank you, Arya. Thank you, Sasmita. Thanks a lot, Anshika. Ma'am, if we don't take 5 as negative, then also it is okay.

5 as negative. You're talking about the next question here. So, this question could be understood in this way also that we are spending 5 every week.

In 6 weeks, we'll be spending 5 every week. spending 30 then later on even if you're subtracting it you get 90 but I tell you about a subjective paper when talking about integers the right way to represent it answer will be same is this only right but still even when you are saying we are taking it as 5 and then we say money spent is 30 you will have to write the statement for that here minus 30 itself is representing that he has lost that money he don't have 30 rupees anymore Thank you, Kajal. I hope this is clear now, right? All right, so this was about this question that was 90. Let's move ahead. So now we will be talking about, so till now we learnt about how to do the, how to find out the product of two integers.

What if we have to find out the product of three or more negative integers? Let's take a look at this. Minus 4 times minus 3. Simply I know 4 times 3 is 12. That I know.

Now something else, the new thing here is both of them are negative and we learn that if the signs are same, we get a positive result. Why? Because negative, negative cancel. I tell you one more thing over here. Here we have got one number, second number.

Even number of digits. Even number, right? I am not talking about this is an even number, this is an odd number.

I am saying even number of digits you have. Two numbers, that means they are even. Whenever we are multiplying the numbers, right, even, if the number of negative integers in a product is even, then always the result is going to be positive. Let me give you one more example.

Let's say we have minus 2 times minus 4 minus times minus 3. This time we have got three numbers. This is odd. So, I will be getting a negative result. Why?

Because one negative sign will cancel out the other. Still, other one would be left. Yes? So, 2 times 4 is 8. 8 times 3 is 24, you get minus 24. Thank you, Zasmita.

Wow, that's amazing. Yes, Zinnia, that's right. So, I hope this is clear to everyone, right?

So, whenever the number of integers in a product are even, we get a positive result. If number of negative integers in a product, negative integers, right? In a product are odd, you get a negative result, otherwise positive result. So, here you can see 1, 2, 3, 4. Even, right?

All of them are negative, right? Even number of digits. Result would be positive. Reason is one negative will cancel other, one negative will cancel other. 1 times 2 is 2, 2 times 4 is 8 and 4 times, I am sorry, 8 times 3 is 24. Thank you.

Yes. Abhiraj, one more time. So this we have we all have understood this right that one negative cancels the other one negative negative cancel each other keep this in mind.

Second thing if in a if the number of negative integers in a product they are even you always get a positive result but if the number of integers in a product are odd we always get a negative we always get a negative result otherwise positive result. Did I say something else? I think if number of negative integers in a product are even you get a positive result.

If they are odd you get a negative result. I'm just writing down here. They are even you get positive. If they are odd you get a negative result. Yes?

For next class please subscribe the channel. You will get notifications about all the sessions. I hope this is clear. Yes? Alright, no doubt still here, this is clear to everyone.

If we have three or more negative integers, so if you come across with such questions, will you show four digit in the number line? Four digit in the number line, what does that mean? Four digits, are you talking about this thing?

So for such things, number line is not needed. You can do it this way only. Yes, I think this is more easier than the number line. Alright, this is clear to everyone. Great, let's move ahead.

So till now we talked about multiplication of numbers with number line, without a number line. Now we are reaching our final topic of today's session that is division of integers. Yes, so now we will see how to do division of integers.

Thank you Arya. So let's take an example. So here you can see we have got 12 apples, right?

Now we need to divide it among 3 people. So How are we going to do it? How to do that?

Yes? So, we can say that division is something that in which splitting of a large, we are doing a splitting of large group into smaller groups and such that every group get equal number of items. That's what division is, right? That's how we divide things when everybody is getting the equal number of items.

So, 12 apples are here, right? If I have to divide them, amongst three people what we can do is we can distribute one one apple to each one of them again one more apple to each one of them like this we would keep doing this repeating this process until all the Apple finishes and at the end we see that each one of them is getting four apples right absolutely Sakshi right each one of them will get four apples each group so another way to understand this is basically this is the first way what we can do is simply We can divide this 12 by 3, right? We get 4. Now what if we can also get this answer by a repeated subtraction method, division as repeated subtraction. So here what we will be doing is there will be a total of 4 subgroups, right?

You can see 4 subgroups over here, right? Of 3 apples and it can also be repeated, shown like this. 12 minus 3, you get 9. That's the first group. Then you are left with 9. 9 minus 3, you get 6 apples. That's the second group.

6 minus 3, you get 3. And then 3 minus 3, finally 0 apples are left. So again, what we can see here is, this is used 4 times. So 12 divided by 3, again this is 4. So this is division as repeated subtraction.

Another way to show it. Yes. Yes. Now we are...

minus 15625 by minus 25. See, simply minus minus as I told you, right? They will cancel out each other. Simply you can divide this with 125. Simple division.

Yes, answer would be positive in that case. Yes, that would be 25. All right, this is clear to everyone? Yes? All right, let's move ahead.

So now just like we learned about these signs in multiplication similarly yes similarly you can we and we will understand this in division also same thing will happen when we are dividing two numbers they both are positive right or either they both are negative signs are same again the result would be positive no new rule we are learning only the operation is changing if the signs are same you are dividing numbers your result would be positive but if the signs are different you can see here signs are different you are dividing them result would be negative so yes so what is the crux two negatives or two positive they make a positive so same signs will give you a positive result different signs will give you a negative result yes Yes, Aarti Jaswini, whatever doubt you have, you can just write in the comment section. Yes. What you cannot understand.

Absolutely, Ravindra. Yes. The recorded session would be there on YouTube.

Yes. Now, let's try out a few questions to get a better understanding. Yes, division without number line.

So, plus 8 divided by minus 2. So, we will be using the same logic that we used while doing multiplication, right? So, 8 divided by 2 is what? That's 4. Now, we will think about the sign.

The signs are different. What did I tell you when the signs are different, when the signs are different, your result would be negative but when the signs are same, the result would be positive. Again 8 divided by 2, I'm sorry this would be negative, 8 divided by 2 would be 4. Again signs are different, this is negative, this is positive. So our result is going to be negative.

I'll show you that aria. But simply rather taking a look at that, I would say simply keep this thing in your mind. If signs are same, I'll get a positive result. If signs are different, I'll get a negative result.

Yes, Bidu, Bhushan, Mohapatra, right? Absolutely Anik Chatterjee, right? That's what I'm saying. Rules are same.

Rules are not different. Now you see both of them are negative. Minus 8 minus 2. So definitely 8 divided by 2 is 4. Both signs are same. So result would be positive. So I am writing 4 only.

Because negative negative cancel out each other. Yes? Okay.

8 divided by 2. Nothing is written with 8. That means it is positive. Both of them are positive. Signs are same. So 8 divided by 2 is 4. When signs are same, we get a positive result.

No new rule we are learning. Just keep one thing in mind. Different signs, negative results, same signs. positive result.

Yes? I hope this is clear to everyone. No doubt still here? Quickly give me thumbs up or smileys if you have understood this. So this is division in the same signs and this is division in the different signs.

And why is the positive number inside the bracket? This one. That doesn't matter. Even if it is written this way, it is positive only. Doesn't matter.

Even if I write it as 2 only or positive 2 inside the bracket. That's okay. Yes, Arya. Rules are same. Nothing new we need to learn.

Wow! Lots of thumbs up and smileys I can see. Now, let's try out a few questions to take your understanding.

So, solve the following problem. First is minus 90 divided by minus 15. What we will do is simply first we will divide them. What is 90 divided by 15? That's 6. Both the numbers are negative. When signs are same, we get a positive result.

So it's going to be positive 6. I told you the reason also. Two negatives, negative, negative cancel out each other. Right?

Correct. Right, Aarshi, Asnagendra, Deepa, Biswarupa, absolutely. Minus 54 divide by 6. So what is 54 divide by 6?

That's basically 9. Now signs are different. This is negative but this is positive. Different signs, you get a negative result. Minus 9 is going to be the answer.

Right, Sunita Chaudhary, Dibyanshi? Yes, absolutely, minus 9. No, Kajal, it's going to be negative 9, not positive. See, signs are different.

Different signs give you a negative result. Yes, all right. Great, so we have understood this.

Now again, it's quiz time. The favorite part of the session, yes? So let's try out a few questions. So here we go.

Ben and his four friends borrowed a total of rupees 500 from their parents to go on a picnic. If each one of them has equal share in the borrowed money, what is the amount each one of them owes? So I'll give you 30 seconds to answer this question. I'm starting the timer now.

Quickly answer this question in the comment section. Yes, I can still see the answers of the previous question, I think. Okay, so the Banshee, Mrinal, S. Nagendra, Harshi, everyone is saying 100. You gave the answer so quickly.

Ravindra says it's 250. C. Okay. All right. So time is up. Let's see what the right answer is.

It's A. 100. It's not 250. Ben and his four friends. So total five.

people including Ben, right? They have a total money of 500. Now they are going on a picnic and it has to be divided equally amongst them. When we are dividing equally, so obviously we will be dividing 500 with 5. That's simple.

Both are positive. You will get a positive result. Answer would be 100. Option A. I hope whomsoever gave a different answer, you have understood where you went wrong. Yes?

Alright, let's try out another question. Fill in the boxes with appropriate values. Now this puzzle is interesting. So I am giving you 30 seconds for this. Let's start the timer.

Yes. That's okay, Rabindra. So first read the question carefully. You can break it down into small, small pieces. Whenever you come across a long question, a big question.

Sure, Sohini. This is just a concept session. We will come up with more sessions where we will be discussing questions only. So, don't worry about that.

So, Ben and four friends, yes. That's why we say that read the question carefully first. Alright, alright.

So, time is up. I can see answers. A minus 8, A minus 8, B minus 4. Okay, let's check the result.

So, we are saying 64, 64 divided by A gives us minus 8. So, what is A going to be in this case? When I am getting... know that 64 divided by 8 will give me 8. Since answer is negative, so definitely one of them has to be negative. So, A in this case is going to be minus 8. I'm writing the results here.

A would be minus 8 in that case, right? Absolutely, you all are giving the right answer. Talking about B, yes, so let's 64 divide by B, that's simple.

It gives us 16. So, definitely B is going to be 4 because 64 divide by 4 will give me 16. So, B is 4 in this case, yes. B would be positive, why negative? They both are positive. See, this is positive, result is also positive.

We will only be getting the positive result when the signs are same, right? So if this is positive this has to be positive also. Thank you Nandita. Talking about C. So B divides C give us 2. What is B?

B is 4. 4 divide by C give us 2. So C that's very simple that's going to be 2 only. This was a very small value right? C would be 2. Okay talking about D.

Yes so minus 8 divide by 2 gives me D. Minus 8 divide by 2. So 8 divide by 2 gives me 4 and there are signs are different. So D in this case would be minus 4, right? D would be minus 4, not positive because 8 is negative here. Talking about E, E divided by D gives me 2. So, what is E?

We don't know what E is but D is minus 4. That gives me 2. So, definitely, I know that it is going to be 8 but it will be negative 8. Why? Because result is positive. When signs are same, only then I can get a positive result. So, E in this case would be, is going to be minus 8. right? Yes, talking about f, so minus 6 divided by f give me 2, so minus 6, I am getting 2, definitely I am dividing this by 3 but only that means f would be negative because when signs are same then only we get a positive result, so 6 is negative, so f is also going to be negative in this case, that is going to be minus 3. I hope this is clear, yes I can see answers over here, everyone is giving the right answer.

So that was an interesting puzzle, right? Awesome, let's move ahead now. So that was about the quiz.

Now you can see that this kid is relaxing because it's time to end our today's journey over here. So it's time to relax. Now first quickly let's take a look at the summary, what all we have covered today. So we talked about the board mass which we will be using in our questions, right?

And we know what board mass is actually. Then we talked about how to do multiplication on a number line. We used the example of that frog, right?

And how to do multiplication without number lines. So, multiplication of two or more integers without number line, we have seen that and we have learned about the rules also, how to observe the signs and all. And we talked about the division of integers. And we learned that the signs thing, right?

Those rules remain the same. There is nothing different. Now, it's time for homework.

Quickly take a look at this. So, you have to solve this expression and four options are given over here. You need to give the right answer and you can let us know the correct option in the comment section after this session and don't worry we have got you covered we have lined up many more sessions for you from every Monday to Friday to make you exam ready so everything will be covered whatever questions you have in your ncrt books whatever is there now let me give you a glimpse of the upcoming session so our next session which is the concept session part 2 of integers it's on 25th April that is Monday at 5 p.m.

so do not miss the session And we have free trial classes as well. The link for that is given in the description below. Please click on that link and get all your doubts clarified instantly during the class. And please like, share and subscribe so that you do not miss any new updates from us.

For homework question, you give your answers after this session in the comment section. Alright. So, I will see you soon.

Thank you. Bye-bye.