 Hello friends welcome back to this session on number system now today in this video We are going to learn representing rational numbers on a number line Hope you remember now what rational numbers are if you don't know or don't remember you can go back and watch the previous session So just to give you a quick recap a rational number is of the form of P by Q where P and Q are integers are Integers and In many literature you will see this written as P comma Q and this Greek letter epsilon belongs to Z right this is a mathematical way of writing P and Q are integers P and Q This notation means belongs to belongs to Z that means set of Set of integers right so P and Q belongs to set of integers Okay, so and then second this was criteria number one Criteria number two was Q is not equal to zero the denominator cannot be zero and three was that GCD of P and Q that means the HCF of P and Q should be one Right, so let us now understand what a number line is and how do we represent rational numbers most of you But I've all already represented integers on number lines, isn't it so you take a number line You take a line basically and put a zero somewhere and then you divide the line into Equal parts right so I have shown here. This is point one this this point represent one So every point on the number line represents a number What type of number we are going to study in detail any which way right so right now I have represented zero one two three and minus one minus two minus three on the number line So one point to be noticed here is the gap between the two consecutive integers is always the same That's what is the key Key thing in this number line, isn't it now obviously we cannot show all the numbers on the number line because it's infinitely many So hence we have represented only a few now Let us say if I have to represent one upon two is it of rational number? Definitely it's a fraction. It's a rational number and even by the definition of rational number You can see one and two are integers Two is not equal to zero and GCD or it's CF of one and two is one So by definition one by two is a rational number, and it is very reasonable also to you know You know that half is nothing but 50% or something Rational number it is a very much reasonable number half, but where does it lie right? So half you know is less than one but greater than zero isn't it so definitely half is more than nothing But definitely less than the full right so that means Logically speaking the position of half must be somewhere between zero and one But there are infinitely many positions between zero and one so where in where exactly? So as the number suggests itself, it is half that is exactly half of one So ends it is logical or reasonable to make a point or find a point exactly in the middle of middle of Zero and one and say that this is half Isn't it so basically if you notice what did we do? So see the numer then denominator now so denominator is what is the denominator here denominator is two So basically what I did is I divided between the zero and one into two parts and the first part Wherever it ends is my one by two Let us understand another take another example. Let us say we say five upon three So I have to represent five upon three on the number line. What is five upon three? So if you notice it is nothing but it is one Hole two upon three. I understand that or I assume that you know how to reduce a Fraction into a mixed fraction right NYC workshop. So it is a mixed fraction. It's a one hole Two upon three. That means one full and then two upon three That means clearly this number is greater than one. Isn't it? it is more than one because one and two-third or something and Definitely this number is also less than two. Isn't it? So hence Intuition says it was somewhere in this part somewhere in this part But where so if you see again take the denominator so denominator is three so let us take the denominator and divide the Number one between other the length one between the one and two right so first of all ascertain the lower lower limit So it is between one definitely and two So this number Lies between one and two. So take that segment one and two. I have highlighted there Now divide this in how many parts denominator? How many denominator parts are there three? So one so now if you see there are three parts now and then second part of This wherever it ends. So second part is this so this point represents Five one two one whole two upon three or five by three. Isn't it? Let's take another number let's take Something between two and three Right or let us say we are now a decimal number So let us say we take two point say two Okay, so what is it basically if you see 2.2 is nothing but you must have studied before so 2.2 can be represented as 22 by 10 is it just put a 10 so 22 divided by 10 is 2.2 Now is this a fraction number? No, but it can be reduced to and it is 11 upon 5 if you cancel to from numerator and denominator You'll get 11 upon 5 which is nothing but one Sorry, not one it is two whole one upon five isn't it so if you noticed I converted 2.2 into a Fraction and then into a mixed fraction so two whole one upon five that means this number is greater than two clearly No problem, and it is also less than three, right? So the number is between two and three so that means I have to divide two and three But to a between the gap between two and three but in how many parts again I said look for the denominator of five parts So let us divide this into five parts So five parts means I have to put four points one two three and four Right, so it might not look like equal parts, but that's what I mean So I have divided into five equal parts And then I have to take the first out of this first isn't it first part So first part ends here. So I encircle that so this point my dear friends this point represents two whole one upon Five which is equal to eleven upon five which is equal to two point two Right similarly, you can do all this for negative numbers as well We can take one example for example, let me say I am taking a number Minus two point two. Let us say the same number minus two point two, right? So it is somewhere between minus three and minus two isn't it and so hence What will we and where how to locate it? So it is simply it is simply minus 22 by 10 which is equal to minus 11 by Five right so hence you will do what whatever you did on the right-hand side You will do the same thing, but here you will start counting from the Upper limit here What does it mean? Let me show you so again you have to divide this into five parts one two three and four Right, so hence it is nothing but minus two one upon five so five parts. I have divided and first Right, so now I will take from here from the right-hand side not from the left-hand side because it is a negative number, right? so this number is minus eleven upon five or minus two point Two right well again. I'm repeating. I'm not taking from there I'm not taking this as you know unlike this case We had taken just next to two here also just next to minus two, right? So I'll start from minus two only but in the left direction here I started from two but in the right direction. This is happening because I am taking a negative number I'm representing a negative number on the Number line so now I think you understood how to represent Numbers on a number line will take problem-solving sessions where it will be more clear you can look for those sessions there in the Playlist and try and understand how the problems are being solved Thank you