 Hi folks, welcome to this session on number system. So continuing with our sessions on Rational and irrational numbers here I have come up with a table which explains some of the important results of Rational and irrational number operation. So what I have done is I have I have made a table where x is one of the Rational or irrational numbers. These are numbers x and y are numbers and we are doing some operation on an x and y Okay, so let us try and understand what exactly this means So hence if you take a rational number x and add and subtract another rational number The result is always going to be a rational. So this is what you need to know Example so 3 by 5 plus 1 is 8 by 5. So what does it mean? So whenever any time you add or subtract a rational from another rational number You are never going to get an irrational number. You'll always get a rational number Secondly rational number second this one rational number multiplied or divided by rational number mind you division by zero is not allowed So hence I have written except zero so rational number into Rational number and rational number divided by another rational number except zero always lead to lead to a rational number Right examples you can try 2 into 5 is 10 minus 1 into 3 by 2 is minus 3 by 2 You can take some examples for a division as well. You'll always end up with the rational number Third is rational plus minus and irrational Always will be irrational number. You will never get a rational if you add or subtract an irrational number from a rational number So zero is a rational plus root 3 which is irrational will give you root 3 here and Root 3 plus 2 is a sum of rational and irrational which is an irrational number Next rational number multiplied or divided by irrational number again We are not so rational number which we are taking should not be zero here because zero into anything will lead to zero So hence Except zero if you have a rational number and an irrational number if you multiply and divide you will always get an Irrational number right so hence rational number when multiplied by Irrational number or divided by rational irrational number will be an irrational number now most interestingly Irrational plus minus irrational is Needs not necessary a irrational it may be rational or it may be irrational as well Okay, so example examples are here if you see Root 3 minus root 3 is 0 which is a rational number now root 3 was a Was a Irrational number when subtracted or added to minus root 3 you will get 0 similarly 2 minus root 3 plus 2 plus root 3 these are two irrational numbers if you sum them up you will get 4 which is a rational number right Going forth irrational multiplied divided by another irrational need not be a irrational number It may be a rational also so you can see root 3 divide by 2 root 3 will be 1 by 2 Which is a rational number so hence in case of multiplication and division irrational multiplied or divided by irrational number may lead to a rational or irrational number so you keep these Results in mind and you might be interested in proving them and In the subsequent sessions we'll see how to prove such results. Thank you