Properties of Whole Numbers - Part 1

 Properties of Whole Numbers - Part 1 

                                                                                                          

 

we know that four and five are whole numbers. What's four plus five it's nine. Nine is additionally an entire number. Even the numbers 22 and 33 are whole numbers. What's 22 plus 33 you're correct it's 55 and 55 is additionally an entire number. Are you getting a gist of what I'm trying to mention also if I add two whole numbers 350 and 620 the solution there is again an entire number similarly 28,000 plus 50 ,000 also end in an entire number whenever we add any two integer s the resultant number that we get may be a additionally an entire number and this is often  the primary property of an entire number. However rather than this we are saying that integers are closed under addition. This is just a way of claiming it. This statement is really an equivalent as this if I add any two whole numbers the amount that I buy also will be an set of number now here may be a question for you to answer our whole numbers closed under subtraction. First of all let's understand what the question means what can we mean by closed under subtraction it means if we take any two whole numbers and subtract them then we'll always get whole number will this manner always happen

Let's attempt to find this out by subtracting any two random whole numbers 35 minus 20 is adequate to 15. We subtracted two whole numbers and then we got whole number again similarly one thousand minus 999 will give us one an entire number. Again what about five minus eight what is going to we get once we subtract eight from five wait a flash can we even subtract eight from five? No we'll not do this , we attempt to subtract them here's what we get a negative number we aren't talking about negative numbers now you'll learn that within the future lessons but we all know that this is never an entire number hence we will term this subtraction as invalid similarly if you subtract 100 from 50 the solution that you simply will get is a negative number both numbers aren't whole numbers so we will say whole numbers aren't closed under subtraction. What about multiplication.  whole numbers closed under multiplication yes they're closed under multiplication. Once number multiplied by any two whole numbers you'll always get an entire number here are a couple of examples to support this argument 5 times 5 is 25 an entire no 1 times 1,000 is 1,000 an entire number. Again let's involve the entire numbers 0  times 10 is what ? Once you multiply any number with 0 we get 0 again so it's 0 we take any two integers and multiply them the solution that we get will always be an entire number here's a fast recap of what we studied thus far during this  we learned that whole numbers are closed under addition not closed under and closed under multiplication these three are arithmetic operations that we commonly use is that the another one which is the fourth commonest operation that you simply know of its division. I'm sure that you must have already guessed subsequent question that I'm getting to ask you our whole numbers closed under division four and two are whole numbers and if we divide 4 by 2 we get an entire number again but if we divide 6 by 5 the solution we'll get are going to be in decimals which isn't an entire number similarly examples like 3 divided by 12 4/9 won't end in whole numbers hence we are saying that whole numbers aren't closed under division. What's 0 divided by 4 it's 0 and what's 4 divided by 0 is it also 0 or perhaps another number. So as to know this we first got to make certain that we all know the meaning of division we've studied arithmetic operations and therefore the fact is that among all the arithmetic operations students find division to be the foremost difficult one what's division once we divide variety 8 but therefore what actually are we doing imagine the scenario there are 8 chocolates and 4 people which we want to distribute these 8 chocolates to 4 people such everyone gets equal number of chocolates what percentage chocolates will one person get everyone will get 2 chocolates. How did we get this to yes we divided 8 by 4 and that gave us 2 or in other words, we divided the amount of chocolates available equally among all the people now for instance rather than 4 there are two people now how will we divide ate chocolates between two people what percentage chocolates will everyone get? You're absolutely correct all will get 4 chocolates let's act a touch crazy now allow us to divide eight chocolates equally among zero folks that is 8 divided by zero does it even is sensible to divide eight chocolates amongst nobody no it doesn't hence we are saying this is often undefined or in other words any whole number divided by zero is undefined on an equivalent lines these are all undefined quantities we'll see another property of whole numbers within the next post