 Hi and welcome to the session. Today we will learn about division of integers. Suppose we have two integers 7 and 2 then 7 into 2 is equal to 14. Now if we divide 14 by 7 then we get 2 and if we divide 14 by 2 then we will get 7. So from this we can conclude that division is the inverse operation of multiplication. Now suppose we want to divide a negative integer by a positive integer then for any two positive integers a and b minus a divided by b will be equal to for this first of all we will divide a by b as whole numbers and then we will put a negative sign before the question where b is not equal to 0. So this will give us a negative integer. Also if we want to divide a positive integer by a negative integer then for any two positive integers a and b a divided by minus b will be equal to minus of a divided by b where b is not equal to 0. Thus from these two statements we can say that minus a divided by b is equal to a divided by minus b where b is not equal to 0. Let's take an example for this. Suppose we have two positive integers 75 and 5. Now minus 75 divided by 5 will be equal to minus of 75 divided by 5 which will be equal to minus 15. Also 75 divided by minus 5 will be equal to minus of 75 divided by 5 which will also be equal to minus 15. Now let's see how to divide a negative integer by a negative integer for any two positive integers a and b. If we want to divide minus a by minus b then first of all we will divide a by b as whole numbers and then we will put a positive sign before the question. So we can simply write it as a divided by b. For example for two positive integers 75 and 5 minus 75 divided by minus 5 will be equal to 75 divided by 5 which will be equal to 15. Now let's move on to our next topic properties of division of integers. First of all we have division of any integer by 0 is not defined that is for any integer a divided by 0 is not defined. But division of 0 by any integer is equal to 0 provided that integer is not equal to 0. Thus for any integer a 0 divided by a is equal to 0 itself where a is not equal to 0. For example minus 5 divided by 0 is not defined but 0 divided by minus 5 is equal to 0. Next we have any integer divided by 1 gives the same integer that is for any integer a a divided by 1 is equal to a itself. For example 49 divided by 1 is equal to 49 itself. Now integers are not closed under division. For example minus 2 divided by minus 4 is equal to 1 upon 2 which is not an integer thus integers are not closed under division. Now division is not commutative for integers. For example if we have two integers 15 and 5 then 15 divided by 5 will not be equal to 5 divided by 15. Thus we can say that division is not commutative for integers also division is not associative for integers. For example minus 36 divided by 6 the whole divided by minus 3 will not be equal to minus 36 divided by 6 divided by minus 3 the whole because this will give us 2 and this will give us 18. So this implies that division is not associative for integers. Now let's try to solve one question. Suppose we are given that the cost of 12 tables is equal to rupees 420 and we need to find out the cost of one table. Then cost of one table will be equal to cost of 12 tables that is rupees 420 divided by number of tables that is 12. So this will be equal to rupees 35. Thus over here to find out the cost of one table we use the concept of division of integers. Thus in this session we have learnt division of integers and properties of division of integers. With this we finish this session. Hope you must have understood all the concepts. Goodbye, take care and have a nice day.