 Hi and welcome to the session. Today we will learn about properties of whole numbers. First of all we have closure property. This states that whole numbers are closed under addition multiplication. Let us understand this with the help of example. Suppose we have two whole numbers 6 and 2. Now let's see how whole numbers are closed under addition. So here 6 plus 2 is equal to 8 and 8 is a whole number that means whole numbers are closed under addition. Now 6 into 2 is equal to 12 and 12 is a whole number that means whole numbers are closed under multiplication also. Now we have a property that division of a whole number by 0 is not defined. Let's say the division of a whole number 7 by 0 is not defined. Next property is commutativity of addition and multiplication. This states that addition and multiplication relative whole numbers. For example, suppose we have two whole numbers 5 and 2 then 5 plus 2 is equal to 2 plus 5 is equal to 7 that means addition is commutative for whole numbers also we have 5 into 2 is equal to 2 into 5 is equal to 10 that means multiplication is commutative for whole numbers. Next property we have associativity of addition and multiplication. This states that addition and multiplication are associative for whole numbers. For example suppose we have three whole numbers 2 4 and 5 then 2 plus 4 the whole plus 5 is equal to 2 plus 4 plus 5 the whole which is equal to 11 that means addition is associative for whole numbers also 2 into 4 the whole into 5 is equal to 2 into 4 into 5 the whole which is equal to 40 so this implies that multiplication is associative for whole numbers. Now next property is distributivity of multiplication over addition this states multiplication is distributive over addition for whole numbers for example 2 into 3 plus 5 the whole is equal to 2 into 3 the whole plus 2 into 5 the whole. Next let us see the identities for addition and multiplication so first of all we have 0 is the identity for addition of whole numbers that is if we add 0 to any whole number same 2 then we will get the same whole number that is 2 itself. Now let's see the identity for multiplication so the whole number 1 is the identity for multiplication of whole numbers that is if we multiply any whole number say 2 by the identity 1 then we will get the same whole number that is 2 itself. Now our next topic is patterns in whole numbers now we can arrange numbers in elementary shapes made up of dots the shapes we take are a line a rectangle a square and a triangle so first of all we have every number can be arranged as a line for example let's take the number 3 we can arrange this as a line and the number 4 can be arranged as a line like this now we have some numbers can be shown as a rectangle for example let us try to arrange it as a rectangle so we can arrange it like this this is a rectangle now we can also arrange some numbers as squares for example like this this is a square now we can arrange some numbers as triangles let's see one example let us try to arrange 10 as a triangle so here we have one two three four five six dots now we are left with four more so here are 10 dots and we have arranged 10 as a triangle now our last topic is patterns observation first of all let us try to find out a shortcut method to multiply a number by the numbers of the form 9 99 999 and so on let's take an example try to multiply the number 74 by 999 now we can write 999 as 1000 minus 1 so this will be equal to 74 into 1000 minus 1 so this will give us 74000 minus 74 which is equal to 73926 so this is how we can multiply a number by the number 999 next let us find a shortcut method to multiply a number by the numbers of the form 5 15 25 35 and so on let us multiply the number 74 by 25 now here 25 can be written as 50 upon 2 so this will be equal to 74 into 50 upon 2 now first of all we will divide 74 by 2 and we will get 37 into 50 now 3370 and we are left with 5 so we have into 5 so 317 to 5 is equal to 1850 thus in this session we have learnt properties of whole numbers patterns in whole numbers so with this we finish this session hope you must have understood all the concepts goodbye take care and have a nice day