Are the values of 5 × 2 × 6 and 2 × 5 × 6 same? Is there any other way of rearranging these three numbers?

Given: 5 × 2 × 6 and 2 × 5 × 6 5 × 2 × 6 = ( 5 × 2 ) × 6 = 10 × 6 = 60 Again, 2 × 5 × 6 = 2 × 5 × 6 = 10 × 6 = 60 So, the values are the same for the given expressions. Yes, there are other ways to rearrange these three numbers. They can also be arranged as 5 × 6 × 2 and 6 × 5 × 2 .

What is 15 ÷ 5 ? Is it the same as 5 ÷ 15 ? Why?

Given: 15 ÷ 5 Let us first find the quotients from the expressions: 15 ÷ 5 = 3 and 5 ÷ 15 = 0 . 333 So, it is evident that both the answers are not the same. This is because, in the case of divisions, the dividend and divisor are interchanged if the order of the number changes. Thus, the order of the numbers matters here. So, the commutative property does not hold true for division of whole numbers.

What is the value of ( 100 ÷ 10 ) ÷ 5 ? Is it the same as 100 ÷ ( 10 ÷ 5 ) ? Why?

Given: 100 ÷ 10 ÷ 5 Let us first find the value of both the expressions: ( 100 ÷ 10 ) ÷ 5 = 10 ÷ 5 = 2 100 ÷ 10 ÷ 5 = 100 ÷ 2 = 50 So, it is evident that both the answers are not the same. Thus, if we change the order of the numbers, there will be a change in the answer. So, order of the numbers is important here and associative property does not hold true for division of whole numbers.

Is 10 ÷ 5 , the same as 5 ÷ 10 ? Justify it by taking two more combinations of numbers.

Given: 10 ÷ 5 and 5 ÷ 10 If the order of the numbers does not affect the result of the operation being performed, then that is called commutative property. The commutative property does not hold true for the division of whole numbers. Let us consider the examples below: (i) 15 ÷ 3 ≠ 3 ÷ 15 Because 15 ÷ 3 is 5 and 3 ÷ 15 is 0 . 2 (ii) 16 ÷ 2 ≠ 2 ÷ 16 Because 16 ÷ 2 = 8 and 8 ÷ 16 = 0 . 5 This is because, in the case of divisions, the dividend and divisor are interchanged if the order of the number changes. Thus, order of the numbers matters here. So, division is not commutative.

Complete the following table. 9 + 0 = 9 7 + 0 = 0 + 17 = 17 0 + = 37 0 + =

Given: 9 + 0 = 9 7 + 0 = 0 + 17 = 17 0 + = 37 0 + = We know that, When zero is added to any number, we get the same number. So, zero is called the additive identity for whole numbers. Thus, the completed table is as follows: 9 + 0 = 9 7 + 0 = 7 0 + 17 = 17 0 + 37 = 37 0 + 27 = 27