Quick rivision of the chapter '' integers'' for K5 to K7 currriculum

Properties

3. commutative property – If the places of Integers are interchanged with each other , their value does not change for operations like addition and multiplication .

Ex- 23 + 45 = 45 + 23

5678 + 4351 = 4351 + 5678

8 +  9 + 4 = 9 + 4 + 8 = 8 + 4 + 9,  these are examples of commutative property of addition.

67 × 58 = 58 × 67

48 × 32 × 2 = 2 × 32 × 48 = 48 × 2 × 32

45 × 54 = 54 × 45 ,  etc . Remember that property does not applicable for other two basic operations like subtraction and division. Could you find out with examples?

Is 560 – 162 = 162 – 560?

Is 69 ÷ 23 = 23 ÷ 69? No. That’s how this commutative property is not applicable for SUBTRACTION and DI 8 )VISION. Could you apply this for negative Integers for a try?

4. Associative property –  this is another form of only the previous property. Don’t get confused or annoyed. It will be quite fun when we will compare this two properties simultaneously. Believe me it is going to be great fun.

Let’s start. If you have three Integers and you put them either under addition or multiplication; couple either the first two numbers or the last two numbers with the help of a bracket , both of them will be equal.

Ex -  3 + 8 + 9 , now put the first two in a bracket like (3 + 8 ) + 9 ; or put a bracket taking the last two digits inside the bracket and the let the first one as it is like 3 + ( 8 + 9 ).

Now if we solve , both of them will give equal value; ( 3 + 8 ) + 9 = 3 + ( 8 + 9 ) = 20. Same integers could also go under the operation multiplication also.

For example (3 × 8 ) × 9 = 3 × ( 8 × 9 )

This is known as the ASSOCIATIVE PROPERTY of addition/multiplication accordingly. Here addition and multiplication are associated over these three numbers to give the same numerical value. Next episode we will discuss how to differentiate between these two properties and that’s where real fun lies. By for now.