Let us understand the term associate - let us say we have three friends, they associate with each other or we can say they mix with each other. So how many of us have friends? Infact, we all do isn’t ? if we lined up the three friends together, and could we switch places , as we will still remain friends . so in the same rule also works in the math world too.
In assoc. Prop. of addition, if the numbers put together, let us use an equation ( 39 + 21) + 62 , now here we have an equation, so what do we notice about these three number? Well all the numbers are in the same line but the two numbers are grouped and the third number is kept aside but does not mean will not be counted. Let us sum them so 39 plus 21 is 60 and finally add 62 with 60 gives us 122, now in the next equation firstly always try and get rid from the brackets so the numbers inside the brackets are 21+62, whose sum is 83 now add with 39 which also gives us 122 as our final solution. Thus their sum will be always the same. If we group the numbers in different way also still the sum will be same. So let us take the same example as above, which is 39+ (21+ 62). So we get the sum as 122 for both the equation.
We define associative property of addition is when we are adding more than two numbers the grouping the adding’s does not change the sum. Let us say, (1+2)+4 = 1+(2+4) here we notice that the adding’s of the both sides are the same. 1+2+4 the associative property of addition, in the left hand side as we see, 1+2 is 3 and then +4 results in 7. The same way on right side 2+4 is 6 and then +1 is 7. So both have the same sum, regardless the way in which the way it’s adding’s group. This is how we define the Asso. Prop.of Addition and these were few Associative Property of addition examples that we understood.
Associated property of addition is nothing but the grouping three or more number in any order without affecting our sum. A more general way to write the associative properties of addition is (a + b) + c = a + (b + c).