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Associative Property of Addition

Kundan Pandey
The basic concept of associativity can be grasped by considering the fact that both addition and multiplication produce the same result, regardless of the order of the elements. Read on to know more about this fundamental mathematical concept...
One of the first mathematical operators that we learn in our lower classes is addition. Signified by a 'plus' (+) sign, it is probably the easiest concept to understand in mathematics, and students are most comfortable while performing addition.

Understanding Associativity

Addition is a process that gives the same result regardless of the order or grouping we follow while considering the elements in a mathematical statement. Hence, regardless of the grouping of numbers, the net result is going to be the same in addition.
3 or more numbers need to be involved when we discuss associative property. A unit of two (or more) of the three (or more) numbers is put in a parenthesis to symbolize a separation from the rest of the addition problem.

For instance, (3+5+9) + 8. Here (3+5+9) has been placed inside brackets to mark it as one 'unit'.
Remember that the numbers in the groupings are added first (since any operation inside brackets is performed the first in any mathematical problem). So in essence, given three numbers, x, y, and z, the associative property states that, (x + y) + z = x + (y + z).
It has to be understood that not all operations are associative. It is essential to mention the order of operation while performing subtraction and division.

Learning Through Examples

1. Prove that (4 + 5) + 9 = 4 + (5 + 9) by using associative property of addition

In this problem, L.H.S. (Left Hand Side) = (4 + 5) + 9 = 18; R.H.S. (Right Hand SIde) = 4 + (5 + 9) = 18

Since, L.H.S. = R.H.S. = 18, the associative rule of addition is seen to be true.
2. Show that (-2 + 7) + 9 = -2 + (7 + 9)

In this problem, L.H.S. = (-2 + 7) + 9 = 14 and R.H.S. = -2 + (7 + 9) = 14

Since, L.H.S. = R.H.S. = 14, the associative property of addition holds true.
The associative property also holds true in multiplication, which is basically a process of multiple additions.

(a x b) x c = a x (b x c)

For instance, (2 x 3) x 4 = 2 x (3 x 4) = 24
Now that you know the concept of associativity, just practice some more problems on the same concept to understand it better.