Associative Property of Addition

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 this symbolism in mathematics lays the foundation stone for understanding relatively tougher concepts like multiplication.

Understanding Associative Property

It is essential to make children aware of the fact that addition is a process which will give the same end result no matter what order we follow while adding several numbers in the series. Hence, regardless of the grouping of numbers, the net result is going to be the same in addition. So, according to this property, no matter how we add a group of numbers, following any order, the result is always going to be the same.

Generally, 3 or more numbers are involved when we discuss the associative property and a unit is put in a parenthesis bracket 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 symbolize as one 'unit'. Since groupings are always in brackets, it means the numbers are associated and so the name 'associative property of addition'. Just as a thumb rule, remember that the numbers in the groupings are added first, so that the entire task becomes easier, as the calculation becomes fairly simple. 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 like subtraction and division in which it is essential to mention the order of operation.

Learning Through Examples

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

In this problem, L.H.S. = (4 + 5) + 9 = 18, R.H.S. = 4 + (5 + 9) = 18

Since, L.H.S. = R.H.S. = 18, the associative rule of addition is true.

2. Show that (a + b) + c = a + (b + c), where, a = -2, b = 7, c = 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.

3. Which of the following options holds true for (3+4) + 8 as per the associative property of addition?

1. 3(4+8)
2. (3+4)8
3. 3+ (8 + 4)
4. (3+4)4

As obvious, option no. 3 is correct.

4. Simplify using associative property: Simplify 23 + 54z + 7y - z - y - 27

To simply use associative property, we can group like terms, that is,

(23 - 27) + (54z - z) + (7y - y) = -4 + 53z + 6y

Just like associative property in addition, there is also associative rule in multiplication, that states, for any number, (a x b)c = a x (b x c) which means, (2 x 3) x 4 = 2 x (3 x 4). Thus, we can see that the associative property of addition is very easy to understand. Now that you know the concept of associativity, just practice some more problems on the same concept and understand it in a better way.