Last updated on July 25th, 2025
The associative property of addition states that when three or more numbers are grouped differently, the sum remains the same. In this article, we will discuss the associative property of addition in detail.
The associative law in mathematics states that changing the grouping of numbers using parentheses does not change the result. The associative property applies to both addition and multiplication operations.
The associative law of addition is when the grouping order of the operands does not affect the result of the expression, when an expression contains three or more numbers, and only addition. The formula for the associative law for addition is given by:
(a + b) + c = a + (b + c)
This shows that adding a and b first, and then adding c, is the same as adding b and c together first and then adding a.
A simple example of the associative property is:
(10 + 1) + 5 = 11 + 5 = 16
10 + (1 + 5) = 10 + 6 = 16
This demonstrates that the sum remains the same regardless of how the numbers are grouped.
The associative property applies only to addition and multiplication, and not to subtraction and division. We have learnt that changing the grouping of numbers in addition yields the same result as the original expression. Similarly, in multiplication, changing the order of numbers does not change the product of the numbers. We express the two formulas as:
Associative property of addition: (a + b) + c = a + (b + c)
Associative property of multiplication: (a × b) × c = a × (b × c)
Some important points to remember are:
The associative property of addition is a widely used concept and plays a part in our everyday lives. We use the associative property in our daily life even without knowing it. Here are some real-world applications of the associative property of addition:
When understanding the concept of the associative property of addition, students tend to make small mistakes. Here are some of the common mistakes that students make and ways to avoid them:
Verify the associative property for 4, 7, and 9 using addition.
20
Using the associative property of addition: (a + b) + c = a + (b + c)
(4 + 7) + 9 = 20
4 + (7 + 9) = 20
Show that (12 + 5) + 8 = 12 + (5 + 8)
25
Using the associative property of addition: (a + b) + c = a + (b + c)
(12 + 5) + 8 = 25
12 + (5 + 8) = 25
Use the associative property to simplify (3 + 8) + 2.
13
Use the associative property of addition: (a + b) + c = a + (b + c)
3 + (8 + 2) = 13
Verify the associative property for 1.5, 2.5, and 4.
8
Use the associative property of addition: (a + b) + c = a + (b + c)
(1.5 + 2.5) + 4 = 8
1.5 + (2.5 + 4) = 8
Does (9 + 11) + 5 = 9 + (11 + 5)?
Yes, the answer is 25.
Use the associative property of addition: (a + b) + c = a + (b + c)
(9 + 11) + 5 = 25
9 +(11 + 5) = 25
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.