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What does associative property mean in mathematics?
Associative property means we can group numbers in different ways while adding or multiplying, and the answer will still be the same.
What does the associative property of multiplication mean?
The associative property of multiplication means while multiplying three numbers, we can change how the numbers are grouped, and still the product will remain the same. Example: (2 × 3) × 4 = 2 × (3 × 4)
What is the associative property of addition in math?
The associative property of addition in math implies that while adding three numbers, we can add any two numbers first, and the answer will not change. Example: (5 + 6) + 3 = 5 + (6 + 3).
Can we apply the associative property in division?
No, the associative property does not work in division. Grouping the numbers differently in division can give different answers.
What is Associative Property? Definition With Examples
Associative Property explains how changing the grouping of numbers in addition or multiplication does not change the result. Learn the definition of associative property with examples.
Shivam Singh31 Jul, 2025
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What is Associative Property?: The Associative Property is a rule in mathematics that tells us we can change the way numbers are grouped while adding or multiplying them, and the answer is still going to be the same. But it is important to remember that the associative law in math only works for addition and multiplication.
For example, if you are adding 2 + 3 + 4, you can first add 2 and 3, then add 4 — or first add 3 and 4, then add 2. In both ways, you’ll get the same answer, which is 9. This happens because of the associative property. To understand it better, keep reading to know the definition and example of associative property.
When this chapter is introduced for the first time, the first question that usually comes to mind is, "What is Associative Property?" It is one of the basic rules in mathematics that helps in solving problems easily. This rule explains that while adding or multiplying numbers, the way we group them using brackets (parentheses) does not change the final answer.
Still feeling confused? That’s okay! The definition of associative property becomes easier to understand when we go through a few simple examples, just like the ones given here.
Did you observe that even after changing the grouping of numbers, the product which is 48, stays the same? This shows the associative property of multiplication.
Associative Property of Addition
The associative property of addition states that while adding three or more numbers, the way the numbers are grouped using brackets or parentheses does not change their final sum or product. In simple words, it means that no matter how we put the brackets, the answer will always be the same. Let’s take an example to understand it clearly:
Suppose you are adding these three numbers: 4, 6, and 5. Now, you can add them in two different ways:
First way: (4 + 6) + 5 = 10 + 5 = 15
Second way: 4 + (6 + 5) = 4 + 11 = 15
As you can see, the answer is 15 in both ways, even though the grouping of numbers or the placement of brackets is different. This is called the associative property of addition. We can also write it using letters like this: (A + B) + C = A + (B + C)
What is the Associative Property of Multiplication?
When multiplying a set of three or more numbers, the associative property of multiplication tells us that the way we group the numbers doesn’t change the final result (sum or product). This means, no matter how we arrange or group the numbers, the product will always remain the same. Let’s take an example to understand this better:
You are multiplying 5, 3, and 2. So you can group them in two ways:
First, group (5 × 3) and then multiply by 2: (5 × 3) × 2 = 15 × 2 = 30
Second, group (3 × 2) and then multiply by 5: 5 × (3 × 2) = 5 × 6 = 30
In both cases, you can see that the final product is 30, even though you grouped the numbers differently. This Associative Property of Multiplication can also be written as: (A × B) × C = A × (B × C).
Associative Property of Subtraction
As mentioned above, the associative property is a math rule that you can apply to some mathematical operations, such as addition and multiplication. But, when it comes to subtraction, the associative property does not work in the same way. This means that the answer to the subtraction of three or more numbers can change depending on how the numbers are grouped.
To understand how the Associative Property of Subtraction doesn't work, take a look at an example here: Suppose you are solving these two calculations: (8 - 4) - 2 and 8 - (4 - 2).
In the first way, group the numbers as (8 - 4) - 2:
First, subtract 8 - 4 (applying the BODMAS rule), which gives 4.
Now, subtract 4 - 2, which gives the final answer of 2.
In the second way, now group the numbers differently: 8 - (4 - 2):
First, subtract 4 - 2 (applying the BODMAS rule), which gives 2.
Now, subtract 8 - 2, which gives the final result of 6.
As you can see, the answers for both ways are different: 2 from the first case and 6 from the second case. This shows that the associative property is not followed in subtraction, because the way we group the numbers is going to change the final answer.
Rational numbers follow the associative property when we add or multiply them. This means that the grouping of the numbers differently while adding or multiplying is not going to affect the final answer. Suppose that we have three rational numbers: a/b, c/d, and e/f, let’s add and subtract them using associative law.
For Addition: If we add the second and third numbers first and then add the first number, or we add the first and second numbers first and then add the third number, the sum will be the same.
But here, the numbers grouped are not the same, so this is not an example of associative property. Even if the answers match, the grouping should be done on the same numbers.
Example 6: Fill in the missing number using the associative property: (6 + 9) + 3 = (6 + 3) + ___ = 18
