117 LearnersLast updated on July 25th, 2025
Associative Property of Addition
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.
What is Associative Law?
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.
Associative Property of Addition and Multiplication
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 can only be applied to addition and multiplication.
- Associative property is about changing the grouping of numbers and not the order of numbers.
- Since the associative property is more about grouping numbers, it will not work with subtraction and division.
Real-Life Applications on Associative Property of Addition
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:
- Grocery shopping: When grocery shopping, we add up the prices of multiple grocery items and come to a total bill. We can group the items in a different order, and the total would still be the same.
- Calculating travel distance: When taking multiple flights or bus rides, they can add up different parts of their trips in any order without changing the total distance traveled.
- Scheduling: When calculating work hours for the week, an employee can first sum up the hours of the first few days and then add the remaining days, without affecting the total number of hours.
Common Mistakes on Associative Property of Addition and How to Avoid Them
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:
Mistake 1
Confusing the associative property with the commutative property
Students may assume that the associative property allows changing the order of numbers and not groups. Students must remember that the associative property allows for changing of groups, and the commutative property allows for changing the order of the numbers.
Mistake 2
Assuming the associative property can be applied to subtraction
When solving problems involving subtractions, students assume that the associative property can be applied. This is incorrect because the associative property can only be applied to addition and multiplication. Subtraction does not follow the associative property since changing the grouping of numbers results in a different answer.
Mistake 3
Ignoring the parentheses in the questions
Students may assume that the parentheses are irrelevant in the questions and do not affect the steps. Students must note that the parentheses indicate the grouping, which is what the property changes, but the sum stays the same.
Mistake 4
Ignoring decimals and fractions
Students assume that the associative property can only be applied to whole numbers. Remember that the associative property can also be applied to decimals and fractions.
Mistake 5
Not recognizing its use in word problems.
The Associative property can be applied to a lot of real-world situations; however, students may struggle to understand how it works in real-life situations. Students must practice applying the associative property with real-life situations, such as grouping expenses in a shopping bill or splitting work hours.
Solved Examples on Associative Property of Addition
Problem 1
Verify the associative property for 4, 7, and 9 using addition.
20
Explanation
Using the associative property of addition: (a + b) + c = a + (b + c)
(4 + 7) + 9 = 20
4 + (7 + 9) = 20
Problem 2
Show that (12 + 5) + 8 = 12 + (5 + 8)
25
Explanation
Using the associative property of addition: (a + b) + c = a + (b + c)
(12 + 5) + 8 = 25
12 + (5 + 8) = 25
Problem 3
Use the associative property to simplify (3 + 8) + 2.
13
Explanation
Use the associative property of addition: (a + b) + c = a + (b + c)
3 + (8 + 2) = 13
Problem 4
Verify the associative property for 1.5, 2.5, and 4.
8
Explanation
Use the associative property of addition: (a + b) + c = a + (b + c)
(1.5 + 2.5) + 4 = 8
1.5 + (2.5 + 4) = 8
Problem 5
Does (9 + 11) + 5 = 9 + (11 + 5)?
Yes, the answer is 25.
Explanation
Use the associative property of addition: (a + b) + c = a + (b + c)
(9 + 11) + 5 = 25
9 +(11 + 5) = 25
FAQs on Associative Property of Addition
1.What is the associative property of addition?
2. Does the associative property work for decimals and fractions?
3. Is the associative property the same as the commutative property?
4.Why is the associative property so important in algebra?
5. Can the associative property be used with negative numbers?
6.How can children in Australia use numbers in everyday life to understand Associative Property of Addition?
7.What are some fun ways kids in Australia can practice Associative Property of Addition with numbers?
8.What role do numbers and Associative Property of Addition play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Associative Property of Addition skills?
Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
