101 LearnersLast updated on August 6th, 2025
Properties of Addition
Addition is a fundamental mathematical operation that has several key properties. These properties help students simplify arithmetic and algebraic expressions. The properties of addition include the commutative, associative, identity, and distributive properties. These properties help students analyze and solve problems related to arithmetic operations efficiently. Now let us learn more about the properties of addition.
What are the Properties of Addition?
The properties of addition are simple, and they help students to understand and work with arithmetic operations. These properties are derived from the principles of mathematics. There are several properties of addition, and some of them are mentioned below: Property 1: Commutative Property The order in which two numbers are added does not change the sum. For example, a + b = b + a. Property 2: Associative Property The way in which numbers are grouped in addition does not change the sum. For example, (a + b) + c = a + (b + c). Property 3: Identity Property The sum of any number and zero is the number itself. For example, a + 0 = a. Property 4: Distributive Property (over addition) For multiplication over addition, a(b + c) = ab + ac.
Tips and Tricks for Properties of Addition
Students tend to confuse and make mistakes while learning the properties of addition. To avoid such confusion, we can follow the following tips and tricks: Commutative Property: Students should remember that swapping the order of numbers in addition does not change the result. Associative Property: Students should remember that changing the grouping of numbers in addition does not affect the sum. Identity Property: Students should remember that adding zero to any number leaves it unchanged. Distributive Property: Students should remember that multiplication distributes over addition.
Confusing the Identity Property with Zero
Students should remember that the identity property of addition involves zero, where adding zero to any number gives the number itself.
Mistake 1
Misapplying the Associative Property
Students should know that the associative property only changes the grouping of numbers, not their order, and applies to addition and multiplication.
Mistake 2
Forgetting the Commutative Property
Students should practice recognizing that the order of numbers in addition can be swapped without affecting the sum.
Mistake 3
Misusing the Distributive Property
Students should remember that the distributive property applies to multiplication over addition, not to addition directly.
Mistake 4
Overlooking Zero's Role in Addition
Students must remember that zero is the additive identity, meaning adding zero to a number does not change the number.
Mistake 5
Solved Examples on the Properties of Addition
If 5 + 3 = 8, what is 3 + 5 according to the commutative property of addition?
3 + 5 = 8.
Problem 1
According to the commutative property of addition, the order of numbers can be swapped, so 5 + 3 = 8 means 3 + 5 = 8.
Using the associative property, simplify (2 + 3) + 4.
Explanation
2 + (3 + 4) = 9
Problem 2
Using the associative property, we can change the grouping: (2 + 3) + 4 is the same as 2 + (3 + 4). Thus, 2 + 7 = 9.
What is the result of 9 + 0 according to the identity property of addition?
Explanation
9 + 0 = 9.
Problem 3
According to the identity property of addition, adding zero to any number results in the number itself.
If a = 7 and b = 5, verify the commutative property for a + b.
Explanation
b + a = 5 + 7 = 12.
Problem 4
According to the commutative property, a + b = b + a. Therefore, 7 + 5 = 5 + 7 = 12.
Use the distributive property to expand 3(4 + 2).
Explanation
3(4 + 2) = 3×4 + 3×2 = 12 + 6 = 18.
The commutative property of addition states that the order of numbers does not affect the sum, i.e., a + b = b + a.
1.What is the associative property of addition?
2.What is the identity property of addition?
3.How does the distributive property relate to addition?
4.Can addition change the order of numbers without affecting the result?
5.How can children in United States use numbers in everyday life to understand Properties of Addition?
6.What are some fun ways kids in United States can practice Properties of Addition with numbers?
7.What role do numbers and Properties of Addition play in helping children in United States develop problem-solving skills?
8.How can families in United States create number-rich environments to improve Properties of Addition skills?
Common Mistakes and How to Avoid Them in Properties of Addition
Students tend to get confused when understanding the properties of addition, and they tend to make mistakes while solving problems with these properties. Here are some common mistakes the students tend to make and the solutions to these common mistakes.
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.
