119 LearnersLast updated on July 5th, 2025
Properties of Addition
When adding two or more integers, we follow a certain set of rules known as the properties of addition. These properties help solve algebraic expressions, fractions, decimals, and integers easily. In this topic, we will learn about the properties of addition in detail.
What is Addition?
One of the basic arithmetic operations is addition, where we combine two or more numbers to determine their sum. This arithmetic operation is represented using the symbol “+”. Addition is used to calculate the total cost of products, expenses, or measurements. For example:
- 3 + 6 = 9
- 10 + 4 = 14
What are the Properties of Addition?
The properties of addition are a set of rules that tell us how numbers can be added to find their sum. Below are the main properties of addition used in mathematics:
Commutative Property:
The commutative property states that changing the order of numbers does not change the sum.
Example: 3 + 7 = 7 + 3 = 10
Associative Property:
In the associative property, the grouping of numbers does not change the sum.
For example, (5 + 2) + 1 = 5 + (2 + 1) = 8
Identity Property:
The identity property is the addition of zero to any number, keeping the result unchanged. Example: 8 + 0 = 8
Distributive Property:
The distributive property states that multiplying a number by a sum is equal to multiplying each term separately and then adding the results.
Example: 3 × (2 + 6) = (3 × 2) + (3 × 6) = 6 + 18 = 24
Real-Life Applications of Properties of Addition
The properties of addition play a significant role in our everyday tasks. The set of rules, when adding numbers, helps you solve problems efficiently. Here are a few real-life examples you might not have explored:
- We apply the commutative property to add the expenses in any order to get the total.
- When purchasing multiple items, the distributive property is used for quicker total cost calculations.
- The property is helpful in financial contexts, such as when repaying debts, the amount owed and the payment cancel each other.
Common Mistakes and How to Avoid Them in Properties of Addition
Students often make mistakes when working with the properties of addition. Given below are a few common mistakes and the solutions to overcome them:
Mistake 1
Not Understanding the Identity Property
Some students mistakenly believe that adding zero to any number changes its value.
Remember that the identity property means that when zero is added to any number, the value stays the same.
For example: 4 + 0 = 4
Mistake 2
Forgetting the Parentheses
It is common for students to ignore parentheses in the associative property, which can be confusing.
Use parentheses or brackets correctly to avoid inaccuracy in the result. First, find the sum of the numbers inside the parentheses. For example: (2 + 1) + 3 = 2 + (1 + 3)
Mistake 3
Understanding the Inverse Property of Addition Incorrectly
Students often forget that the additive inverse of a number is the value that, when added to it, results in zero.
To understand the concept easily, take any number and add its opposite; the result will always be zero.
For example: 8 + (- 8) = 0
Mistake 4
Mixing Up Commutative and Associative Properties
Some students assume that the commutative property changes the grouping and that the associative property is related to the order.
In the commutative property, the order of numbers is changed, and the grouping remains the same. Example: 8+ 3 = 3 + 8. In the associative property, the grouping changes, but the order remains unchanged. Example: (1 + 2) + 3 = 1 + (2 + 3)
Mistake 5
Using Distributive Property Incorrectly
In some cases, students might forget to distribute the number to all terms inside the parentheses.
Ensure that you first multiply the number by each term inside the parentheses before adding. Example: 5 × (2 + 3) = (5 × 2) + (5 × 3) = 10 + 15 = 25
Solved Examples of Properties of Addition
Problem 1
Verify the associative property for (4 + 5) + 3 and 4 + (5 + 3).
Since both sides are equal, the associative property is verified.
Explanation
We use the associative formula:
(a + b) + c = a + (b + c)
Then, substitute the values:
(4 + 5) + 3 and 4 + (5 + 3)
Solve the LHS:
(4 + 5) + 3 = 9 + 3 = 12
Similarly, solve the RHS:
4 + (5 + 3) = 4 + 8 = 12
Comparing both sides:
(4 + 5) + 3 = 4 + (5 + 3)
12 = 12
Here, as both sides are equal, the associative property is verified.
Problem 2
Verify the inverse property for 11+ (-11).
The inverse property is verified because – 11 and 11 are additive inverses of each other.
Explanation
The sum of any number and its additive inverse always results in zero
a + (–a) = 0
Substitute the given values:
11 + (– 11) = 0
The inverse property is verified because – 11 and 11 are additive inverses of each other.
Problem 3
Verify the identity property for 55 + 0.
We have the formula:
a + 0 = a
Add the given numbers:
55 + 0 = 55
Since the sum we get is the same, we conclude that the identity property is verified.
Explanation
the sum we get is the same, we conclude that the identity property is verified.
Problem 4
Find the sum of 30 + 8 applying the commutative property.
both give the same result, so the commutative property is verified.
Explanation
We first write the given expression:
30 + 8 = 38
Then, swap the order of numbers:
8 + 30 = 38
Add the numbers in both ways:
30 + 8 = 38, 8 + 30 = 38
Here, both give the same result, so the commutative property is verified.
Problem 5
Verify the distributive property for 2 × (8 + 3).
22=22
Explanation
Use the distributive formula:
a × (b + c) = a × b + a × c
Given:
2 × (8 + 3)
We first solve the LHS:
2 × (8 + 3) = 2 × 11 = 22
Then, solve the RHS using distribution:
(2 × 8) + (2 × 3)
Now, multiply each term separately:
16 + 6 = 22
Here, we compare both sides:
2 × (8 + 3) = (2 × 8) + (2 × 3)
22 = 22
FAQs on Properties of Addition
1.What are the different properties of addition?
2.What is the significance of the properties of addition in math?
3.Can we apply the associative property to more than three numbers?
4.Give an example of the inverse property of addition.
5.Does the commutative property work for subtraction?
6.How can children in Philippines use numbers in everyday life to understand Properties of Addition ?
7.What are some fun ways kids in Philippines can practice Properties of Addition with numbers?
8.What role do numbers and Properties of Addition play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Properties of Addition skills?
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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.
