PROPERTIES OF ADDITION: EXAMPLES AND EXERCISES - CULTURE VOCABULARY - 2025

The properties of addition or addition are the commutative property, the associative property, and the additive identity property. Addition is the operation in which two or more numbers are added, called addends and the result is called addition. The set of natural numbers (N) begins, ranging from one (1) to infinity. They are denoted with a positive sign (+).

When the number zero (0) is included, it is taken as a reference to demarcate the positive (+) and negative (-) numbers. These numbers are part of the set of integers (Z), which ranges from negative infinity to positive infinity.

The operation of the addition in Z, consists of adding positive and negative numbers. This is called algebraic addition, as it is the combination of addition and subtraction. The latter consists of subtracting the minuend with the subtrahend, resulting in the remainder.

In the case of the numbers N, the minuend must be greater than and equal to the subtrahend, obtaining results that can go from zero (0) to infinity. The result of the algebraic sum can be negative or positive.

What are the properties of the sum?

1- Commutative property

It is applied when there are 2 or more addends to be added without specific order, the result of the sum does not always matter. It is also known as commutativity.

2- Associative property

It is applied when there are 3 or more addends, which can be associated in different ways, but the result must give equal in both members of the equality. It is also called associativity.

3- Additive identity property

It consists of adding zero (0) to a number x in both members of the equality, giving the sum as the result the number x.

Examples

Exercises on the properties of addition

Exercise N ° 1

Apply the commutative and associative properties for the detailed example:

Resolution

There are the numbers 2, 1 and 3 in both members of the equality, represented in the yellow, green and blue boxes respectively. The figure represents the application of the commutative property, the order of the addends does not alter the result of the addition:

• 1 + 2 + 3 = 2 + 3 + 1
• 6 = 6

Taking the numbers 2, 1 and 3 of the illustration, associativity can be applied in both members of the equality, obtaining the same result:

• (3 + 1) + 2 = 1 + (3 + 2)
• 6 = 6

Exercise N ° 2

Identify the number and the property that applies in the following statements:

• 32 + _____ = 32 __________________
• 45 + 28 = 28 + _____ __________________
• (15 + _____) + 24 = 39 + (24 + 15) _________________
• (_____ + 49) - 50 = 49 + (35 - 50) __________________

Answers

• The corresponding number is 0 and the property is the additive identity.
• The number is 45 and the property is the commutative one.
• The number is 39 and the property is associative.
• The number is 35 and the property is associative.

Exercise N ° 3

Complete the corresponding answer in the following statements.

• The property in which the addition is made regardless of the order of the addends is called _____________.
• _______________ is the property of addition in which any two or more addends are grouped, in both members of the equality.
• ________________ is the property of addition in which the null element is added to a number in both sides of the equality.

Exercise N ° 4

There are 39 people to work in 3 work teams. Applying the associative property, reason what 2 options would be.

In the first member of the equality, the 3 work teams can be placed in 13, 12 and 14 people respectively. The addends 12 and 14 are associated.

In the second member of the equality, the 3 work teams can be placed in 15, 13 and 11 people respectively. The addends 15 and 13 are associated.

The associative property is applied, obtaining the same result in both members of equality:

• 13 + (12 +14) = (15 + 13) + 14
• 39 = 39

Exercise N ° 5

In a bank, there are 3 lockers that serve 165 clients in groups of 65, 48 and 52 people respectively, to make deposits and withdrawals. Apply the commutative property.

In the first member of the equality, the addends 65, 48 and 52 are placed for lockers 1, 2 and 3.

In the second member of the equality, add the addends 48, 52 and 65 for lockers 1, 2, and 3.

The commutative property is applied since the order of the addends in both members of equality does not affect the result of the sum:

• 65 + 48 + 52 = 48 + 52 + 65
• 166 = 166

Addition is a fundamental operation that can be explained with multiple examples from everyday life through its properties.

In the field of education, it is recommended to use everyday examples so that students can better understand the concepts of fundamental basic operations.

References

1. Weaver, A. (2012). Arithmetic: A Textbook for Math 01. New York, Bronx Community College.
2. Practical Approaches to Developing Mental Maths Strategies for Addition and Subtraction, Professional Development Services for Teachers. Recovered from: pdst.ie.
3. Properties of Addition and Multiplication. Recovered from: gocruisers.org.
4. Properties of Addition and Substraction. Recovered from: eduplace.com.
5. Mathematic Properties. Recovered from: walnuthillseagles.com.