**What are the properties of addition?**

The **addition properties** or addition are the commutative property, the associative property, and the additive property of identity. Addition is the operation in which two or more numbers are added, called addends, and the result is called a sum.

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

In the case of 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 addition can be negative or positive.

**Addition Properties**

**1. Commutative property**

It is applied when there are 2 or more addends to be added without a specific order, the result of the addition 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 be the same in both members of the equality. It is also called associativity.

**3. Property of additive identity or neutral element**

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

**examples**

**Exercises on the properties of addition**

**Exercise #1**

Apply the Commutative and Associative Properties for the numbers listed:

1 2 3 = 1 2 3

**Resolution**

We have the numbers 2, 1 and 3 in both members of the equality. 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, the associativity can be applied to both members of the equality, obtaining the same result:

– (3 + 1) + 2 = 1 + (3 + 2)

– 6 = 6

**Exercise No. 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 commutative.

– The number is 39 and the property is associative.

– The number is 35 and the property is the associative one.

**Exercise No. 3**

Complete the corresponding answer in the following statements.

– The property in which 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 addition property in which the null element is added to a number on both sides of the equality.

**Exercise No. 4**

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

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

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

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

– 13 + (12 + 14) = (15 + 13) + 14

–39 = 39

**Exercise No. 5**

In a bank, there are 3 ticket offices 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, addends 65, 48 and 52 are placed for lockers 1, 2 and 3.

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

The commutative property applies, since the order of the addends in both members of the equality does not affect the result of the addition:

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

**References**

Properties of Addition and Multiplication. Retrieved from gocruisers.org.

Properties of Addition and Subtraction. Retrieved from eduplace.com.