Adding Numbers Correctly Using 4 Critical Properties of Addition

The phrase “addition” refers to combining two or more values to form a new object. This is supposed to be the total of the numbers. In math, options and their qualities involve proposing multiple ways to add a given assortment of numbers, which is finished by utilising key properties of addition. Everybody uses expansion in their regular routines, and in light of its significance, you will become familiar with the characteristics and standards of expansion by means of models. Let us get started.

What You Should Know About Addition

Adding or summing together two or more numbers to obtain the final result is known as an addition. In the domains of mathematics and statistics, adding is a very significant and common operation. The addition is denoted by the plus (+) symbol. Addends are the numbers that need to be added together. The total is the value obtained as a consequence of this summing step. It is possible to add and sum any digit with any number of units. Regardless of its sign, any integer type may be simplified using addition, from fractional integers to decimal values. Let us now look at the four most basic properties of addition.

The four properties are listed below and explained:

  1. Commutative Property
  2. Association Property
  3. Distribution Property
  4. Additive Identity Property

These properties will help us distinguish the numerous necessities and norms that should be clung to while adding an assortment of numbers. The four qualities of the option recorded above give a very end to adding objects. Significantly, increase, deduction, and division have their numerical provisions. Each kind of activity has its arrangement of rules. We should examine every property in more profundity.

Commutative Property 

This characteristic states that when two numbers or integers are added, the sum remains the same regardless of the sequence in which the numbers/integers are added. In the case of multiplication, this property also applies. It can be expressed with the help of the following example given below:

B + A = A + B


Let’s say A is ten and B is five.

5 + 10 = 10 + 5

15 = 15

As you can see in the example above, when we add the two numbers, 10 and 5, and then swap the two numbers, the result is still 15. As a result, addition obeys the commutative rule. The word “commute” is an excellent way to recall this characteristic. It entails switching between two locations.

Association Property 

When we add three numbers, this property or law states that adding numbers in a different pattern does not affect the outcome. It indicates that when three or more numbers are added together, the total/sum remains the same, even if the order of the addends is modified. This characteristic may be expressed as A (B + C) Equals (A + B) C.


Let us take A = 3, B = 4 and C = 5

L.H.S =A (B + C) = 3 (4 + 5) = 12

R.H.S = (A + B) C = (3 + 4) 5 =12

The left-hand side is equivalent to the right-hand side, as you can find in the model above. Therefore, the cooperative property is set up. This trademark applies to augmentation also. The bracket is utilised to sort out the addends in this property. It makes activities using a bunch of whole numbers. The expression “partner” is an excellent way of recalling the cooperative component since it implies “to connect with a gathering of people.”

Distribution Property 

This attribute is not the same as the Commutative or Associative properties. In this example, the total of two numbers multiplied by the third number equals the sum multiplied by the third number.

D (E + F) is equal to D * E + D * F

The monomial factor is D, while the binomial factor is (E + F).


Let’s say D = 1, E = 3, and F = 5.

L.H.S =D * (E + F)= 1 * (3 + 5) = 1 * 8 = 6

R.H.S = D * E + D * F = 1 * 3 + 1 * 5 =3 + 3 =8

L.H.S = R.H.S

8 = 8

Regardless of whether we have appropriated A (monomial factor) to each worth of the binomial factor, B and C, the worth stays something very similar on the two sides in the model above. The distributive property is fundamental since it joins both the expansion and augmentation activities.

Additive Identity Property 

The attributes of this property say that there is an exceptional, genuine number for each number which, when added to the number, yields the actual number. Zero is a stand-out genuine number that is added to a number to make the number. Subsequently, zero is alluded to as the character component of expansion. Allow us to check out a model given beneath:

B + 0 = B or 0 + B = B

For instance, 2 + 0 = 2 (or) 0 + 2 = 2

The character nature of the expansion is handily reviewed by mulling over everything and posing and addressing inquiries. It shows that we should consider which number should be added to the provided number to protect the first number’s worth. If you accept that, your reaction ought to be zero. Thus, the expansion activity’s character component is zero.


The method involved with adding at least two numbers to get an eventual outcome is known as an option. This is instructed to understudies in grade school and is frequently considered the foundation of any remaining numerical ideas. It is utilised in different everyday issues also. Be it charging clients, tackling complex numerical conditions, maintaining a business or some other fundamental work, expansion is constantly used.

Commutative, affiliated, distributive, and added substance characters are the four primary components of option. They have been clarified in an exceptionally escalated and illustrative way above. The term commutative alludes to how the result of expansion stays as before, paying little heed to the request. The related property expresses that the request wherein three numerals are added makes little difference to the eventual outcome. Suppose the second and third numbers are increased and added by the first. In that case, the distributive property expresses that adding two numbers and duplicating with a third number will bring about consistent arrangements. Added substance personality says that each number increased by 0 delivers a similar number. Since you thoroughly understand expansion and its properties, continue learning and perusing to accumulate more information.

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