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What Is Associative Property? Explain With Examples

Referencing Styles : MLA | Pages : 1

The associative property helps in defining and stating that there can be addition as well as multiplication regardless of how the different numbers are being grouped. In the concept of mathematics, the associative property is related to some binary functions and operations.  In the formal manner, the binary operation * on the set of the S is known as associative if the same satisfies the associative law.

(x  y)  z = x  (y  z) for all x, y, z in S.

In the respective scenario, the symbol * has been used in order to replace the symbol of operation which can be any kind of symbol and even the absence of the symbol as for multiplication. In addition, the associative law can be expressed in the functional notion which is explained as follows:

= f (f (x, y), z) = f (x, f (y, z))

In the case of the associative law, it can be identified that associate means to join or connect with something. As per the associative property of addition, the sum of three or more numbers will be remaining the same regardless of how the different numbers are being grouped. In case of mathematics, associative property is the math rule which says that the ways in which the different factors are being grouped in the multiplication related problem does not change the product.

For instance- 5*4*2

In this aspect, the grouping should be done between 5 and 4 together and the step can be evaluated in a step by step process:

(5*4) *2

= 20 * 2

= 40

On the other hand, the grouping of 4 and 2 should be done in a manner which includes the following aspects:

5* (4*2)

= 5*8

= 40

From the respective example, it can be stated that in the associative property, there can be both addition or subtraction regardless of how the different numbers are being grouped. In the respective case, grouped means that while adding or multiplying, it does not matter where the parenthesis is being kept. It refers to the grouping of the different numbers or variables in algebra and there can be re-grouping of the number of variables and there can be arriving at the same answer. It is the mathematical aspects, the other terms such as subtraction and division are not associative in nature.

For instance- Both the approaches of the calculation can be taken into consideration which will be helpful for generating the similar results after addition. The other example which can be helpful for understanding the associative property is the combination of three ingredients which includes- cement, water and gravel. In such scenario, when the bag of cement in the bucket along with gravel and then adding water, the entire mixture will be fine. However, on the other hand, if the cement is being poured along with water, the gravel will not be mixed.

Furthermore, the associative property is essential and important in nature as it allows the different mathematicians to add as well as multiply the numbers with ease and the associative property can be used for multiplication and addition. In addition, the order of the different numbers should not be changed, on the contrary, the grouping should be changed. The associative property becomes essential as it allows the mathematician to add as well as multiply the different numbers with ease. In other words, the main aspect which should be maintained in the respective aspect is related to putting the parenthesis and adding of the parenthesis wherever it is liked is the other aspect which is being included in the respective aspect.

The word associative in the respective mathematics aspect is to join or combine and it can be explained with the help of the instance- Suppose an individual goes to the restaurant and buy ice cream of more than twelve dollars, bread for 8 dollars and milk for 15 dollars. In the respective scenario, the amount of money that has been owned to the cashier is associative property in mathematics term.

From the respective example, it can be identified that the overall calculation can be done in such a manner wherein the total can be calculated by me in my head through combining the price of milk and bread and then after totalling the same, the price of the ice-cream can be calculated. On the contrary, the price of the bread and ice-cream can be taken into consideration and after calculating those two, the milk can be calculated with the total of the two.

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