What does the order of the factors mean?

Initially, it is known that multiplication is a way to perform large sums in an easy and efficient way. Now, in mathematics, this operation consists of a composition that requires repeatedly adding a number according to the number of times indicated by another. In addition; multiplication is a system that consists of folding or unfolding the quantity or number of a thing several times. 

It is important to highlight; multiplication is constantly used in activities of daily life to process data and balances at the moment: when we make an acquisition of a product and we need to know how much we spend when buying three (3) items of the same price, to make purchases in the supermarket, including the professional form in business and research. 

Within this framework of ideas; M. Morris. (2003) defines "Multiplication as a binary operation between factors, in which the number that is multiplied is called a multiplicand, the number by which it is multiplied is called a multiplier, and the resulting number is called a product," (p .317). 

According to the author, it ultimately consists of taking the multiplicand and adding it as many times as the multiplier contains units; Thus, operating 7 x 3 = 21 (seven multiplied by three equals twenty-one), where 7 is the multiplicand, 3 is the multiplier and 21 is the product, it is observed that (7 x 3 = 7 + 7 + 7 = 21). 

On the other hand, exchanging the order of the factors as 3 x 7 = 21 (three times seven equals twenty-one) implies that 3 is the multiplicand, 7 the multiplier and 21 is still the product, then (3 x 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21). It is evident that the product does not change, but the idea regarding the order of the factors should not be maintained, since according to their position they acquire different meanings. 

Dear reader, based on the above, we present the following. 

CHALLENGE: Buba Burger, is a fast food stand, located in the Simón Bolívar Guanare Venezuela urbanization, main entrance of the Orlando Gil Casadiego School, where Burgers are sold, under multiplicative codes. So, an order with Code: 2x4 (it means to distribute 8 Burgers equally among 4 clients). Argue numerically, if there is a difference or not between 3x5 and 5x3 codes based on the exposed definitions?

Participate by sending the solution step by step correctly to the email: juancarlosdorante@gmail.com, if you are interested in making an economic contribution for the research, you can do so in the following digital accounts:

PAYEER wallet: P1006219399 or 1006219399

AIRTM email: juancarlosdorante@gmail.com or juan84400c95

Prepared by: Graduate. Juan Carlos Dorante (Magister).