If I multiply two negative numbers the result will be a positive one, why does it happen?

short answers for big questions

In order to understand this multiplication we have first to understand what’s the meaning of multiplying a positive number by a negative one. Let’s suppose that we have to pay a loan of 300 Euros every month. It means that every month the bank will change the balance of our bank account upon the value of `-300`. After 6 months how much money has been withdrawn from the bank to pay the loan? It is easy to answer. We just have to do the following: `6 xx -300 = -1800`. Let’s now suppose that one of our well off uncles has decided to pay us the loan during a year. How much will you gain if it happens? In this case we will forget about the fact that our account will have a discount of `-300` Euros every month during one year. So, we will have: `-12 xx -300 = 3600`. So, at the end of the year we will have saved 3600 Euros.

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I did not understand: could you give another example?

There are several examples and so it wouldn’t be difficult to give you a mathematical evidence concerning the concept that underlies the multiplication of two negative numbers. However, to avoid the use of formulas, I will show you another practical example. According to our vocabulary, the words “No” and “Never” often have a negative connotation. For instance: “Today you are not going to visit your cousin” is the opposite of saying “Today you are going to visit your cousin”. Let’s us suppose a sentence that includes these two negative words: “I do not want you to never visit your cousin”. This double negative can be seen as a request, meaning that you sometimes have to visit the mentioned relative, that is, the two negatives neutralize each other. In Mathematics something similar happens when we multiply two negative numbers and the result is appositive number!

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