What is subtraction?

What Does subtraction Mean

The remainder , also known as subtraction is an operation consisting in pull, cut, dwarfing, reducing or removing some of all . Subtraction is one of the essential operations of mathematics and is considered the simplest together with addition , which is the inverse process.

Subtraction consists of the development of a decomposition : before a certain quantity, we must eliminate a part to obtain the result, which is called difference . For example: if I have nine pears and give three, I will keep six pears ( 9-3 = 6 ). In other words, I take three away from the number nine and the difference will be six. The first number is known as a minuend and the second as a subtrahend ; therefore: minuend - subtrahend = difference.

Subtracting is the inverse of adding: a + b = c , while c - b = a (3 + 6 = 9, 9 - 3 = 6). It is important to note that, in the framework provided by natural numbers , it is only possible to subtract two numbers as long as the first (minuend) is larger than the second (subtrahend). If this is not true, the difference (the result) that we will obtain will be a negative (unnatural) number: 5 - 4 = 1, 4 - 5 = -1 .
The ability to subtract two natural numbers and get a negative number makes it a subtraction operation slightly more complex than the sum where an operation with two positive numbers will never result in other negative.
Subtraction in advanced mathematics, therefore, does not consist in subtracting, but in carrying out an addition of the opposite number : the formula x - y is not used , but x + (-y) . In this case, -y is the element that is opposite y against the sum.
Sometimes the subtractions give less graphic results than in the arithmetic of popular knowledge, used to operate with units of currency or grams of food. When two vectors are subtracted, for example, they don't even have to lie on the same line. If we understand that each vector has an origin and an end, then the difference between the two will have its origin at the end of the minuend and end at the subtrahend.
In the case of fractions, the subtraction becomes more complicated, since it is generally not a direct operation and requires more abstraction . The simplest cases are those in which the second component, called the denominator , is the same in all the fractions that will participate in the subtraction; If we have, for example, 4/20 and we want to subtract 3/20 from it, we will not have to do anything other than subtract its numerators, in this case 4 and 3, to obtain the following result: 1/20, which reads a twentieth .

On the other hand, if we had the need to perform the 4/8 - 1/6 operation, we should add a step to obtain two compatible fractions, that is, with the same denominator. To do this, we will look for the least common multiple of 8 and 6, which in this case will not take much work; the number sought is 24, which is obtained with the 8 x 3 and 6 x 4 accounts. Before proceeding to the subtraction of the fractions, it is absolutely necessary to calculate the new numerators, those that in combination with the common denominator reflect the original proportions .
The formula for this adaptation is very simple: first we divide the common denominator by the original and multiply the result by the numerator. Using the first of the aforementioned fractions, the calculation would look like this: 4 * 24/8 = 12 (new numerator). Once we obtain both numerators, it is possible to do the subtraction as explained above, which will give us: 12/24 - 4/24 = 8/24, which reads eight twenty- fourths .

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