Subtraction of decimal numbers

Perhaps the most recommendable thing, before advancing in an explanation on the correct way in which all operation of subtraction of decimal numbers must be solved, is to revise some concepts that will allow to understand this operation within its just mathematical context.


Fundamental definitions

In this sense, it may also be convenient to delimit this conceptual revision to two specific notions: Decimal numbers and the Subtraction because they are the types of numbers and the operation directly related to this operation. Next, each one of them:

Decimal numbers

In this way, we will begin by saying that the Decimal Numbers have been defined by Mathematics as a type of number, composed of two parts, which are united -and at the same time separated- by the symbol of the comma, and can be explained in turn in the following way:

Known as Units, this part will be constituted by integers, elements that will be arranged in the comma to the left. In this part, because they are numbers of the decimal system, each element will have a positional value, being able to find in them the units, tens, hundreds, units of a thousand, tens of a thousand, etc.

The second part of the decimal Numbers will be the incomplete Units, conformed always by a number smaller than the unit, and always between 0 and 1. In this segment of the decimal numbers it will also be possible to speak of the positional value of its elements, being then -from left to right, and after the comma- the tens, hundreds, thousandths, ten thousandths, etc.

The subtraction

In another order of ideas, it will also be necessary to throw lights on the definition of Subtraction, which can be understood as the operation, whose objective is to suppress in a number – which acts as a minuende – the amount specified by the second number involved, which receives the name of subtracting.

Subtraction of decimal numbers

Once each of these definitions has been reviewed, it may be much simpler to address the definition of Decimal Number Subtraction, which will basically be conceived as the operation of subtraction between two decimal numbers.

Also, Mathematics has enumerated the series of steps that must be followed at the time of carrying out this operation, and that must be developed in the following order:

  • In the first place, the decimal numbers between which the subtraction will be carried out must be arranged, which cannot be more than two, and will be placed in the form of a column, verifying that always the decimal number with the highest value is over the lowest number. It should also be verified that each element of a number coincides with the positional pair that exists in the second number.
  • Likewise, verify that the two decimal numbers involved in the subtraction operation have the same number of decimal places. If some of them are missing at their ends, it will be completed with zeros. For example, if you had to subtract 311,988 and 23,9 you would have to arrange the factors of the operation in the following way:

Once this is done, we will then proceed to subtract each of the elements that coincide by their position in each column. In general, the upper elements should be larger than the lower ones. If the opposite is the case, then the upper number should borrow a unit from the element it has immediately to the left, to increase its value and suppress in it the amount indicated by the lower element. As for the element that lends the unit, it begins to be counted as one unit less:

Once it has been verified that the difference obtained coincides fully as for the number of its elements with those that had the minuendo and the subtracting, the operation is assumed resolved.

If we want to check if the correct result has been obtained, it will be necessary to add the difference obtained with some of the two elements that participated in the operation, whether it is the minuende or the subtracting.

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Subtraction of decimal numbers
Source: Education  
October 29, 2019


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