Definition of Algebraic Subtraction
Miscellanea / / November 13, 2021
By Dra. Maria de Andrade, CMDF 21528, MSDS 55658., on Jul. 2015
The subtraction It is a mathematical operation in which a part is eliminated from a quantity, which is represented by two numbers or figures separated by the minus sign (-), it is also known as a difference. For the purposes of arithmetic the subtraction always implies a decrease, in the case of algebra it can mean decrease or increase which will depend on the signs of the numbers to be subtracted from each other.
This operation can be carried out with positive, negative numbers, integers, decimals, fractions or with more complex structures such as polynomials, vectors, imaginary numbers, among others, but always between like terms.
Subtraction properties
The substraction algebraic constitutes the inverse operation to the algebraic sum and its properties they are also inverse.
Property associative. Unlike addition, in subtraction if there is a difference in the final result if the order of the subtracted numbers changes, it is not the same to subtract 34 - 12 - 8 as 12 - 8 - 34.
Commutative property. If the order of the numbers is changed this will affect the sign of the final result of the operation.
Procedure for subtraction
Before carrying out this mathematical operation it is important define what is the number from which a certain amount is going to be subtracted, this is known as a minuend, as well as what is the amount that is going to be subtracted, which is called a subtrahend. Once this operation is carried out, the result is the subtraction or difference.
There are several methods to carry out this operation, however the most used is the method American in which the subtrahend is subtracted from the minuend in the sense from right to left, in the case that the minuend is less than the subtrahendo "borrows" the number to the left to continue doing the subtraction, the latter can be repeated every time necessary.
Effect of the signs on the result
The subtraction also obeys the rule of signs, so:
If the two numbers are positive: the subtrahend is subtracted from the minuend.
If the two numbers are negative: both numbers are added and a negative sign is placed on the result.
If one is negative and the other positive: We proceed to obtain the difference of the values absolute numbers of the numbers and the sign of the number with the highest absolute value is placed on the result.
Topics in Algebraic Subtraction