Subtraction
Subtraction is a fundamental mathematical operation represented by the minus sign (–) and involves deducting one quantity from another. It comprises two key components: the minuend, which is the number being subtracted from, and the subtrahend, the number being taken away. The result of this operation is known as the difference. Subtraction is essential in various everyday contexts, from managing finances to cooking, as it helps determine quantities remaining after an amount has been taken away.
The operation can be performed using multiple methods, including traditional techniques such as long subtraction and modern approaches like using calculators. Subtraction is unique in that it is neither commutative nor associative, meaning that the order of numbers affects the outcome. When subtracting larger numbers, specific strategies such as regrouping, or borrowing, may be necessary, especially when dealing with multi-digit numbers or decimals. Overall, subtraction serves as a critical tool in both basic arithmetic and complex mathematical calculations, helping individuals understand and manipulate quantities effectively.
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Subtraction
This mathematical operation is represented by the minus sign (–) and can be broken down into two parts, namely the minuend (the number from which a specific amount is taken) and subtrahend (the amount to be deducted). The resulting operation is referred to as the difference. Subtraction can be achieved by different methods ranging from abacus to computer utilization.
Generally speaking, subtraction refers to the deduction of specific objects from a collection. For instance, if you and a friend have three chocolate bars, and you both decide to share one of these bars after lunch, there will still be two bars left for later. This is an example of a simple subtraction operation done over integers. However, subtraction can be more complex, especially when subtracting from numbers with more than one digit.
Subtraction is a mathematical operation that is commonly used. Whether it is used to calculate the end-of-the-month disposable income after paying the bills or to determine the leftover number of eggs after baking a cake, subtraction is part of everyone’s daily routine.
Overview
Subtraction is expressed as
, where
is the minuend,
is the subtrahend, and
is the difference. Regarding its properties, subtraction is neither commutative, that is,
; nor associative, that is
; and it holds true for the zero property, that is,
.
This mathematical operation can be seen from different perspectives, namely number and operation. Regarding the number perspective, subtraction can be done by several methods. The minuend and subtrahend can be split to facilitate subtraction. In stringing, only the subtrahend is decomposed. Alternatively, varying (minuend and/or subtrahend are changed) allows easy subtraction.
Direct subtraction is simply deducting the subtrahend from the minuend, but another method is also used in which the subtrahend is added to until minuend is found. This method is called indirect addition. Indirect subtraction (deducting from minuend until the subtrahend is found) is a third method.
The simplest way of carrying out a subtraction of whole numbers is aligning the digits of the minuend and subtrahend, and performing the deduction for each respective column. When a digit of the subtrahend is greater than the digit of the minuend in the same column (for example, 32 – 15), subtraction takes place with borrowing, as shown in Figure 1.
In the ones column, because 5 > 2, the minuend 2 must borrow 1 ten from minuend 3. This process is referred to as regrouping. Thus, with the new minuend in the ones column, 12 – 5 = 7, and on the tens column, 2 – 1 = 1. This same approach is used to subtract decimals, such as 2.3, where the only requirement is to align numbers on their decimal points.
Bibliography
Caron, Lucille, and Philip M. St Jacques. Addition and Subtraction Smarts! New York: Enslow, 2011.
Peltenburg, Marjolijn, Marja van den Heuvel-Panhuizen, and Alexander Robitzsch. "Special Education Students’ Use of Indirect Addition in Solving Subtraction Problems up to 100—A Proof of the Didactical Potential of an Ignored Procedure." Educational Studies in Mathematics 79.3 (2012): 351-369.
Torbeyns, Joke, et al. "Solving Subtraction Problems by Means of Indirect Addition." Mathematical Thinking and Learning 11.1-2 (2009): 79-91.
Tussy, Alan, and Diane Koenig. Basic Mathematics for College Students with Early Integers. Cengage, 2014.
Wingard-Nelson, Rebecca. Subtraction and Addition: It's Easy. New York: Enslow, 2014.