Subtraction of fractions is a mathematical operation.
A fraction subtraction is a mathematical operation . To understand the concept, it is necessary to first focus on several terms .
The term subtraction usually refers to the operation that consists of subtracting . This verb, in turn, refers to reducing, shrinking or separating a part from a whole . If we focus on mathematics, subtracting consists of finding the difference that exists between two expressions or quantities.
In this way we can talk about different types of subtraction, such as algebraic subtraction , polynomial subtraction , vector subtraction and matrix subtraction . In this case, as we already indicated, we are going to focus on the subtraction of fractions.
Development of subtraction of fractions
To understand this operation, we must know that, in mathematics, a fraction is an expression that reveals a division . In other words, it is a quantity that is divided by another quantity.
A fraction is made up of two numbers : the upper one is called the numerator , while the lower one is called the denominator . The way to develop a fraction subtraction will depend on whether both fractions have the same denominator or not.
When fractions have the same denominator , we simply subtract the numerators as in any algebraic subtraction and keep the denominator. For example:
7/2 – 4/2 = (7 – 4)/2 = 3/2
If the denominators are different, we must first equalize them by finding the common denominator . To do this we can multiply each fraction by the denominator of the other:
9/7 – 2/3
(9 x 3) / (7 x 3) – (2 x 7) / (3 x 7)
27/21 – 14/21
Once we find a common denominator, we proceed to subtract as explained in the previous example:
(27 – 14)/21 = 13/21
Subtracting fractions can have different complexities.
Learning
Students in the early childhood stage, before entering secondary school, begin to learn to add and subtract fractions , since these mathematical operations are basic and fundamental when it comes to expanding their knowledge in this subject.
Specifically, they begin by doing problems with two fractions and then, to reinforce what they have learned, they proceed to do the same operation but with three or more. In this case, the procedure is similar. Thus, if they share a denominator, everything is much simpler because they will only have to proceed to subtract the numerators.
If what happens is that they have a different denominator, then you will have to follow the previously mentioned process of finding what the least common multiple is and from this, once it has been achieved, develop what would be the subtraction with the numerators.
Other operations beyond the subtraction of fractions
Addition and subtraction are the simplest operations to carry out with the aforementioned fractions. However, it should not be overlooked that multiplication and division can also be performed. In the first case, what must be done is to multiply the numerators on one side and the denominators on the other. Example: 3/2 x 5/4 = (3 x 5) / (2 x 4) = 15/8
In the second case, when dividing two fractions, what you have to do is multiply the numerator of one fraction by the denominator of the other to obtain the final numerator and multiply the denominator of the first fraction by the numerator of the second to obtain the final denominator. Example: 3/2 : 5/4 = (3 x 4) : (2 x 5) = 12/10 .