The word denominator is used in the field of mathematics to be able to name one of the parts that make up a fraction which indicates two different or equal numbers that are separated by a horizontal line and that can also be interpreted as different ways.
What is the denominator?
The denominator of a fraction is the part that is responsible for naming, in other words, it names or indicates the equal parts in which the unit has been divided.
- What is the denominator for
- Common denominator
- Sum of fractions
- Subtraction of fractions
In order to better understand the concept of denominator, it is important to understand where its etymological origin comes from . This word comes from the Latin language , from the word “denominator” which is translated into Spanish as “the smallest number or figure that makes up a fraction” . It is therefore defined as the part of the fraction indicated by the equal parts in which the unit can be defined.
What is the denominator for
The denominator is used to give a name in the fractions to those digits that indicate the equal parts in which the unit is divided. It is also used to indicate the parts into which rational numbers can be divided , which are those that are related to the terms “a” and “b”. Finally, sive to perform sums or subtract fractions with different denominators.
Among the main characteristics found in the denominator, the following are mentioned:
- It can never be zero .
- It is placed under the numerator and separated from it by a line as horizontally .
- It is considered as the divisor in the fraction .
- It is used in fractions .
The common denominator refers to the common number that exists between two or more fractions. This term then tells us that the numbers in the denominators are common or in other words, identical. It is used mainly to be able to perform addition and subtraction of fractions with greater ease and is used only when the denominators are equal.
It may be that sometimes the denominators are not equal , for this reason, the common denominator of all the fractions that make up a certain mathematical operation must be found. It can also be any of the multiples of the numbers located in the denominator.
Sum of fractions
The addition or addition of fractions is considered a basic operation in the field of mathematics and allows us to be able to combine two or more fractions into a number that is equivalent. Like a traditional addition, use the symbol + to represent the sum . In order to carry out this type of addition, it is important first to determine if the denominators of the fractions are the same or different.
Sum of fractions with the same denominator
This type of addition is known as the sum of homogeneous fractions and it is one of the simplest processes because, since its denominators are the same, only the numerators must be added, keeping the denominator the same. For instance:
1/4 + 2/4 = 3/4
Sum of fractions with different denominators
When the denominators are different, then a different procedure must be carried out, which is known as the sum of heterogeneous fractions . To do this, the least common multiple must first be obtained in order to simplify the equations.
The least common multiple is the smallest number that is also a multiple of two or more numbers. Then, two different methods can be applied to do the addition. The first is a direct method and can be solved in two different ways:
- Method number 1 or method of dividing the denominators by the numerators. It consists of finding the common denominator of the fractions to be added by multiplying the denominators of the fractions.
- Method number 2 or cross multiplication method which is based on finding the common denominator of the fractions to be added and then proceeding to multiply the denominators that the fractions have.
Subtraction of fractions
The subtraction of fractions can occur in two different situations, the first one when the fractions have the same denominator and the second one, when the fractions have a different denominator . When they have the same denominator, the procedure is very simple since only the numerators must be subtracted, keeping the common denominator the same .
When the subtraction is given in fractions that have a different denominator , you must first multiply the numerator of the first fraction by the denominator of the second fraction and then the denominator of the first by the numerator of the second fraction. Then both amounts are subtracted . The next step is to multiply the denominators of the fractions, solve the operations and obtain the result.
Some examples of addition and subtraction in which the denominator can be observed are the following:
- 5/3 – 4/3 = 1/3 In this case the denominator corresponds to the number 3
- 5/8 – 2/8 = 3/8 In this case the denominator corresponds to the number 8