# What is equivalent fraction?

## What Does equivalent fraction Mean

In mathematics , the expression that refers to a division is called a fraction . The fraction 1/3, for example, implies that the number 1 is divided into 3 (or, in other words, 1 divided by 3). Two or more equivalent elements , as long as they are similar or equal .

To construct a mathematical fraction we need to have two components : a numerator and a denominator . In the previous paragraph, example 1/3 is mentioned , which we must read "one third"; in this case we have a numerator of value 1 and a denominator that is worth 3 . The meaning of such a pair is that we are in front of the third part of an integer, a quantity that to reach the other must be multiplied by three.

It is worth mentioning that the numerators and denominators must always be whole numbers with the exception of zero, that is, elements of the set that has the natural numbers from minus infinity to most infinity . Without delving into overly technical issues, it is enough to observe the concept of fraction to understand this rule: since in itself it expresses a ratio, and that the process of dividing its numerator by its denominator many times gives us a result with a comma, it would not be logical build it with decimal numbers .
To read a fraction it is necessary to know a special type of word : the numeral . When we write a number we have two options: use the appropriate figures according to the system used or write their names in words, and for this there are numerals.
The numerals are proper names to designate the numbers; in other words, they are nouns that serve to refer to them through the written or spoken language. There is more than one type of numeral, and the use of one or the other depends on the mathematical concept that we want to express in words. For example, cardinal numerals (also known by the name of common numerals ) are what we use every day to mention numbers when we need to count objects: one, two, three, and so on.
In the case of fractions, both the equivalents and any other, the cardinal numerals are used to refer to their numerator. On the other hand, there are fractional numerals , which are also known as partitive numerals , which serve to express the division of a whole into several parts: half, third, fourth, and so on. The denominator of a fraction is read using these terms.
The equivalent fractions , thus, are those which, although written differently, represent a same amount . 5/10 , 15/30 and 20/40 , to name a few, are equivalent fractions. Let's see a check that is obtained by dividing their numerators by their denominators:

5/10 = 0.5

15/30 = 0.5

20/40 = 0.5
It can be stated that these fractions ( 5/10 , 15/30 and 20/40 ) are equivalent fractions since all three indicate the same amount: 0.5 .
An easy way to find out if two or more fractions are equivalent is to multiply the numerator and denominator of each one by the same number. This process is known by the name of amplification .
Returning to the previous example, we can try the number 3 :
(5 x 3) / (10 x 3) = 15/30 = 0.5

(15 x 3) / (30 x 3) = 45/90 = 0.5

(20 x 3) / (40 x 3) = 60/120 = 0.5
The simplification is a similar process, but based on the division of the numerator and denominator by the same number. It is important to note that in order to complete this operation, the two terms must be divisible by the number in question. If the result is the same, then we are dealing with equivalent fractions. We can do the test with the previous examples and number 5 :
(5/5) / (10/5) = 1/2 = 0.5

(15/5) / (30/5) = 3/6 = 0.5

(20/5) / (40/5) = 4/8 = 0.5
La utilidad de las fracciones equivalentes reside en la posibilidad de hallar una versión más pequeña de otra, que nos vuelva menos complicado un determinado cálculo, por ejemplo. Por otro lado, reconocer dos o más fracciones equivalentes en una operación puede simplificarla si nos permite eliminarlas o asociarlas.

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