In the field of math, is called fraction to the expression that refers to a division. 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 items equivalents, meanwhile, are similar or equal.
To construct a mathematical fraction we need to have two components: a numerator and a denominator. The example above is mentioned 1/3, which we must read “a third”; in this case we have a numerator of value 1 and a denominator that is 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 should be mentioned that the numerators and denominators must always be integer numbers except for zero, that is, elements of the set that has the natural numbers from the minus infinity until the more infinite. 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 numbers decimals.
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, the numerals cardinal (also known by the name of common numerals) are the ones 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 equivalent and any other, the cardinal numerals are used to refer to their numerator. On the other hand are the fractional numerals, which are also known as partitive numerals, which serve to express the division of a whole in several parts: middle, third, fourth, and so on. The denominator of a fraction is read using these terms.
The equivalent fractionsIn this way, they are those that, although written differently, represent a same amount. 5/10, 15/30 Y 20/40To cite a few cases, they 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 Y 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. East process It is known by the name of amplification.
Returning to the previous example, we can try with 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 It is a similar process, although based on the division of the numerator and the 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 the 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
The usefulness of equivalent fractions lies in the possibility of finding a smaller version of another, which makes a certain calculation less complicated, for example. On the other hand, recognizing two or more equivalent fractions in a operation You can simplify it by allowing us to remove or associate them.