equivalent fractions they are fractions which represent the same amount. To better understand this definition and the methods that can be used to find equivalent fractions, it is necessary to remember some definitions involving fractions and detailing the definition of equivalent fractions.
fractions
One fraction it is a rational number and represents parts of objects that have been divided in installmentsequals. Fractions are represented by reasons: the dividend is called the numerator and the divisor is called the denominator. For a reason to really be a fraction, numerator and denominator must be whole numbers. Example:
1
4
In this fraction, 1 is the numerator and 4 the denominator.
Every fraction represents a reason, therefore, every fraction can be written as a decimal number. Dividing 1 by 4 into the fraction above, we find 0.25. Soon:
1 = 0,25
4
So, this fraction can be understood as follows: an object was Divided in four partsequals and one of these parts is under analysis, is in use, etc.
The fraction above can represent the following situation: a piece of pie that has been divided into four equal parts. O decimal can be turned into a percentage by being multiplied by 100. Thus, it can be said that a piece of a pie that has been divided into four equal parts equals 0.25·100 = 25% of the pie.
equivalent fractions
Suppose individual A gets 25% of a pie. Knowing that this pie was divided in four partsequals, we can say that this individual received one of the four pieces of pie, as the fraction representing 25% is:
1 = 0,25
4
However, if this same pie had been divided into eight equal pieces, we should find the x number of pieces that individual A received so that:
x = 0,25
8
To find x, notice that 8 = 2·4. So we can assume that x will be equal to 2·1. To be sure, just divide 2 by 8. The result will actually be 0.25:
2·1 = 2 = 0,25
2·4 8
This ensures that the 2 octaves and 1 quart fractions represent the same numberdecimal, therefore, these fractions are called equivalents. As such, we also introduce a method that can be used to find fractionsequivalents.
In short, equivalent fractions are all those that represent the same decimal number.
Methods for finding equivalent fractions
There are two ways you can find fractionsequivalents. The first is to multiply the numerator and denominator of fractions by the same number, as was done in the previous example.
It is important to note that, given a fraction, the number of fractions equivalent to it is infinite, as the numbers chosen for multiply your numerator and denominator are also infinite.
For example, some of the fractions equivalent to one third are:
1 = 2 = 3 = 4 …
3 6 9 12
Note that the second fraction is a product of the numerator and denominator of the first by 2, the third is a product of the same elements as the first by 3, and so on.
The second way you can find fractionsequivalents is analogous to the first, but using divisions instead of multiplications. It is evident that at some point, in this second process, it will no longer be possible to carry out divisions. The fraction obtained when this happens is called the irreducible fraction.
Example:
20:2 = 10
40:2 = 20
Therefore, the fraction 20 fortyths is equivalent to the fraction 10 twenties.
It is also possible to determine the equivalencein betweenfractions dividing numerator by denominator. Those that have the same result are equivalent.
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-sao-fracoes-equivalentes.htm