Fractions are representations of parts of a whole. Both in mathematics and in life, when we talk about equivalence, we are talking about equality between two objects, two elements.
Equivalent fractions are fractions written in different ways, yet representing the same part of a whole, that is, they are equal fractions, but represented in different ways.
See the following situation.
“Pedrinho bought a candy bar, so his friend Lucas asked him to divide it in half and each one would eat ½ of the candy bar. Pedrinho replied that he would divide the chocolate into four parts and each would eat 2 pieces. So Lucas agreed, saying they would eat the same amount of chocolate.”
Was Lucas right that they would eat the same amount of chocolate? For Lucas' initial proposal was to divide the chocolate half and half.
There is only one way to explain this, using equivalent fractions.
Let's make the representation of the division proposed by Lucas.
See that the amount of chocolate is the same, just changed the way to distribute the chocolate.
But making representations like this whenever it was necessary to find equivalent fractions would become tiresome and unnecessary, as there is a less laborious way to find equivalent fractions, using only the operation of the multiplication.
Note that the method for finding the equivalent fraction does not determine which number this is, it is up to you which number to use. The only restriction is: the number by which the numerator is multiplied must also be multiplied by the denominator. Let's see in the case of Pedrinho.
The original fraction was 1/2.
We find the 2/4 fraction equivalent to it. Note that the numerator and denominator were multiplied by two.
Let's multiply the numerator and denominator by three:
See that you can get several fractions equivalent to fraction 1/2, just go testing the multiplication with different numbers.
By Gabriel Alessasndro de Oliveira
Graduated in Mathematics
Take the opportunity to check out our video lesson on the subject:
