Think of puzzle games: each and every game of this type is made up of several pieces that make up a whole number, right? In mathematics, we see the concept of a fraction: a part of a whole that can be represented geometrically or numerically.
We can divide the whole into several parts that will represent different quantities and others that will represent the same quantity. Different fractions that represent the same amount are called "equivalent fractions."
In this way, equivalent fractions are those written in different ways, but that represent the same part of a whole. For example, the following fractions are equivalent.
How to find equivalent fractions?
There is a very practical way to find equivalent fractions, using only the multiplication operation.
To find equivalent fractions, we must multiply the numerator and denominator by the same natural, nonzero number.
Pay close attention to the following example:
Example: Get fractions equivalent to the fraction.
To solve what was asked in this example, we will do what the theory tells us: we will multiply the numerator and denominator by the same natural number, which is different from zero.
Therefore, we will have the following:
Pay attention to the following: the method for finding the equivalent fraction does not determine the number you should use, you can choose, as long as this number is natural and not zero. Although you can choose which number to use, you must respect the following rule: the number by which the numerator is multiplied, must also be multiplied by the denominator.
Concluding the previous example, we have:
Fractions are some of the fractions equivalent to ½. Note that you can find several fractions equivalent to the fraction ½, just try the multiplication with different numbers.
Equivalent fractions have a different number representation, but they express the same amount.
To indicate that two or more fractions are equivalent, the symbol ~ or the equality symbol = is used.
Simplification of fractions.
And if we want to "prove" that two or more fractions are really equivalent, how can we do it? For that, we only need to apply the principles of simplifying fractions. But what would that be?
Simplifying fractions consists of dividing the numerator and denominator by the same number, reducing the fraction until it reaches its irreducible form, that is, when it can no longer be simplified. If we arrive at irreducible identical forms, it means that the fractions are equivalent.
Note that when they are reduced as much as possible (irreducible way), the fractions become identical and therefore they are equivalent.