How to know if two fractions are equivalent

Are you wondering how to know if two fractions are equivalent even if they are formed by different numbers? There are several methods to perform this mathematical verification and see if one fraction equals the other. In case they are, we can place an equality sign between them, since their value will be the same. In this way, we want to explain two ways of knowing if two fractions are equivalent.

Steps to follow:


If we have two fractions with different numerators and numerators, at first sight it can be difficult to know if they are equivalent . That is why we must check it mathematically with one of the methods that we explain.


One of the most common ways to check if two fractions are equivalent is to multiply crosswise, that is, the numerator of one fraction by the denominator of the other and vice versa to check if the result is the same. In case the resulting number is equal, the fractions will be equivalent.

We must perform these operations and compare the result:

- axd

- bxc


Let's see an example, to know if 2/6 and 3/9 are equivalent, we will have to multiply:

- 2 x 9 = 18

- 6 x 3 = 18

We can see that the result of both operations is the same, so the fractions are equivalent.


There is another way to perform the test that two fractions are equivalent, consisting of dividing the numerator of each fraction between its denominator and compare again the result of both fractions. If it is the same, they will be equivalent; In case they are not equal, they will not be.


Let's check with the same example:

- 2: 6 = 0'33333333 ...

- 3: 9 = 0'33333333 ...

We see that the result is the same, so we can conclude again that these two fractions are equivalent.


However, if we try to perform the check with this other example:

- 5 x 8 = 40 and 4 x 7 = 28 the results of cross multiplication do not match

- 5: 4 = 1'25 and 7: 8 = 0.875 do not match the divisions between numerators and denominators

We can conclude that these two fractions are not equivalent .