Equivalent fractions are those that express the same number, even if they do not share the same numerator and denominator.
Equivalent fractions, in other words, are those in which dividing the numerator by the denominator we obtain the same result. However, despite presenting the same result, the components of the fractions are different.
Equivalent fractions is one of the types of fractions, according to the relationship they have with each other.
To find equivalent fractions, having a given fraction, you can divide or multiply both the numerator and the denominator by the same number.
In that sense, we must bear in mind that every fraction has an infinite number of equivalent fractions.
Also, remember that a fraction is the division of a number into equal parts.
Understanding equivalent fractions
To understand equivalent fractions, let’s imagine we have a cake and divide it into three equal parts, and then take one of those pieces.
Now, if that same cake were divided into six equal parts and took 2, we would be taking the same amount of cake as in the previous case. This is because 1/3 and 2/6 are equivalent.
Examples of equivalent fractions
Some examples of equivalent fractions are:
6/9 and 2/3 = 0.6667.
7/21 and 84/28 = 3.
12/60, 3/15 and 1/5 = 0.2.
How to know if two fractions are equivalent?
To find out if two or more fractions are equivalent, you can divide the denominator and the numerator by the same number. This, until having fractions that are irreducible, that is, where the numerator and the denominator do not have divisors in common and that, therefore, cannot be simplified.
Then, if the resulting irreducible fractions are equal, the fractions are equivalent.
Let’s see an example:
Are 48/108 and 32/72 equivalent?
48/108 = 16/36 = 4/9 (We divide by three and then by four each of the components).
32/72 = 4/9 (We divide both components by 8).
We can conclude, then, that 48/108 and 32/72 are equivalent fractions.
Now let’s look at another example. If we have 6/70 and 12/56.
6/14 = 3/7 (We divide both components by two).
12/56 = 3/14 (We divide both components by four).
Since 3/7 ≠ 3/14, 6/70 and 12/56 are not equivalent.