Check out the following examples of equivalent fractions

1/2 2/4 4/8

These are obviously different fractions but they are equivalent in nature. Equivalent refers to being equal in value, function, amount or meaning and such things. Since the above fractions are equivalent, we can write them as

1/2 = 2/4 = 4/8

But, it is clearly seen that the above fractions have different numbers as numerators and denominators, so what makes them equal? If we take the fraction 4/8 and simplify it, we are left with?

\(\frac{4\div 4}{8\div 4}\)= \(\frac{1}{2}\)

In the same way, if we simplify 2/4, again get 1/2.

\(\frac{2\div 2}{4\div 2}\)= \(\frac{1}{2}\)

**EQUIVALENT FRACTIONS**

These fractions are actually the same because when we multiply or divide both, the numerator and the denominator by the same number, the value of the fraction actually doesn’t change. Therefore, equivalent fractions when reduced to their simplified value will all be the same.

In the above example, we divided the numerator and denominator by the same number to reduce the value of the fraction to its simplest form. If we multiply a fraction by the same value both, in the numerator and denominator, we end up with different equivalent fractions. For example, consider the fraction ⅕.

Multiplying numerator and denominator with 2, we get 1/5 = 2/10

Multiplying numerator and denominator with 3, we get 1/5 = 3/15

Multiplying numerator and denominator with 4, we get 1/5 = 4/20

Therefore, we can conclude that,

\(\frac{1}{5}\) = 2/10 = 3/15 = 4/20

Keep in mind that, we can only multiply or divide by the same numbers to get an equivalent fraction, and not add or subtract. Simplification to get equivalent numbers can be done till a point where both, the numerator and denominator should still be whole numbers.

Try the following question to check your understanding of the concept of equivalent fractions.

**Example: The given fractions \(\frac{5}{6}\) and x/12 are equivalent fractions, then find the value of x. **

**Solution:**

Given- \(\frac{5}{6} = \frac{x}{12}\)

\(\Rightarrow x = \frac{5 \times12}{6}\) \(\Rightarrow x = 10\)Have persisting doubts in any topic? Try reaching out to our mentors only with BYJU’s – The Learning App.