## Equivalent Fractions

The equivalent fractions are defined as a type of fraction, which seems to be different or not having the exact numbers but they are equivalent in nature or we can say that they are having exactly equal value when we simplify them. The meaning of word equivalent refers to being equal in value, function, amount etc. There are some example of equivalent fractions, such as equivalent fractions of \(\frac{1}{4}\) are \(\frac{2}{8}\), \(\frac{3}{12}\), etc. Let us now discuss equivalent fractions in detail.

Source: en.wikipedia.org

**Equivalent Fractions Definition**

According to the definition of equivalent fractions, it states that two or more than two fractions are said to be equal if both results are the same fraction after simplification. The equivalent fractions have equal values in both numerator and denominator after simplification of given fractions. If we cancel the common factors from numerator and denominator, these fractions produce the same number.

For example, the equivalent fraction of \(\frac{1}{2}\) is \(\frac{5}{10}\), because if we simplify \(\frac{5}{10}\) i.e by dividing the numerator and denominator by the common factor 5 then the resulted factor is the same.

**For example:**

\(\frac{1}{4}\) = \(\frac{2}{8}\)=\(\frac{3}{12}\)

As we can see that, the above fractions have different numbers as numerators and denominators.

Dividing both numerator and denominator by their common factor, we have:

3÷3 and 12÷3

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

In the same way, if we simplify \(\frac{2}{8}\), again get \(\frac{1}{4}\).

2÷2 and 8÷2

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

**How to Find Equivalent Fractions?**

Equivalent fractions are the fractions whose value are same because when we multiply or divide both, the numerator and the denominator by the same number, the value of the fraction actually does not change. Therefore, when do the simplification or reduce the equivalent fraction in their simplest form the value of the fraction will be the same.

For example, consider the fraction \(\frac{1}{6}\)

Multiplying numerator and denominator with 2, we get \(\frac{1}{6}\)= \(\frac{2}{12}\)

Multiplying numerator and denominator with 3, we get \(\frac{1}{6}\)= \(\frac{3}{18}\)

And, Multiplying numerator and denominator with 4, we get \(\frac{1}{6}\)= \(\frac{4}{24}\)

Therefore, we can conclude that,

\(\frac{1}{6}\) = \(\frac{2}{12}\)= \(\frac{3}{18}\)= \(\frac{4}{24}\)

While finding the equivalent fraction we can only perform multiplication or division by the same numbers to get an equivalent fraction. We cannot get equivalent fraction either by addition nor by subtraction. We perform simplification to get equivalent numbers and it can be done until a point where both, the numerator and denominator should still be whole numbers.

In other words, simplification of the fraction is done until we get the common factor of both numerator and denominator as 1. We represent equivalent fractions in an image by shading the particular potion, this type of methods used for the students who are pursing grade 3, grade 4 and grade 5.

**Equivalent Fractions Chart:**

Unit Fraction |
Equivalent Fractions |

\(\frac{1}{2}\) | \(\frac{2}{4}\),\(\frac{3}{6}\),\( \frac{4}{8}\).. |

\(\frac{1}{3}\) | \(\frac{2}{6}\), \(\frac{3}{9}\), \(\frac{4}{12}\).. |

\(\frac{1}{4}\) | \(\frac{2}{8}\), \(\frac{3}{12}\), \(\frac{4}{16}\).. |

\(\frac{1}{5}\) | \(\frac{2}{10}\), \(\frac{3}{15}\), \(\frac{4}{20}\).. |

\(\frac{1}{6}\) | \(\frac{2}{12}\), \(\frac{3}{18}\), \(\frac{4}{24}\),.. |

\(\frac{1}{7}\) | \(\frac{2}{14}\), \(\frac{3}{21}\), \(\frac{4}{28}\).. |

\(\frac{1}{8}\) | \(\frac{2}{16}\), \(\frac{3}{24}\), \(\frac{4}{32}\).. |

\(\frac{1}{9}\) | \(\frac{2}{18}\), \(\frac{3}{27}\), \(\frac{4}{36}.\). |

**Solved Examples for You**

Q.1: The given fractions \(\frac{4}{16}\) and \(\frac{x}{12}\) are equivalent fractions, then find the value of x.

Solution:

Given: \(\frac{4}{16}\) = \(\frac{x}{12}\)

x = \(\frac{(4 x 12)}{16}\)

x = \(\frac{48}{16}\)

=\(\frac{12}{4}\)

Therefore, the value of x is 3

Q.2: Two fractions \(\frac{2}{5}\) and \(\frac{4}{x}\) are equivalent. Find the value of x.

Solution: Given,

\(\frac{2}{5}\) = \(\frac{4}{x}\)

x = \(\frac{(4 x 5)}{2}\)

x = \(\frac{20}{2}\)

= 10

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