Question

Write two equivalent fractions of the following:
\[\dfrac{12}{5}\].

Answer 1

Hint: In this question, to find the equivalent fraction of the given fraction \[\dfrac{12}{5}\] we need to multiply the numerator and denominator with the same number. Now, again multiply the numerator and denominator of \[\dfrac{12}{5}\]with another number to get other equivalent fractions.

Complete step-by-step solution -
EQUIVALENT FRACTIONS: Two fractions are said to be equivalent fractions when they have the same value when written in lowest terms.
Now, to find the equivalent fractions we need to multiply the numerator and denominator of the reduced form of the given fraction by any integer number.
Equivalent fractions may look different, but when they are reduced to the lowest terms we get the same value.
Here, to check whether two fractions are equivalent or not we need to multiply the numerator of fraction 1 with the denominator of fraction 2 and numerator of fraction 2 with a denominator of fraction 1 which should give the same value.
Now, to find the equivalent fractions of \[\dfrac{12}{5}\]
Let us first multiply the numerator and denominator with 2
\[\Rightarrow \dfrac{12\times 2}{5\times 2}\]
Now, on further simplification we get,
\[\Rightarrow \dfrac{24}{10}\]
Thus, \[\dfrac{24}{10}\] is one of the equivalent fraction of \[\dfrac{12}{5}\]
Now, let us find another equivalent fraction of \[\dfrac{12}{5}\]
Let us now multiply the numerator and denominator with 5
\[\Rightarrow \dfrac{12\times 5}{5\times 5}\]
Now, on further simplification we get,
\[\Rightarrow \dfrac{60}{25}\]
Hence, the two equivalent fractions of \[\dfrac{12}{5}\] are \[\dfrac{24}{10},\dfrac{60}{25}\].

Note: Instead of multiplying the numerator and denominator with 2 and 5 we can also multiply them with other integers to get the equivalent fractions. It is important to note that we need to multiply both the numerator and denominator with the same number because multiplying them with different numbers gives another fraction which on writing in lowest terms does not give the one that we considered.