What are equivalent fractions for \[\dfrac{2}{7}\] ?

Hint: To find out the equivalent fraction for any given fraction in the form of \[\dfrac{p}{q}\], we have to multiply any natural number to both the numerator and denominator and hence we obtain the equivalent fraction of the required fraction. There exists an infinite number of equivalent fractions to a fraction \[\dfrac{p}{q}\].

Complete step-by-step solution:
Let us see a rule regarding the equivalent fractions I.e. we can only multiply or divide the fraction with the same amount but can never add or subtract to get an equivalent fraction. Equivalent fractions are to be divided only when both numerator and denominator remain as whole numbers. However, if the denominator is 0, then the fraction is denoted as an undefined fraction. If both the numerator and denominator are 0, then it is called as an undetermined fraction.
Now let us find out the equivalent fractions for \[\dfrac{2}{7}\].
In order to find them, let us consider some random natural numbers which are to be multiplied to \[\dfrac{2}{7}\]. They are: 2,45,67,89,234
Now let us multiply them and find out the equivalent fractions.
Case 1: \[2\]
On multiplying we get,
\[\dfrac{2}{7}\times \dfrac{2}{2}=\dfrac{4}{14}\]
Case 2: \[45\]
On multiplying we get,
\[\dfrac{2}{7}\times \dfrac{45}{45}=\dfrac{90}{315}\]
Case 3: \[67\]
On multiplying we get,
\[\dfrac{2}{7}\times \dfrac{67}{67}=\dfrac{134}{469}\]
Case 4: \[89\]
On multiplying we get,
\[\dfrac{2}{7}\times \dfrac{89}{89}=\dfrac{178}{623}\]
Case 5: \[234\]
On multiplying we get,
\[\dfrac{2}{7}\times \dfrac{234}{234}=\dfrac{468}{1683}\]
\[\therefore \] The obtained equivalent fractions are \[\dfrac{4}{14}\], \[\dfrac{90}{315}\], \[\dfrac{134}{469}\], \[\dfrac{178}{623}\], \[\dfrac{468}{1683}\].

Note: The list of equivalent fractions goes on. We can obtain our given fraction just by simplifying the equivalent fraction obtained. This process can be used in verifying whether the obtained equivalent fraction is the correct one or not.