Question

A rational number equivalent to \[\dfrac{5}{7}\] is ?

Answer 1

Hint:In this question, we have to find a rational number which is equivalent to \[\dfrac{5}{7}\] . Here, the word equivalent means ‘equal to’. We will multiply both the denominator and numerator with any number (say \[2\] or \[3\] etc. ) To get the equivalent rational number of the given fraction.

Complete step by step answer:
This problem is based on the Equivalent fraction. Equivalent stands for ‘equal to'. Two fractions are said to be equivalent fractions, if their simplest form is equal. For example, \[\dfrac{1}{2}\] and \[\dfrac{2}{4}\] are equivalent fraction, since the simplest form of \[\dfrac{1}{2}\]and \[\dfrac{2}{4}\] is \[\dfrac{1}{2}\], thus the fraction is equal.
A fraction is said to be in simplest form if there is no common factor of numerator and denominator other than one.

To find an equivalent fraction, we simply multiply both the numerator and denominator by different numbers. Consider the given question,
The given fraction is \[\dfrac{5}{7}\] .
Multiplying the numerator and denominator by \[2\] , we have
\[\dfrac{5}{7} = \dfrac{{5 \times 2}}{{7 \times 2}}\]
On solving, we get \[\dfrac{{10}}{{14}}\].

Hence, a rational number equivalent to \[\dfrac{5}{7}\] is \[\dfrac{{10}}{{14}}\].

Note:A rational number is any number of form \[\dfrac{p}{q}\] where \[p\] and \[q\] are integers and \[q\] is not equal to zero. Every fraction is a rational number. To find the simplest form of any given fraction, we find the HCF (highest common factor) of numerator and denominator and then divide the numerator and denominator with the resultant HCF.For example, the simplest form of \[\dfrac{2}{4}\] is \[\dfrac{1}{2}\] which is obtained by dividing the numerator and denominator by HCF (i.e. \[2\] ) of \[2\] and \[4\].