Question

Give three rational numbers equivalent to \[\dfrac{7}{{11}}\]

Answer 1

Hint: We have to find three rational numbers which are equivalent to the given value . We solve this question using the concept of multiplications of fractions and the concept of rational numbers . To solve this question we should have the knowledge of the definition of a rational number and its equivalent values . We will simply multiply both the numerator and the denominator of the given rational number by any real number except zero to get the value of the rational number equivalent to the given rational number .

Complete step-by-step answer:
Given :
The given rational number is \[\dfrac{7}{{11}}\] .
Now , we also know that multiplying both the numerator and denominator by the same value will give us the equivalent rational number to the given rational number .
Three equivalent rational numbers can be written as :
\[\dfrac{7}{{11}} = \dfrac{7}{{11}} \times \dfrac{2}{2}\]
\[\dfrac{7}{{11}} = \dfrac{{14}}{{22}}\]
Similarly , other values can be :
\[\dfrac{7}{{11}} = \dfrac{7}{{11}} \times \dfrac{3}{3}\]
\[\dfrac{7}{{11}} = \dfrac{{21}}{{33}}\]
Again , we get the value as
\[\dfrac{7}{{11}} = \dfrac{7}{{11}} \times \dfrac{4}{4}\]
\[\dfrac{7}{{11}} = \dfrac{{28}}{{44}}\]
Hence , the three equivalent rational number to \[\dfrac{7}{{11}}\] are \[\dfrac{{14}}{{22}}\] , \[\dfrac{{21}}{{33}}\] and \[\dfrac{{28}}{{44}}\] .

Note: The equivalent rational numbers obtained may not look equal to the given rational number but , even after the multiplication we can get to the given rational number by cancelling the terms of the numerator and the denominator which will give us the given original rational number . We can take any real value either positive or negative for the multiplication of the denominator and the numerator except zero as it will give an indefinite value or not defined value , as we would get a \[\dfrac{0}{0}\] value on the multiplication of the terms . We multiply both the numerator and denominator so as the value remains unchanged.