Question

Give four rational numbers equivalent to \[- \dfrac{2}{7}\]

Answer 1

Hint: In the given question, we need to find the four rational numbers equivalent to the given rational number. In arithmetic, Rational numbers are the numbers which can be represented in the form \[\dfrac{p}{q}\] where \[p\] and \[q\] are integers and \[q \neq 0\]. By multiplying , the given rational number with any four numbers gives an equivalent rational number.

Complete answer: Given, a rational number \[- \dfrac{2}{7}\]
We need to find another four rational numbers equivalent to this number.
By multiplying both the numerator and denominator of the given rational number with any four numbers , we get another four rational numbers equivalent to this rational number.
Step 1 of 4 :
By multiplying both the numerator and denominator of the given rational number with \[2\] where \[2 \in N\] , we get one rational number equivalent to \[- \dfrac{2}{7}\]
\[- \dfrac{2}{7} \times \dfrac{2}{2} = - \dfrac{4}{14}\]
Step 2 of 4 :
Similarly, on multiplying with \[3\] ,we get
\[- \dfrac{2}{7} \times \dfrac{3}{3} = \ - \dfrac{6}{21}\]
Step 3 of 4 :
By multiplying with \[4\], we get
\[- \dfrac{2}{7} \times \dfrac{4}{4} = - \dfrac{8}{28}\]
Step 4 of 4 :
By multiplying with \[5\], we get
\[- \dfrac{2}{7} \times \dfrac{5}{5} = - \dfrac{10}{35}\]
Now ,
Therefore , The four equivalent rational numbers are
\[\ - \dfrac{4}{14}, - \dfrac{6}{21}, - \dfrac{8}{28}, - \dfrac{10}{35}\]
Final answer :
The four equivalent rational numbers are \[\ - \dfrac{4}{14}, - \dfrac{6}{21}, - \dfrac{8}{28}, - \dfrac{10}{35}\]

Note:
Mathematically, Rational numbers are denoted by latin capital letters \[Q\]. The rational numbers are included in the real numbers. Basically, rational numbers form a dense subset of real numbers. We need to know that two different rational numbers may correspond to the same rational number. For example, in this question \[\ -\dfrac{2}{7}\] and \[\ - \dfrac{4}{14}\] are the same .