Rational Numbers Test - 18

$$\textbf{Step -1: Find required rational numbers.}$$

                 $$\text{We need five rational numbers between }1\text{ and }2.$$

                 $$\text{So, multiply and divide the numbers with a natural number greater or equal to } 5+1=6.$$

                  $$\text{Lets take }7.$$

                  $$1=1\times\dfrac{7}{7}=\dfrac{7}{7}$$

                  $$\text{and }2=2\times\dfrac{7}{7}=\dfrac{14}{7}$$

                  $$\text{Thus, }1\text{ and }2\text{ becomes }\dfrac{7}{7}\text{ and }\dfrac{14}{7}\text{ respectively.}$$

                  $$\text{Since, }7<8<9<10<11<12<13<14$$

                  $$\therefore 1=\dfrac{7}{7}<\dfrac{8}{7}<\dfrac{9}{7}<\dfrac{10}{7}<\dfrac{11}{7}<\dfrac{12}{7}<\dfrac{13}{7}<\dfrac{14}{7}=2$$

                  $$\text{Hence, five rational numbers between }1\text{ and }2\text{ are }\dfrac{8}{7},\dfrac{9}{7},\dfrac{10}{7},\dfrac{11}{7},\text{ and }\dfrac{12}{7}.$$

$$\textbf{Hence , the correct option is D.}$$

Consider given the rational numbers$$-\dfrac{2}{5}$$ and $$-\dfrac{1}{5}$$

Now, given both rational numbers are negative numbers so the number which lies between them will be negative.

So,$$\dfrac{3}{10}$$ will not lie between them,

Hence, this is the answer.