Question

Find five rational numbers between $\frac{-3}{2}$ and $\frac{5}{3}$.

• A. $\frac{-8}{6},\frac{-13}{6},\frac{0}{6},\frac{1}{6}$ and $\frac{2}{6}$
• B. $\frac{-8}{6},\frac{-7}{6},\frac{0}{6},\frac{1}{6}$ and $\frac{13}{6}$
• C. $\frac{-8}{6},\frac{-7}{6},\frac{0}{6},\frac{1}{6}$ and $\frac{11}{6}$
• D. $\frac{-8}{6},\frac{-7}{6},\frac{0}{6},\frac{1}{6}$ and $\frac{2}{6}$

Answer 1

Answer: (D)

$\frac{-8}{6},\frac{-7}{6},\frac{0}{6},\frac{1}{6}$ and $\frac{2}{6}$

Converting the given rational numbers with the same denominators

$\frac{-3}{2}=\frac{-3\times 3}{2\times 3}=\frac{-9}{6}$ and $\frac{5}{3}=\frac{5\times 2}{3\times 2}=\frac{10}{6}$

We know that $-9<-8<-7<-6<\dots <0<1<2<8<9<10$

$\Rightarrow \frac{-9}{6}<\frac{-8}{6}<\frac{-7}{6}<\frac{-6}{6}<\dots <\frac{0}{6}<\frac{1}{6}<\frac{2}{6}<\dots <\frac{8}{6}<\frac{9}{6}<\frac{10}{6}$.

Thus, we have the following five rational numbers between $\frac{-3}{2}$ and $\frac{5}{3}$

$\Rightarrow \frac{-8}{6},\frac{-7}{6},\frac{0}{6},\frac{1}{6}and\frac{2}{6}$