Question

Find ten rational numbers between $\frac{-2}{5}and\frac{1}{2}$.

• A. $\frac{-7}{20},\frac{-11}{20},\frac{-5}{20},\frac{-4}{20},\frac{-3}{20},\frac{-2}{20},\frac{-1}{20},0,\frac{1}{20}and\frac{2}{20}$
• B. $\frac{-7}{20},\frac{-6}{20},\frac{-5}{20},\frac{-4}{20},\frac{-3}{20},\frac{-2}{20},\frac{-1}{20},0,\frac{1}{20}and\frac{2}{20}$
• C. $\frac{-7}{20},\frac{-6}{20},\frac{-5}{20},\frac{-4}{20},\frac{-3}{20},\frac{-2}{20},\frac{-1}{20},0,\frac{1}{20}and\frac{13}{20}$
• D. $\frac{-7}{20},\frac{-6}{20},\frac{-5}{20},\frac{-4}{20},\frac{-3}{20},\frac{-2}{20},\frac{-1}{20},0,\frac{15}{20}and\frac{2}{20}$

Answer 1

The correct option is B $\frac{-7}{20},\frac{-6}{20},\frac{-5}{20},\frac{-4}{20},\frac{-3}{20},\frac{-2}{20},\frac{-1}{20},0,\frac{1}{20}and\frac{2}{20}$

Converting the given rational numbers with the same denominators.

$\frac{-2}{5}=\frac{-2\times 4}{5\times 4}=\frac{-8}{20}$ and $\frac{1}{2}=\frac{1\times 10}{2\times 10}=\frac{10}{20}$

We know that $-8<-7<-\mathrm{6...}<10$

$\Rightarrow \frac{-8}{20}<\frac{-7}{20}<\frac{-6}{20}<...<\frac{10}{20}$

Thus, we have the following ten rational number between $\frac{-2}{5}$ and $\frac{1}{2}$

$\frac{-7}{20},\frac{-6}{20},\frac{-5}{20},\frac{-4}{20},\frac{-3}{20},\frac{-2}{20},\frac{-1}{20},0,\frac{1}{20}$ and $\frac{2}{20}$