### Rational Numbers - Solutions 1

CBSE Class –VII Mathematics
NCERT Solutions
Chapter 9 Rational Numbers (Ex. 9.1)

Question 1. List five rational numbers between:
(i) $-1$ and 0
(ii) $-2$ and $-1$
(iii) $\frac{-4}{5}$ and $\frac{-2}{3}$
(iv) $\frac{-1}{2}$ and $\frac{2}{3}$
Answer: (i) $-1$ and 0
Let us write $-1$ and 0 as rational numbers with denominator 6.
$⇒$ $-1=\frac{-6}{6}$ and 0 = $\frac{0}{6}$
$\therefore$ $\frac{-6}{6}<\frac{-5}{6}<\frac{-4}{6}<\frac{-3}{6}<\frac{-2}{6}<\frac{-1}{6}<0$
$⇒$ $-1<\frac{-5}{6}<\frac{-2}{3}<\frac{-1}{2}<\frac{-1}{3}<\frac{-1}{6}<0$
Therefore, five rational numbers between $-1$ and 0 would be
$\frac{-5}{6},\frac{-2}{3},\frac{-1}{2},\frac{-1}{3},\frac{-1}{6}$
(ii) $-2$ and $-1$
Let us write $-2$ and $-1$ as rational numbers with denominator 6.
$⇒$ $-2=\frac{-12}{6}$ and $-1=\frac{-6}{6}$
$\therefore$ $\frac{-12}{6}<\frac{-11}{6}<\frac{-10}{6}<\frac{-9}{6}<\frac{-8}{6}<\frac{-7}{6}<\frac{-6}{6}$
$⇒$ $-2<\frac{-11}{6}<\frac{-5}{3}<\frac{-3}{2}<\frac{-4}{3}<\frac{-7}{6}<-1$
Therefore, five rational numbers between $-2$ and $-1$ would be
$\frac{-11}{6},\frac{-5}{3},\frac{-3}{2},\frac{-4}{3},\frac{-7}{6}$
(iii) $\frac{-4}{5}$ and $\frac{-2}{3}$
Let us write $\frac{-4}{5}$ and $\frac{-2}{3}$ as rational numbers with the same denominators.
$⇒$ $\frac{-4}{5}=\frac{-36}{45}$ and $\frac{-2}{3}=\frac{-30}{45}$
$\therefore$ $\frac{-36}{45}<\frac{-35}{45}<\frac{-34}{45}<\frac{-33}{45}<\frac{-32}{45}<\frac{-31}{45}<\frac{-30}{45}$
$⇒$ $\frac{-4}{5}<\frac{-7}{9}<\frac{-34}{45}<\frac{-11}{15}<\frac{-32}{45}<\frac{-31}{45}<\frac{-2}{3}$
Therefore, five rational numbers between $\frac{-4}{5}$ and $\frac{-2}{3}$ would be
$\frac{-7}{9},\frac{-34}{45},\frac{-11}{15},\frac{-32}{45},\frac{-31}{45},\frac{-2}{3}$
(iv) $\frac{-1}{2}$ and $\frac{2}{3}$
Let us write $\frac{-1}{2}$ and $\frac{2}{3}$ as rational numbers with the same denominators.
$⇒$ $\frac{-1}{2}=\frac{-3}{6}$ and $\frac{2}{3}=\frac{4}{6}$
$\therefore$ $\frac{-3}{6}<\frac{-2}{6}<\frac{-1}{6}<0<\frac{1}{6}<\frac{2}{6}<\frac{3}{6}<\frac{4}{6}$
$⇒$ $\frac{-1}{2}<\frac{-1}{3}<\frac{-1}{6}<0<\frac{1}{6}<\frac{1}{3}<\frac{1}{2}<\frac{2}{3}$
Therefore, five rational numbers between $\frac{-1}{2}$ and $\frac{2}{3}$ would be $\frac{-1}{3},\frac{-1}{6},0,\frac{1}{6},\frac{1}{3}$.