# Ex.9.1 Q5 Rational-Numbers Solution - NCERT Maths Class 7

## Question

The points \(P, Q, R, S, T, U, A \) and \(B\) on the number line are such that, \(TR = RS = SU\) and \(AP = PQ = QB\). Name the rational numbers represented by \(P, Q, R\) and \(S\).

## Text Solution

**Steps:**

Distance between \(U\) and \(T = 1\) unit. It is divided into three equal parts

\[\begin{align}{\rm{TR}} = {\rm{RS}} = {\rm{SU}} = \frac{1}{3}\\{\rm{R}} = - 1 - \frac{1}{3} = \frac{{ - 4}}{3}\\{\rm{S}} = - 1 - \frac{2}{3} = \frac{{ - 5}}{3}\end{align}\]

Similarly, \(AB = 1\) unit

It is divided into three equal parts

\[\begin{align}{\rm{AP}} = {\rm{PQ}} &= {\rm{QB}} = \frac{1}{3}\\{\rm{P}} = 2 + \frac{1}{3} &= \frac{6}{3} + \frac{1}{3} = \frac{7}{3}\\{\rm{Q}} = 2 + \frac{2}{3} &= \frac{6}{3} + \frac{2}{3} = \frac{8}{3}\end{align}\]

\[\begin{align}\text{Thus, the rational number P, Q, R and S are}\, \frac{7}{3},\frac{8}{3},\frac{{ - 4}}{3}\,\,{\rm{and}}\,\frac{{ - 5}}{3}\end{align}\]