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 $S$.

[4 marks]
[NCERT - Ex:9.1, Q5]
[Rational numbers on number line]

Answer 1

Solution:
The portion between $A$ and $B$ is divided into three equal parts. So, we can write, $A=2=\frac{6}{3}$ and $B=3=\frac{9}{3}$ (in one of its rational forms).

Since, $P$ and $Q$ is in between $A$ and $B$, and the only values available in between $A$ and $B$ are $\frac{7}{3}$and$\frac{8}{3}$ that is representing even partition.

Thus, we can conclude that,
$P=\frac{7}{3}andQ=\frac{8}{3}$
[2 marks]

Similarly, the portion between $T$ and $U$ is divided into three equal parts. So, we can write, $T=-1=\frac{-3}{3}$ and $U=-2=\frac{-6}{3}.$

Since, $S$ and $R$ is in between $T$ and $U$, we have,
$S=\frac{-5}{3}$ and $R=\frac{-4}{3}$
[2 marks]

Thus, the rational numbers representing $P,Q,R$ and $S$ are $\frac{7}{3},\frac{8}{3},\frac{-4}{3}$ and $\frac{-5}{3}$ respectively.