# Ex.1.1 Q3 Rational Numbers Solution - NCERT Maths Class 8

## Question

Verify that \(\begin{align}- \left( { - x} \right) = x\end{align}\) for

(i) \(\begin{align} x = \frac{{11}}{{15}}\end{align}\)

(ii) \(\begin{align} x = - \frac{{13}}{7}\end{align}\)

## Text Solution

**What is known?**

Rational number.

**What is unknown?**

The negative of the negative of a rational number.

**Reasoning:**

The negative of the negative of a rational number is that rational number of Self.

**Steps:**

(i) \(\begin{align} \quad x = \frac{{11}}{{15}}\end{align}\)

\[\begin{align}- ( - x)&= - \left( { - \frac{{11}}{{15}}} \right)\\&= \frac{{11}}{{15}}\\&= x\end{align}\]

Hence Proved.

(ii) \(\begin{align}\quad x = - \frac{{13}}{7}\end{align}\)

\[\begin{align}- ( - x) &= - \left[ { - \left( { - \frac{{13}}{{17}}} \right)} \right]\\&=- \left[ {\frac{{13}}{{17}}} \right]\\&= - \frac{{13}}{{17}}\\&= x\end{align}\]

Hence Proved.

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