Ex.1.1 Q4 Rational Numbers Solution - NCERT Maths Class 8

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Question

Find the multiplicative inverse of the following.

(i) \(\begin{align} \; - 13 \end{align}\)

(ii) \(\begin{align} \; \frac{{ - 13}}{{19}}\end{align}\)

(iii) \(\begin{align} \;\frac{1}{5}\end{align}\)

(iv) \(\begin{align} \; \frac{{ - 5}}{8} \times \frac{{ - 3}}{7} \end{align}\)

(v) \( \begin{align} \; - 1 \times \frac{{ - 2}}{5} \end{align}\)

(vi) \(\begin{align} \; - 1\end{align}\)

Text Solution

What is known?

Rational number

What is unknown?

The multiplicative inverse.

Reasoning:

The reciprocal of the given rational number is the multiplicative inverse. [The product of the rational number and its multiplicative inverse is \(1\)]

Steps:

(i) \(\begin{align} \; - 13 \end{align}\)

The Multiplicative inverse of \(\begin{align} - 13 \end{align}\) is \(\begin{align} \frac{{ - 1}}{{13}} \end{align} \)

 \[\begin{align}\left[ { - 13 \times \frac{{ - 1}}{{13}} = 1} \right]\end{align}\]

(ii) \(\begin{align} \; \frac{{ - 13}}{{19}}\end{align}\)

The Multiplicative inverse of \(\begin{align}\frac{{ - 13}}{{19}}\end{align}\) is \(\begin{align}\frac{{19}}{{ - 13}}\end{align}\)

\[\begin{align}\left[ {\frac{{ - 13}}{{19}} \times \frac{{19}}{{ - 13}} = 1} \right]\end{align}\]

(iii) \(\begin{align} \; \frac{1}{5}\end{align}\)

The Multiplicative inverse of \(\begin{align}\frac{1}{5}\end{align}\) is \(\begin{align}\frac{5}{1}\end{align}\)

\[\begin{align}\left[ {\frac{1}{5} \times \frac{5}{1} = 1} \right]\end{align}\]

(iv) \(\begin{align} \; \frac{{ - 5}}{8} \times \frac{{ - 3}}{7}=\frac{{15}}{56} \end{align}\)

The Multiplicative inverse of \(\begin{align}\frac{{15}}{{56}}\end{align}\) is \(\begin{align}\frac{{56}}{{15}}\end{align}\)

\[\begin{align}\left[ {\frac{{15}}{{56}} \times \frac{{56}}{{15}} = 1} \right]\end{align}\]

(v) \( \begin{align} \; - 1 \times \frac{{ - 2}}{5} \end{align}\)

This can be simplified as:

\[\begin{align} - 1 \times \frac{{ - 2}}{5} &= \frac{{( - 1) \times ( - 2)}}{5}\\ &= \frac{2}{5}\end{align}\]

The multiplicative inverse of \(\begin{align}\frac{2}{5} \end{align}\) is \(\begin{align}\frac{5}{2} \end{align}\)

\[\begin{align}\left[ {\frac{2}{5} \times \frac{5}{2} = 1} \right]\end{align}\] 

(vi) \(\begin{align} \; - 1\end{align}\)

The multiplicative inverse of \(\begin{align} - 1\end{align}\) is \(\begin{align} - 1\end{align}.\)

\[\begin{align}( - 1) \times ( - 1) = 1\end{align}\]