Ex.9.2 Q4 Rational-Numbers Solution - NCERT Maths Class 7

Find the value of:

(i) \(\begin{align}\,\,\left( { - 4} \right) \div \frac{2}{3}\;\;\;{\mkern 1mu}\end{align} \)

(ii) \(\begin{align}\frac{{ - 3}}{5} \div 2\end{align}\)

(iii) \(\begin{align}\frac{{ - 4}}{5} \div \left( { - 3} \right)\end{align}\)

(iv) \(\begin{align}\frac{{ - 1}}{8} \div \frac{3}{4}\;\;\end{align}\)

(v) \(\begin{align}\frac{{ - 2}}{{13}} \div \frac{1}{7}\end{align}\)

(vi) \(\begin{align}\frac{{ - 7}}{{12}} \div \left[ {\frac{{ - 2}}{{13}}} \right]\end{align}\)

(vii) \(\begin{align}\frac{3}{{13}} \div \left[ {\frac{{ - 4}}{{65}}} \right]\end{align}\)

Text Solution

What is known?

Two numbers.

What is  unknown?

Value of given numbers.

Reasoning:

In such type of questions, convert the denominator into its reciprocal. When you convert the denominator into its reciprocal, the sign of division will also convert into multiplication and now you can find out the product of the given numbers.

Steps:

(i) 

\[\begin{align}(- 4) \! \div \! \frac{2}{3} \! = \! - 4 \! \times \! \frac{3}{2} \! = \! -2 \! \times \! 3 \! = \! -6\end{align}\]

(ii) 

\[\begin{align}\frac{{ - 3}}{5} \div 2\; = \frac{{ - 3}}{5} \times \frac{1}{2} = \frac{{ - 3}}{{10}}\end{align}\]

(iii) 

\[\begin{align}\frac{{ - 4}}{5} \div \left( { - 3} \right) = \frac{{ - 4}}{5} \times \frac{{ - 1}}{3} = \frac{4}{{15}}\end{align}\]

(iv) 

\[\begin{align}\frac{{ - 1}}{8} \div \frac{3}{4} = \frac{{ - 1}}{8} \times \frac{4}{3} = \frac{{ - 4}}{{24}} = \frac{{ - 1}}{6}\end{align}\]

(v) 

\[\begin{align}\frac{{ - 2}}{{13}} \! \div \! \frac{1}{7} \! = \! \frac{{ - 2}}{{13}} \! \times \! \frac{7}{1} \! = \! \frac{{ - 2 \! \times \! 7}}{{13}} \! = \! \frac{{ - 14}}{{13}}\end{align}\]

(vi) 

\[\begin{align}\frac{{ - 7}}{{12}} \div \left[ {\frac{{ - 2}}{{13}}} \right] &= \frac{{ - 7}}{{12}} \times \frac{{13}}{{ - 2}}\\& = \frac{{ - 7 \times 13}}{{12 \times - 2}} \\&= \frac{{ - 91}}{{ - 24}} = \frac{{91}}{{24}}\end{align}\]

(vii) 

\[\begin{align}\frac{3}{{13}} \div \left[ {\frac{{ - 4}}{{65}}} \right] &= \frac{3}{{13}} \times \frac{{65}}{{ - 4}} \\&= \frac{{3 \times 65}}{{13 \times - 4}}\\& = \frac{{3 \times 5}}{{ - 4}} = \frac{{ - 15}}{4}\end{align}\]