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

Go back to  'Ex.9.2'

## Question

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}

Video Solution
Rational Numbers
Ex 9.2 | Question 4

## 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}

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school