Ex.9.2 Q2 Rational-Numbers Solution - NCERT Maths Class 7

Go back to  'Ex.9.2'

Question

Find

(i) \(\begin{align}{\frac{7}{{24}} - \frac{{17}}{{36}}}\end{align}\) (ii) \(\begin{align}{\frac{5}{{63}} - \left[ {\frac{{ - 6}}{{21}}} \right]}\end{align}\)
(iii) \(\begin{align}{\left.{\frac{{ - 6}}{{13}} - \left[ {\frac{{ - {\rm{7}}}}{{{\rm{15}}}}} \right.} \right]} \end{align}\) (iv) \(\begin{align}\frac{{ - 3}}{8} - \frac{7}{{11}}\end{align}\)
(v) \(\begin{align} - 2\frac{1}{9} - 6\end{align}\)  

Text Solution

What is known?

Two rational numbers

What is unknown?

Difference between the given two rational numbers.

Reasoning:

In such type of questions take the \(L.C.M\) of denominator or convert them into like fractions, then find their difference between them. You can also reduce them to the lowest or simplest form.

Steps:

(i) \(\begin{align}{\frac{7}{{24}} - \frac{{17}}{{36}}}\end{align}\)

Taking \(L.C.M\) of \(24\) and \(36\), we get \(72\)

\[\begin{align}\frac{7}{{24}} - \frac{{17}}{{36}} &= \frac{{7 \times 3}}{{24\times3}} - \frac{{17 \times 2}}{{36\times3}}\\&= \frac{{21}}{{72}} - \frac{{34}}{{72}}\\&= \frac{{21 - 34}}{{72}}\\&= \frac{{ - 13}}{{72}}\end{align}\]

(ii) \(\begin{align}{\frac{5}{{63}} - \left[ {\frac{{ - 6}}{{21}}} \right]}\end{align}\)

Taking \(L.C.M\) of \(63\) and \(21\), we get \(63\)

\[\begin{align}\frac{5}{{63}} - \left( {\frac{{ - 6}}{{21}}} \right) &= \frac{5\times1}{{63\times1}} + \frac{{6{\times3}}}{{21\times3}}\\ &= \frac{5}{{63}} + \frac{{18}}{{63}}\\ &= \frac{{5 + 18}}{{63}}\\ &= \frac{{23}}{{63}}\end{align}\]

(iii) \(\begin{align} {\left.{\frac{{ - 6}}{{13}} - \left[ {\frac{{ - {\rm{7}}}}{{{\rm{15}}}}} \right.} \right]} \end{align}\)

Taking \(L.C.M\) of \(13\) and \(15\), we get \(195\)

\[\begin{align}\frac{{ - 6}}{{13}} - \frac{{ - 7}}{{15}} &= \frac{{ - 6 \times 15}}{{13\times15}} + \frac{{7 \times 13}}{{15\times13}}\\&= \frac{{ - 90}}{{195}} + \frac{{91}}{{195}}\\&= \frac{{ - 90 + 91}}{{195}}\\&= \frac{1}{{195}}\end{align}\]

(iv) \(\begin{align}\frac{{ - 3}}{8} - \frac{7}{{11}}\end{align}\)

Taking \(L.C.M\) of \(8\) and \(11\), we get \( 88\)

\[\begin{align}\frac{{ - 3}}{8} - \frac{7}{{11}} &= \frac{{ - 3 \times 11}}{{8\times11}} - \frac{{7 \times 8}}{{11\times8}}\\&= \frac{{ - 33}}{{88}} - \frac{{56}}{{88}}\\&= \frac{{ - 33 - 56}}{{88}}\\&= \frac{{ - 89}}{{88}}\end{align}\]

(v) \(\begin{align} - 2\frac{1}{9} - 6\end{align}\)

\[\begin{align} - 2\frac{1}{9} - 6 = - \frac{{19}}{9} - \frac{6}{1}\end{align}\]

Taking \(L.C.M\) of \(9\) and \(1\), we get \(9\)

\[\begin{align}- \frac{{19}}{9} - \frac{6}{1} &= \frac{{ - 19}}{9\times1} - \frac{{6 \times 9}}{1\times9}\\&= \frac{{ - 19}}{9} - \frac{{54}}{9}\\&= \frac{{ - 19 - 54}}{9}\\&= \frac{{ - 73}}{9}\end{align}\]

 

 

 

 

  
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