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

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## 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}

Video Solution
Rational Numbers
Ex 9.2 | Question 2

## 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}

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