Ex.9.1 Q10 Rational-Numbers Solution - NCERT Maths Class 7

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Question

Write the following rational numbers in ascending order:

(i) \(\begin{align}\frac{{ - 3}}{5},\frac{{ - 2}}{5},\frac{{ - 1}}{5}\end{align}\)

(ii) \(\begin{align}\frac{{ - 1}}{3},\frac{{ - 2}}{9},\frac{{ - 4}}{3}\end{align}\)

(iii) \(\begin{align}\frac{{ - 3}}{7},\frac{{ - 3}}{2},\frac{{ - 3}}{4}\end{align}\)

Text Solution

What is known?

Three rational numbers.

What is unknown?

Ascending order of the given rational numbers.

Reasoning:

In such type of questions take the \(L.C.M\) of denominator of the rational numbers or convert them into like fractions. After converting them into like fractions comparison will be easy.

Steps:

(i) \(\begin{align}\frac{{ - 3}}{5},\frac{{ - 2}}{5},\frac{{ - 1}}{5}\end{align}\)

Since denominator is same in all the rational numbers, these can be easily arranges into ascending order \( - 3\,\, < - 2\,\, < - 1\)

\[\begin{align}\frac{{ - 3}}{5}\,\, < \frac{{ - 2}}{5}\,\, < \frac{{ - 1}}{5}\end{align}\]

(ii) \(\begin{align}\frac{{ - 1}}{3},\frac{{ - 2}}{9},\frac{{ - 4}}{3}\end{align}\)

\(L.C.M\) of \(3\),\(9\) and \(3\) is \(9\)

\[\begin{align}{\rm{So,}}\,\,\,\frac{{ - 1}}{3} &= \frac{{ - 1 \times 3}}{{3 \times 3}}\\&= \frac{{ - 3}}{9}
\\\frac{{ - 2}}{9}  &= \frac{{ - 2 \times 1}}{{9 \times 1}}\\ &=\frac{{ - 2}}{9}\\{\rm{and}}\,\,\,\frac{{ - 4}}{3} &= \frac{{ - 4 \times 3}}{{3 \times 3}}\\&= \frac{{ - 12}}{9}\end{align}\]

Arranging them into ascending order we get,

\[\begin{align}&\frac{{ - 12}}{9} < \frac{{ - 3}}{9} < \frac{{ - 2}}{9}\\&{\rm{Or}}\;\;\;{\mkern 1mu} \frac{{ - 4}}{3} < \frac{{ - 1}}{3} < \frac{{ - 2}}{9}\end{align}\]

(iii) \(\begin{align}\frac{{ - 3}}{7},\frac{{ - 3}}{2},\frac{{ - 3}}{4}\end{align}\)

\(L.C.M\) of \(7\), \(2\) and \(4\) is \(28\)

\[\begin{align}\frac{{ - 3}}{7}&= \frac{{ - 3 \times 4}}{{7 \times 4}}\\&= \frac{{ - 12}}{{28}}\\\frac{{ - 3}}{2} &= \frac{{ - 3 \times 14}}{{2 \times 14}}\\&= \frac{{ - 42}}{{28}}\\\frac{{ - 3}}{4} &= \frac{{ - 3 \times 7}}{{4 \times 7}} \\&= \frac{{ - 21}}{{28}}\end{align}\]

Arranging them into ascending order we get,

\[\begin{align}\frac{{ - 42}}{{28}} < \frac{{ - 21}}{{28}} < \frac{{ - 12}}{{28}}\end{align}\]

\[\begin{align}\text{Therefore,}\frac{{ - 3}}{2} < \frac{{ - 3}}{4} < \frac{{ - 3}}{7}\end{align}\]

  
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