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

## 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}

Video Solution
Rational Numbers
Ex 9.1 | Question 10

## 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 $$9$$

So,

\begin{align} \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}\end{align}

and

\begin{align} {\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}

Therefore,

\begin{align} \frac{{ - 3}}{2} < \frac{{ - 3}}{4} < \frac{{ - 3}}{7}\end{align}

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