# Ex.9.1 Q3 Rational-Numbers Solution - NCERT Maths Class 7

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## Question

Give four rational numbers equivalent to:

\begin{align}{{\rm{ (i) }}\frac{{ - 2}}{7}}\end{align}

\begin{align}{{\rm{(ii) }}\frac{5}{{ - 3}}}\end{align}

\begin{align}{\rm{(iii)}}\,\,\,\frac{4}{9}\end{align}

## Text Solution

What is known?

Three rational numbers.

What is unknown?

Four rational numbers equivalent to each of the given rational number.

Reasoning:

To find out the equivalent fraction of any rational number, multiply the numerator and the denominator of the given number by the same numbers. Remember here it is asked for four equivalent rational numbers that means you have to multiply four different numbers, one by one in both numerator and denominator of the given number.

Steps:

\begin{align}{\rm{(i)}}\,\,\,\frac{{ - 2}}{7}\end{align}

Multilying both numerator and denominator with the same number, we get

\begin{align}\frac{{ - 2 \times 2}}{{7 \times 2}} = \frac{{ - 4}}{{14}},\frac{{ - 2 \times 3}}{{7 \times 3}} = \frac{{ - 6}}{{21}}\quad ,\frac{{ - 2 \times 4}}{{7 \times 4}} = \frac{{ - 8}}{{28}},\quad \frac{{ - 2 \times 5}}{{7 \times 5}} = \frac{{ - 10}}{{35}}\end{align}

Therefore, the equivalent fractions to the number \begin{align}\frac{{ - 2\;}}{7}\end{align}are,

\begin{align}\frac{{ - 4}}{{14}},\frac{{ - 6}}{{21}},\frac{{ - 8}}{{28}},\frac{{ - 10}}{{35}}\end{align}

\begin{align}{\rm{(ii)}}\frac{5}{{ - 3}}\end{align}

Multiplying both numerator and denominator with the same number, we get

$\frac{{5 \times 2}}{{ - 3 \times 2}} = \frac{{10}}{{ - 6}},\frac{{5 \times 3}}{{ - 3 \times 3}} = \frac{{15}}{{ - 9}}\quad ,\frac{{5 \times 4}}{{ - 3 \times 4}} = \frac{{20}}{{ - 12}},\frac{{5 \times 5}}{{ - 3 \times 5}} = \frac{{25}}{{ - 15}}$

Therefore, the equivalent fractions to the number \begin{align}\frac{5}{{ - 3}}\end{align}are,

\begin{align}\frac{{10}}{{ - 6}},\frac{{15}}{{ - 9}},\frac{{20}}{{ - 12}},\frac{{25}}{{ - 15}}\end{align}

\begin{align}{\rm{(iii)}}\frac{4}{9}\end{align}

Multiplying both numerator and denominator with the same number, we get

\begin{align}\frac{{4{\times2}}}{{9{\times2}}} = \frac{8}{{18}},\frac{{4{\times3}}}{{9{\times3}}} = \frac{{12}}{{27}},\quad \frac{{4{\times4}}}{{9 \times 4}} = \frac{{16}}{{36}},\frac{{4{\times5}}}{{9{\times5}}} = \frac{{20}}{{45}}\end{align}

Therefore, the equivalent fractions to the number \begin{align}\frac{4}{9}\end{align}are,

\begin{align}\frac{8}{{18}},\frac{{12}}{{27}},\frac{{16}}{{36}}\,{\rm{and}}\,\frac{{20}}{{45}}\end{align}

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