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### Answers (1)

(i) Answer.
$-\frac{11}{10}$, $-\frac{6}{5}$
and $-\frac{5}{4}$
Solution.

Any number which can be represented in the form of p/q, where q is not equal to zero, is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.

Between -1 and -2, many rational numbers can be written as:
$-1\cdot 1=-\frac{11}{10}$
$-1\cdot 2=-\frac{12}{10}= -\frac{6}{5}$
$-1\cdot 25=-\frac{125}{100}= -\frac{5}{4}$
$-1\cdot 3=-\frac{13}{10}$
$-1\cdot 4=-\frac{14}{10}= -\frac{7}{5}$

(ii) Answer: $\frac{103}{1000}$,$\frac{104}{1000}$,$\frac{105}{1000}$

Solution.
Any number which can be represented in the form of p/q, where q is not equal to zero, is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.

Between 0.1 and 0.11, many rational numbers can be written as:

0.103 = $\frac{103}{1000}$

0.104 = $\frac{104}{1000}$

0.105 = $\frac{105}{1000}$

(iii) Answer.          $\frac{51}{70},\frac{52}{70}$ and $\frac{53}{70}$
Solution.

Any number which can be represented in the form of p/q, where q is not equal to zero, is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.

We can write $\frac{5}{7}$as $\frac{5\times 10}{7\times 10}= \frac{50}{70}$  and $\frac{6}{7}$ as $\frac{6\times 10}{7\times 10}= \frac{60}{70}$
So, three rational number between $\frac{5}{7}and\frac{6}{7}$ are $\frac{51}{70},\frac{52}{70}$ and $\frac{53}{70}$

(iv) Answer. $\frac{41}{200},\frac{42}{200},\frac{43}{200}$

Solution.

Any number which can be represented in the form of p/q, where q is not equal to zero, is a rational number. Also, both p and q should be rational when the fraction is expressed in the simplest form.

L.C.M. of 4 and 5 is 20.
We can write   $\frac{1}{4}$ as $\frac{1\times 40}{4\times 50}= \frac{50}{200}$
and                  $\frac{1}{5}\, as\, \frac{1\times 40}{5\times 40}= \frac{40}{200}$

So, three rational number between $\frac{1}{4}\, and\,\frac{1}{5}$ are

$\frac{41}{200},\frac{42}{200},\frac{43}{200}$

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