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  • (i)Find three rational numbers between – 1 and – 2.

(i) Find three rational numbers between – 1 and – 2

(ii) Find three rational numbers between 0.1 and 0.11
(iii) Find three rational numbers between \frac{5}{7} and \frac{6}{7}
(iv) Find three rational numbers between \frac{1}{4} and \frac{1}{5}

Answers (1)

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(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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