Rational Numbers between Two Rational Numbers


 
 
Concept Explanation
 

Rational Numbers between Two Rational Numbers

Rational Numbers between Two Rational Numbers:

Rational numbers between two given rational numbers, that there are countless rational numbers between any two given rational numbers. This property of rational numbers is known as the dense property.

Suppose we wish to find two rational numbers between large frac{3}{7} and large frac{6}{7}. Since these two numbers have the same denominator. So, we choose their numerators 3 and 6. Integers between 3 and 6 are 4 and 5. Therefore, large frac{4}{7} and large frac{5}{7} are two rational numbers between large frac{3}{7} and large frac{6}{7} such that

           large frac{3}{7}< frac{4}{7}< frac{5}{7}< frac{6}{7}

Example:  Write any three rational numbers between -2 and 0.

Solution     We can write

                     large -2=frac{-2}{1}=frac{-2times 5}{1times 5}=frac{-10}{5} and large 0=frac{0}{5}

Integers between -10 and 0 are -9, -8, -7, -6, -5,...,-1.

large therefore     large frac{-9}{5},frac{-8}{5},frac{-7}{5},....,frac{-2}{5},frac{-1}{5}  are rational numbers between -2 and 0.

We can choose any three of these rational numbers.

Sample Questions
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Question : 1

A rational number between frac{1}{4};;and;; frac{1}{3} is  

Right Option : D
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Question : 2

A rational number between large dpi{100} frac{1}{4} and   large frac{1}{3} is:

Right Option : D
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Explanation
Question : 3

Choose the rational number which does not lie between rational numbers -frac{2}{5};;and;;-frac{1}{5}

Right Option : C
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Explanation
 
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