Rational Numbers between Two Rational Numbers


 
 
Concept Explanation
 

Rational Numbers between Two Rational Numbers

Rational Numbers between two Rational Numbers:

We will learn to insert rational numbers between two rational numbers. Let us recall integers and properties of various operations on them. We know between two non-consecutive integers x and y there are (x - y - 1) integers. However, there is no integer between two consecutive integers.

For example, between -7 and 7 there are 7 - (-7) - 1 = 7 + 7 - 1 = 14 – 1 = 13 integers. The integers are -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 and 6 but there is no integer between 2 and 3 since they are consecutive integers.

Thus, we find that between two given integers there may or may not lie any integer.

Example: Find out 100 rational numbers lying between -9/19 and 5/19.

Solution:

We have,

-9/19 = -9 × 10/19 × 10 = -90/190 and,

5/19 = 5 × 10/19 × 10 = 50/190

We know that

-90 < -89 < -88 < -87 < -86 < -85 < …….. < -25 < -24 < -23 < -22 < …….. < -1 < 0 < 1 < 2 < …….. < 9 < 10

⇒ -90/190 < -89/190 < -88/190 < -87/190 < -86/190 < -85/190 < …….. < -25/190 < -24/190 < -23/190 < -22/190 < …….. < -1/190 < 0/190 < 1/190 < 2/190 < …….. < 9/190 < 10/190

Hence, < -89/190 < -88/190 < -87/190 < -86/190 < -85/190 < …….. < -25/190 < -24/190 < -23/190 < -22/190 < …….. < -1/190 < 0/190 < 1/190 < 2/190 < …….. < 9/190 < 10/190 are the 100 rational numbers between -9/19 = -90/190 and 5/19 = 50/190.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

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

Right Option : D
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Explanation
Question : 2

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
Question : 3

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

Right Option : D
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Explanation
 
 
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