Question

find a rational number between : a) - 5 and - 6 b) - 8/11 and - 7/11 c). - 4/5 and 4/5 d) 5/14 and 9/14​

Answer 1

Answer:

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Answer

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• -5 and -6 :--

Here ,

Let x = -5 and let y = -6

So, the required rational number lying between x and y is :

=> 1/2 × [-5+(-6)]

=> 1/2 × (-5-6]

=> 1/2 × (-11)

=> $\boxed{-11/2}$ {answer}

• -8/11 and -7/11 :--

Here ,

Let x = -7/11 and Let y = -8/11

So, the required rational number lying between x and y is :

=> 1/2 × [-7/11 + (-8/11)]

=> 1/2 × (-15/11)

=> $\boxed{-15/22}$ {answer}

• -4/5 and 4/5 :--

Here ,

Let x = -4/5 and Let y = 4/5

So, the required rational number lying between x and y is :

=> 1/2 × (-4/5 +4/5)

=> 1/2 × 0/5

=> $\boxed{0/10}$ {answer}

• 5/14 and 9/14 :--

Here,

Let x = 5/14 and let y = 9/14

So, the required rational number lying between x and y is :

=> 1/2 × (5/14 + 9/14)

=> 1/2 × ( 14/14)

=> 1/2 × 1/1

=> $\boxed{1/2}$ {answer}

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Formula Used Here

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• So , let x and y be any two rational number , in which x < y.

Then to find a single (one) rational number lying between them , use the following formula :

=> 1/2 (x+y)

And to find many rational number (let it be n) , use the following formula :

Let d = (y-x) / (n+1)

So , the n rational number will be

(x+d) , (x+2d) , ...(x+nd)