Question

find three rational numbers between -2 and -1

Answer 1

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Let see your answer !!!

- 2 and - 1

n + 1 = 3 + 1 = 4 (denominator)

- 2 = - 8/4

- 3 = - 12/4

3 rational numbers between - 2 and - 1 are -9/4 ; -10/4 and -11/4.





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Answer 2

SOLUTION :

Use the concept that three  rational numbers between x and y are (x+d), (x+2d) and (x+3d) where $\bf d=\frac{y-x}{n+1}, x<y \:\:and\:\: n =3$

Method 1

Let y = -1 and x = -2

Here

x < y and we have to find three rational numbers, so n = 3

∵   $\bf d=\frac{y-x}{n+1}=\frac{-1+2}{3+1}=\frac{1}{4}$

Since,

The three rational numbers between x and y are (x+d), (x+2d) and (x+3d)

now,

$\bf x+d =-2+\frac{1}{4}=\frac{-8+1}{4}=\frac{-7}{4}$

$\bf x+2d =-2+\frac{2}{4}=\frac{-8+2}{4}=\frac{-6}{4}=\frac{-3}{2}$

$\bf x+3d =-2+\frac{3}{4}=\frac{-8+3}{4}=\frac{-5}{4}$

Hence,

Three rational number between -1 and -2 are $\frac{-7}{4},\:\frac{-3}{2},\:\frac{-5}{4}$

Method 2

Let,

x = -1 and y = -2

we know, a rational number between x and y = $\bf \frac{x+y}{2}$

a rational number between -1 and -2 = $\bf \frac{- 1 - 2}{2}=\frac{-3}{2}$

and a rational number between -1 and $\bf \frac{-3}{2}$ = $\bf \frac{-1-\frac{3}{2}}{2}=\frac{-2-3}{4}=\frac{-5}{4}$

similarly

$\bf \frac{-7}{4}$ is a rational number between -1 and -2

Hence,

required solution = $\frac{-3}{2},\:\frac{-5}{4},\:\frac{-7}{4}$