Question

20. Find three rational numbers between - 1 and -2? ​

Answer 1

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The rational number between -1 and -2 is

$\frac{ -1 - 2 }{2} = \frac{ - 3}{2}$

The rational number between -1 and -3/2 is

$\frac{ - 1 - \frac{3}{2} }{2} = \frac{ \frac{ -2 - 3 }{2} }{2} = \frac{ \frac{ -5 }{2} }{2} = \frac{ -5 }{4}$

The rational number between -1 and -5/4 is

$\frac{ -1 - \frac{ - 5}{4} }{2} = \frac{\frac{ - 4 - 5}{4} }{2} = \frac{ - 9}{8}$

Therefore the 3 rational numbers between -1 and -2 are :

$\frac{ - 3}{2} \: and \: \frac{ -5 }{4} \: and \: \frac{ - 9}{8}$

Answer 2

To find:

• Three rational numbers between - 1 and - 2.

Step-by-step explanation:

We can solve this question by 2 methods.

Let's solve the given question by understanding it...

Method 1:

Mean method :- (a+b)/2

Here

a = -1, b = -2

1st rational = (-1-2)/2 = -3/2

a = -1 ,b = -3/2

2nd rational =[-1+(-3/2)]/2

[(-2-3)/2]/2 = (-5/2)/2 = -5/4

a = -1 , b = -5/4

3rd rational = [-1+(-5/4)]/2

[ (-4-5)/4]/2

(-9/4)/2

-9/8

Three rational numbers between - 1 and - 2 are are -3/2, -5/4 , - 9/8.

Method 2:

Given numbers = -1 and -2

Required rationals = 3

Writting the denominator as (3+1) = 4

- 1 = -1 × (4/4) = -4/4

- 2 = -2 × (4/4) = -8/4

The rationals between -1 = -4/4 and -2 = -8/4

The rationals between -1 = -4/4 and -2 = -8/4They are -5/4, -6/4, -7/4.

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