Question

Find three rational numbers between -1/2 and -1/4 step by step

Answer 1

Step-by-step explanation:

Given:-

The two numbers = -1/2 and -1/4

To find :-

Find three rational numbers between them ?

Solution :-

Given numbers are -1/2 and -1/4

Method-1:-

We know that Mean Method

The rational number between a and b is (a+b)/2

Finding first rational number :-

Let a = -1/2 and b = -1/4

The rational number between them

=> [(-1/2)+(-1/4)]/2

LCM of 2 and 4 = 4

=>[{(-2)+(-1)}/4]/2

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

=> -3/(4×2)

=> -3/8

Finding Second rational number :-

Let a = -1/2 and b = -3/8

The rational number between them

=>[(-1/2)+(-3/8)]/2

LCM of 2 and 8 = 8

=> [{(-4)+(-3)}/8]/2

=> (-7/8)/2

=> -7/(2×8)

=> -7/16

Finding third rational number :-

Let a = -1/2 and b = -7/16

The rational number between them

=> [(-1/2)+(-7/16)]/2

=> [{(-8)+(-7)}/16]/2

=> (-15/16)/2

=> -15/(16×2)

=> -15/32

The rational numbers = -3/8,-7/16,-15/32

Method -2:-

Given numbers are -1/2 and -1/4

-1/2 = (-1/2)×(2/2) = (-1×2)/(2×2) = -2/4

Required rational numbers = 3

On writting the denominator as (3+1) = 4 multiple

(-2/4)×(4/4) =-8/16

and

(-1/4)×(4/4) = -4/16

The rational numbers between-8/16 and -4/16 are -5/16, -6/16 , -7/16

Answer:-

1) The three rational numbers between the two given numbers are -3/8 , -7/16 , -15/32 by mean method

2) The three ratioal numbers between the two given numbers are -5/16, -6/16 , -7/16 by general method

Used formulae:-

Mean Method :-

• The rational number between a and b is (a+b)/2

Points to know:-

• There are infinitely number of rational numbers between two numbers. This is called Densitive Property of rational numbers.