Question

Find four rational numbers between (i) -1 and
-1/2

(ii) 3/4 and 2/3​

Answer 1

Answer:-

i) -6/10, -7/10, -8/10, and -9/10.

ii) 41/60, 42/60, 43/60 and 44/60.

Answer 2

-1 and -1/2

let the four rational numbers between them be : q_1 , q_2 , q_3 and q_4

therefore, -1 , q_1 , q_2, q_3 ,q_4 , -1/2

for q_1,

1/2(-1 + (-1/2)

1/2 (-1 -1/2 )

now taking the LCM of (-1 -1/2)

1/2(-3/2)

-3/4

q_1 = -3/4

now , -1 , -3/4 , q_2 , q_3 , q_4 , -1/2

for q_2,

1/2( -3/4 + ( -1/2)

1/2 (-3/4 -1/2)

now taking the LCM of (-3/4 - 1/2)

1/2( -5/4)

-5/8

q_2 = -5/8

now, -1 , -3/4 ,-5/8 , q_3 ,q_4 , -1/2

for q_3,

1/2(-5/8 + ( -1/2)

1/2 (-5/8-1/2)

now taking the LCM of (-5/8-1/2)

1/2( -9/8)

-9/16

q_3 = -9/16

now, -1 , -3/4 , -5/8 , -9/16 , q_4 , -1/12

for q_4,

1/2 ( -9/16+(-1/12)

1/2(-9/16-1/12)

now taking the LCM of ( -9/16-1/12)

1/2(-29/64)

-29/128

q_4 = -29/128

therefore , four rational numbers are -3/4 , -5/8 ,-9/26 , -29/128

see answers may vary as their are many methods to do so.

you can do the next one by yourself as the concept to do others are same

I hope this will help you out........