Question

Insert 3 equivalent rational numbers between `(-1)/2` and `1/5`

Answer 1

We convert the rational numbers `(-1)/2` and `1/5` into rational numbers with same denominator.

`(-1)/2 = (-1 xx 5)/(2 xx 5) = (-5)/10` and `1/5 = (1 xx 2)/(5 xx 2) = 2/10`

The rational numbers between `(-5)/10` and `2/10` are

`(-4)/10, (-3)/10, (-2)/10, (-1)/10, 1/10`.

Consider, `(-2)/10`

Three equivalent rational numbers of `(-2)/10` are 

`(-2 xx 2)/(10 xx 2) = (-4)/20, (-2 xx 3)/(10 xx 3) = (-6)/30` and `(-2 xx 4)/(10 xx 4) = (-8)/40`

∴ 3 equivalent rational numbers between

`(-1)/2 and 1/5` are `(-4)/20, (-6)/30 and (-8)/40`.