Let the number be x.
According to the given question,
5/2x + 2/3 = 7/12
On transposing 2/3 to R.H.S, we obtain
5/2x = -7/12 -2/3
5/2x = -7-(-2 x 4)/12
5/2x = -15/12
On multiplying both sides by 2/5, we obtain
x = -15/12 x 2/5 = -1/2
Hence, the rational number is -1/2