Net force and Newton's laws
Add the forces as vectors first, because it is the net force, not any single force, that equals mass times acceleration.
A worked example
An 8.0 kg crate pushed with 50 N against 14 N of friction has a net force of 36 N, so a = 36 / 8.0 = 4.5 m/s squared.
The mistake people actually make
Weight in newtons is mg, not the mass in kilograms. A third law pair acts on two different objects, so gravity and the normal force on the same book are not a pair.