Rev Matching: Here is why you should do it.
It not only makes your driving smoother, it also helps you have quicker and smoother shifts, which helps not only performance but fuel economy as well, it also reduces wear on the transmission’s synchros and the clutch.
It’s all about matching the engine rpm to the gear and speed you’re in while shifting, this applies for both down and up shifting. For the first, you should increase engine rpm to match the shorter gearing you’re shifting into. For the latter, you should decrease engine speed to match the longer gear you’re selecting.
A detailed explanation can be found in the video below.