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The B Minor melodic is different from some of the other scales, because it has different notes when you come back down the scale than it does when you go up the scale. The notes going up are B, C sharp, D, E, F sharp, G sharp, A sharp, and the return to B. Coming down from that second B the notes are A, G, F sharp, E, D, C sharp and back to B.
The right hand fingering for the scale starts on the thumb. When your third finger hits the D key, bring your thumb under and hit the E. From there, continue on until your pinky hits the B key. Coming down don't forget to hit the A key instead of the A sharp. Then the G instead of the G sharp. Now things are the same as they were going up. When your thumb hits the E, bring your third finger over and use it to hit the D.
The left hand starts off with the fourth finger on the B. The thumb will land on the E and you will bring your fourth finger over to hit the F sharp. You will finish with your thumb on the B. Coming down, don't forget to hit the A key and the G key. When your fourth finger gets back to the F sharp, cross your thumb under and finish the scale.
Next, you should check out the some basic piano time signatures.