How to win against queen with queen+rook, avoiding the draw with multiple checks I recently played the game where I was playing black and during end game I had queen and rook remaining and white had queen and two pawns.

I thought since I had more material, it would be easy for me to win the game but white kept checking me with his queen which left me with no option to sacrifice the rook to avoid draw. But this action got me in a position of losing but fortunately I managed to escape with a draw.

https://www.chess.com/livechess/game?id=2183712648.

[FEN ""]  
[Event "Live Chess"]
[Site "Chess.com"]
[Date "2017.07.02"]
[White "rasimibrahimoqlu"]
[Black "111YearsOld"]
[Result "1/2-1/2"]
[ECO "B40"]
[WhiteElo "1229"]
[BlackElo "1101"]
[TimeControl "900+10"]
[EndTime "4:11:48 PDT"]
[Termination "Game drawn by stalemate"]
[CurrentPosition "7k/7P/5PK1/8/8/8/8/8 b - - 0 71"]

1.e4 e6 2.Nf3 c5 3.d4 Qc7 4.Bd3 h6 5.O-O a6 6.Re1 d6 7.d5 Bd7 8.dxe6 Bxe6 9.e5 b5 10.c4 b4 11.Bf4 d5 12.cxd5 Bxd5 13.Nbd2 Nc6 14.Ne4 O-O-O 15.Qc1 f6 16.Bxa6+ Kb8 17.Nxc5 Bxc5 18.Qxc5 fxe5 19.Qb5+ Ka7 20.Rac1 exf4 21.Nd4 Nge7 22.Rxe7 Qxe7 23.Nxc6+ Bxc6 24.Qxc6 Rd7 25.h3 Rhd8 26.Qa4 Rc7 27.Be2+ Kb8 28.Bf3 Rxc1+ 29.Kh2 Qa7 30.Qxb4+ Kc8 31.Bg4+ Rd7 32.Qxf4 Rc7 33.Qf8+ Kb7 34.Qb4+ Qb6 35.Qe4+ Ka7 36.Qa4+ Kb8 37.Bxd7 Qd6+ 38.g3 Qxd7 39.Qb4+ Kc8 40.a4 Rb7 41.Qf8+ Kc7 42.b4 Qxa4 43.Qxg7+ Kb6 44.Qxh6+ Ka7 45.Qe3+ Rb6 46.h4 Qxb4 47.g4 Qxg4 48.Qe7+ Ka8 49.Qd8+ Rb8 50.Qa5+ Kb7 51.Qb5+ Kc8 52.Qc6+ Kd8 53.Qd6+ Kc8 54.Qc6+ Kd8 55.Qd6+ Qd7 56.Qxb8+ Ke7 57.Qe5+ Qe6 58.Qg5+ Kd7 59.Qg7+ Kd6 60.Qg3+ Kd7 61.f4 Qe2+ 62.Kh3 Qe6+ 63.Qg4 Qxg4+ 64.Kxg4 Ke6 65.Kg5 Kf7 66.h5 Kg7 67.f5 Kh7 68.h6 Kh8 69.Kg6 Kg8 70.f6 Kh8 71.h7  1/2-1/2  


How could I have won this endgame?
In general, if you are materially superior, you should try to trade down into a winning ending. Your extra rook in this situation against your opponent's queen and two unconnected pawns should normally have been enough for you to win.  Unfortunately, in your game the queen was too far away to help support your rook, and you had to permit a draw on moves 52 through 55 by triple repetition. Giving up your rook instead at that point should have ultimately led to a lost king and pawn ending for you after you allowed the queen trade.  You were fortunate to get the draw then.  Your taking the "g" pawn on move 47 led to that particular situation.