This is the 582nd most frequent Turkish word.
söyleyerek
"By saying" or "by telling."
In this sentence, 'söyleyerek' means 'by saying' or 'by telling,' indicating how the action of warning was performed.
O, bana yavaş konuşmamı söyleyerek beni uyardı.
He warned me by telling me to speak slowly.
Here, 'söyleyerek' implies that the act of saying or advising was the manner in which the farewell was expressed.
Annem, evden çıkarken dikkatli olmamı söyleyerek vedalaştı.
My mother said goodbye by telling me to be careful as I left the house.
In this context, 'söyleyerek' describes the means by which the conclusion of the lesson took place, emphasizing communication.