-(으)면서 has two meanings.
The first meaning is ‘during/while’ which two actions happen at the same time. For example,
밥을 먹으면서 TV를 봤어요. I watch TV while I was eating.
음악을 들으면서 공부를 해요. I study while I am listen to music.
요리를 하면서 많이 먹어요. I eat a lot during cooking.
인터넷을 하면서 길을 걸으면 안 돼요. You should not walk while you are using the internet.
운전하면서 핸드폰을 보지 마세요. 정말 위험해요.Do not look at your phone while you are driving. It is dangerous.
제 아내는 자면서 이야기를 해요. My wife talks while she is sleeping.
그 사람이 울면서 말했어요. That person talked while he was crying.
The second meaning is ‘yet, though’ which two opposite actions happen at the same time. Often we add -도 after 으면서 to emphasize the comparison. For example,
돈이 없으면서(도) 돈이 있는 것처럼 행동합니다. Someone acts like he/she has money even though he/she doesn’t have money.
아무것도 모르면서(도) 다 아는 것처럼 말하지 마세요. Do not say like you know everything, yet you don’t know anything.
요리는 안 하면서(도) 먹기만 해요. Someone just eats although he/she doesn’t cook.
-(으)며 also has two meanings.
The first meaning is the same as -(으)면서 which is ‘while/during’ but a little formal. And the second meaning is the same as -고 which is ‘and’. For example,
음악을 들으며 운동을 하고 있습니다. (=들으면서) Someone is working out while listening to music.
그림을 그리며 노래를 했습니다. (=그리면서) Someone sang songs while someone was drawing.
그 사람은 피아노를 치며 노래를 불렀다. (=치면서) That person sang songs while he was playing piano.
서울은 한국의 수도이며 경제의 중심입니다. (=수도이고) Seoul is the capital of South Korea and the center for finance.
그 사람은 피아노도 잘 치고 기타도 잘 치며 노래도 잘합니다. (=치고) That person plays piano, plays guitar and sings songs very well.
제 조카는 공부도 잘하고 춤도 잘 추며 운동도 잘합니다. (=추고) My niece is good at studying, dancing, sports.
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