Sumimasen (すみません - Sorry/Thanks)

Japanese people often say すみません (sumimasen) when they want to express their feelings of apology or appreciation.

"Sumimasen" is a polite form of すまぬ (sumanu), and "sumanu" is composed of the verb 済む (sumu) and the negative word ぬ (nu).

Here, "sumu" originally means "to be finished" or "to be solved," and it can also mean "to feel cheerful" or "to feel comfortable."

That is to say, "sumimasen," the negative form of "sumu," means that "you don't feel cheerful."

If you bring trouble to someone, or are helped by someone while taking much time, your feeling won't be cheerful/comfortable.

Because of this, "sumimasen" has come to be used to express the feeling of apology or appreciation.

すみません

日本では、謝罪や感謝の気持ちを表す時、よく「すみません」と言います。

「すみません」は「すまぬ」の丁寧な形で、「すまぬ」は動詞「済む」に打ち消しの「ぬ」がついた言葉です。

ここで「済む」は、「仕事が終わる」「物事が解決する」のような意味で、「気持ちがはれる」「気持ちが安らぐ」などを意味することもあります。

すなわち、「済む」の否定である「すみません」は、「気持ちがはれない」ことを意味します。

誰かに迷惑をかけたり、手間を大いにかけて助けてもらったら、あなたの気持ちははれず、満足もできないと思います。

このことから、「すみません」は謝罪や感謝の気持ちを表す際に利用されるようになりました。

• Japanese people often say すみません (sumimasen) when they want to express their feelings of apology or appreciation.
• Japanese people often say すみません (sumimasen) when they want to express their apologetic or appreciative feelings.

• "Sumimasen" is a polite form of すまぬ (sumanu), and "sumanu" is composed of the verb 済む (sumu) and the negative word ぬ (nu).
• This sentence is perfect! No correction needed!

• Here, "sumu" originally means "to be finished" or "to be solved," and it can also mean "to feel cheerful" or "to feel comfortable."
• This sentence is perfect! No correction needed!

• That is to say, "sumimasen," the negative form of "sumu," means that "you don't feel cheerful."
• That is to say, "sumimasen," the negative form of "sumu," means that you don't feel cheerful.

  The removal of quotation marks depends. Does the SPEAKER not feel cheerful, or the listener?
  
  If the speaker does not feel cheerful, the correct sentence is as I've written above. If the listener does not feel cheerful, the correct sentence is:
  
  That is to say, "sumimasen," the negative form of "sumu," means, "You don't feel cheerful."

• If you bring trouble to someone, or are helped by someone while taking much time, your feeling won't be cheerful/comfortable.
• If you trouble someone, or someone helps you at their own expense, you are not cheerful/comfortable.

• Because of this, "sumimasen" has come to be used to express the feeling of apology or appreciation.
• This is why "sumimasen" has come to be used to express feelings of gratitude or remorse.

Toru san, how about :

かたじけない
恐れ入ります
お言葉に甘えて

• Sumimasen (すみません - Sorry/Thanks)
• This sentence is perfect! No correction needed!

• Japanese people often say すみません (sumimasen) when they want to express their feelings of apology or appreciation.
• This sentence is perfect! No correction needed!

• "Sumimasen" is a polite form of すまぬ (sumanu), and "sumanu" is composed of the verb 済む (sumu) and the negative word ぬ (nu).
• This sentence is perfect! No correction needed!

• Here, "sumu" originally means "to be finished" or "to be solved," and it can also mean "to feel cheerful" or "to feel comfortable."
• This sentence is perfect! No correction needed!

• If you bring trouble to someone, or are helped by someone while taking much time, your feeling won't be cheerful/comfortable.
• If you bring trouble to someone, or are take too much time to be helped by someone while taking much time, your feeling won't be cheerful/comfortable.

• Because of this, "sumimasen" has come to be used to express the feeling of apology or appreciation.
• This sentence is perfect! No correction needed!

• That is to say, "sumimasen," the negative form of "sumu," means that "you don't feel cheerful."
• This sentence is perfect! No correction needed!

• Because of this, "sumimasen" has come to be used to express the feeling of apology or appreciation.
• This sentence is perfect! No correction needed!

Your English is amazing, Toru! Great job! :D