Both phrases are casual ways to say that you are going to work late or leaving work early. It is commonly used between people.
A half day: implies that you will be working half the time and not the full normal working hours that you usually do as you will be having a mini holiday.
Hope this helps!
どちらも、カジュアルな言い方です。[仕事](https://eikaiwa.dmm.com/uknow/questions/37171/)に遅れて行くこと、または仕事を早めに終えることを表します。よく使われます。
A half day: 通常の勤務時間ではなく、半分の時間働くという意味合いです。ちょっとした[休暇](https://eikaiwa.dmm.com/uknow/questions/35037/)を取るということです。
参考になるといいです！
In the UK, in British English, we would call this 'taking the morning off' or 'taking the afternoon off'. This is because it is the shortened and casual way of saying 'taking the morning off work', or 'taking the afternoon off work'.
イギリス、イギリス英語では、「taking the morning off (午前中休む)」または「taking the afternoon off (午後休む)」と言います。これは「taking the morning off work」「taking the afternoon off work」を短くカジュアルに言ったものです。
Either you take the morning off or the afternoon off you can just say, "I'm taking a half day." It just means you are taking half of a day for self care or for errands.
午前休んでも午後休んでも「I'm taking a half day」と言えます。「(セルフケアや用事で) 半日休みます」という意味になります。
When you want to talk about having taken half a day off work, then you can use the following phrases:
-Half-day
-take the morning/afternoon off
For example, you can say:
-Today, I want to take the afternoon off because I have a doctor's appointment
-I am planning to work half-day on Friday because I have a doctor's appointment.
半日仕事を休んだことを言う場合は、次のフレーズが使えます。
【例】
-Half-day
（半日）
-take the morning/afternoon off
（午前休み/午後休みを取る）
例えば、次のように言うことが出来ます。
【例文】
-Today, I want to take the afternoon off because I have a doctor's appointment
（今日、医者の予約があるので、午後休みをとりたいです）
-I am planning to work half-day on Friday because I have a doctor's appointment
（医者の予約があるので、金曜日は半日働くつもりです）
Just sleep in this morning. You can come back to work tomorrow when you feel better.
When you take off work:
Casual: I'll be free this afternoon.
I'm off this morning.
I'm off this afternoon.
Formal: I'll need to take off all morning. My child has the flu.
I can work the morning shift but I can't work the evening shift because my kids will be home from school.
I can work the evening shift but in the morning I'm busy.
When your manager says you can take off:
Sleep in this morning. You can come back to work tomorrow when you feel better.
Just take the morning off so you can get better faster.
仕事を休むとき：
（カジュアル）
I'll be free this afternoon.
今日の午後は休みだ。
I'm off this morning.
午前は休みだ。
I'm off this afternoon.
午後は休みだ。
（フォーマル）
I'll need to take off all morning. My child has the flu.
午前中は休まないといけません。子供がインフルエンザにかかりました。
I can work the morning shift but I can't work the evening shift because my kids will be home from school.
午前のシフトはできますが、子供が学校から帰ってくるので、夜勤はできません。
I can work the evening shift but in the morning I'm busy.
夜勤はできますが、午前中は忙しいです。
マネジャーが休んでいいと言うとき：
Sleep in this morning. You can come back to work tomorrow when you feel better.
今朝はゆっくり寝て。気分がよくなったら、明日仕事に戻ってきて。
Just take the morning off so you can get better faster.
早く良くなるように、午前中は休みなさい。
Why don't you take the rest of the day off? (I can manage alone)
You go home and rest up today. I'll take care of things here.
In the situation where you are asking or telling someone to go home and relax for the rest of the day, the reason why you are saying this is important. Has this person been working badly? Is he or she a liability to the company? Or have they been working very hard recently and you think they deserve a well-earned rest? The situation always dictates the type of language that is used.
こんにちは。
様々な言い方ができると思いますが、例えば下記のような表現はいかがでしょうか：
・take the morning off
午前を休む
・take the afternoon off
午後を休む
take ... off で「〜を休む」と言うことができます。
take the day off なら「1日休む」となります。
ぜひ参考にしてください。
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