Sorry, I can't look at my phone often because I am studying.
Sorry, I can't talk much, I am busy studying for my entrance exam.
It is polite to start with an apology just to clarify that you actually can't pay too much attention to your phone at this time. We do say we can't look at our phone because most we are getting notifications all the time on smart phones. If someone is trying to talk to you then you can change this to "I can't talk much".
今現在スマホを気にする事があまりできない事を、
最初に謝ると丁寧ですね。
スマホに通知が表示されるので
"We can't look at our phone"
(スマホを見ることが出来ない）
と言う事も出来ます。
誰かがあなたに話しかけようとしてきたら
"I can't talk much"
（あまり話せません）
と言う風に変えることも出来ます。
I don't check my phone much these days 'cause I'm studying for my entrance exam
Don't expect a quick reply these days as I'm studying for my entrance exam
Because I'm studying you can send a text but don't expect a quick response
Of course, some things are more important than casual text messages to friends! In fact most things are more important than text messages to friends - so we all need to get our priorities right, don't we? An entrance exam is a life-changing moment and you should quite rightly relegate your friends to 2nd or 3rd or 95th place in your list of priorities!
My apologies for taking so long to reply. I am busy studying and not paying a lot of attention to my phone.
▪ My apologies for taking so long to reply. I am busy studying and not paying a lot of attention to my phone.
By saying apologies is being polite. In the sentence you are saying sorry and also giving a reason why you do not reply quickly.
Example
Friend: Why do you take so long to reply?
You: My apologies for taking so long to reply. I am busy studying and not paying a lot of attention to my phone.
▪ My apologies for taking so long to reply. I am busy studying and not paying a lot of attention to my phone.
返信に時間がかかってごめんなさい。一生懸命勉強していて、携帯を見ないようにしているの。
apologiesということで、失礼でない態度を表します。この文は、謝ると同時に、なぜ返信が遅いのかを説明しています。
例：
Friend: Why do you take so long to reply?
友人：どうしてそんなに返信に時間がかかるの？
You: My apologies for taking so long to reply. I am busy studying and not paying a lot of attention to my phone.
あなた：返信に時間がかかってごめんなさい。一生懸命勉強していて、携帯を見ないようにしているの。
I am so busy studying for my entrance exam that I don't have time to check my phone for messages.
I am focusing so much on my entrance exam that I hardly find time to check on my phone messages.
When someone is studying hard to pass an entrance exam, that person will definitely be focusing on his/her studies. It becomes difficult for that person to divert his/her attention to the phone just to check on messages. So, what gains priority here is studying for the entrance exam and not phone messages.
So, you may say:
I am so busy studying for my entrance exam that I don't have time to check my phone for messages.
or
I am focusing so much on my entrance exam that I hardly find time to check on my phone messages.
受験勉強中は間違いなくそこに集中していますよね。電話のメッセージを確認するのも難しくなります。携帯のメッセージより受験勉強ですね。
I am so busy studying for my entrance exam that I don't have time to check my phone for messages.
（受験勉強で忙しくて、携帯のメッセージを確認する暇がありません）
I am focusing so much on my entrance exam that I hardly find time to check on my phone messages.
（受験勉強に集中しているから、携帯のメッセージを確認する時間はほとんどありません）
I'm sorry I can't respond to messages on my phone, I am studying for my entrance exam.
I apologize but I will have to wait to chat with you after I pass the entrance exam. I need to study right now.
Passing my entrance exam is very important so please let me study and we will catch up later.
I'm sorry I can't respond to messages on my phone, I am studying for my entrance exam.
I apologize but I will have to wait to chat with you after I pass the entrance exam. I need to study right now.
Passing my entrance exam is very important so please let me study and we will catch up later.
Sorry I am studying right now and will talk to you later.
I will be turning my phone off in order to study but we can talk later on.
I'm sorry I can't respond to messages on my phone, I am studying for my entrance exam.
（携帯のメッセージの返信ができなくてごめん。入試に向けて勉強しているんだ。）
I apologize but I will have to wait to chat with you after I pass the entrance exam. I need to study right now.
（申し訳ないけど、入試に合格するまでおしゃべりできそうにない。今は勉強しないといけないんだ。）
Passing my entrance exam is very important so please let me study and we will catch up later.
（入試に合格するのがとても重要だから、勉強させて。あとで連絡とろう。）
Sorry I am studying right now and will talk to you later.
（ごめん今勉強しているんだ。あとで話そう。）
I will be turning my phone off in order to study but we can talk later on.
（勉強するために携帯の電源をきるけど、後で話そう。）
I'm sorry I'm not on my phone so much as I have to study
"I'm going off the grid"
This expression is used to imply that you are either not on your phone/using your phone and are unable to use it due to location or not being able to access it.
"I'm sorry I'm not on my phone so much as I have to study"
The expression 'On my phone' implies that you are using something, ex. "I'm on the laptop at the moment".
"I'm going off the grid"
（つながらなくなります）
これは、場所やアクセスなどで電話がつながらなくなることを意味します。
"I'm sorry I'm not on my phone so much as I have to study"
（勉強しないといけないから、そんなに電話が使えなくなってごめんね。）
'On my phone'とは、何かを使っているという意味です。
例："I'm on the laptop at the moment".
（今ラップトップを使っています。）
I'm sorry I keep missing your calls/texts. I'm preparing for my entrance exams, so I don't look at my phone much.
I'm not on my phone as much lately because I am studying for my entrance exam. Sorry, friend.
When you want to explain to your friend that you're too busy to be on your phone all the time because you're studying for your entrance exam; then you may explain this in the following ways:
-I'm sorry I keep missing your calls/texts. I'm preparing for my entrance exams, so I don't look at my phone much.
-I'm not on my phone as much lately because I am studying for my entrance exam. Sorry, friend.
受験勉強が忙しくてあまり携帯を見ていないなら、それは次のように説明できます。
-I'm sorry I keep missing your calls/texts. I'm preparing for my entrance exams, so I don't look at my phone much.
（電話に出られず／メールを返信できずごめんなさい。受験勉強をしているので、あまり携帯を見ていないんです）
-I'm not on my phone as much lately because I am studying for my entrance exam. Sorry, friend.
（受験勉強をしているので、最近あまり携帯を見ないんです。ごめんなさい）
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