It is really common to say gently denying compliments or switch the topic in Japan. Few Japanese people accept or say “arigato” to the compliment. It would come from Japanese humbling culture.
ex)
A: Suteki na dan’na san desu ne.
“Your husband is so nice/beautiful.”
B: Iiee, uchi de ha itsumo nete bakari nan desu.
“No~. He always sleeps at home.(so he is not such a guy.)”
C: Kawaii kaban desu ne!
“Your bag is cute!”
D: Honto? kore yasukatta no!
“Really? But this was cheep.”
Please don’t get angry even if your Japanese friends react to your compliment like these. That means they appreciate your comment but they are too shy to accept it.

アヰアンさん
We often say 大事なところで　and お忙しいところ like this;
(仕事の)大事なところで、ミスをした。　
“(As work,)I made a mistake when it is important.”
危ないところを助けてもらった。
“I was rescued when I was in danger.”
お忙しいところをありがとうございます。
“Thank you for sparing your precious time with me.”
お仕事中のところをすみません。
“I’m sorry to bother you when you are busy.”
I hope this helps.

for example, what is the difference between 忙しいです and　忙しいところです?

Does anyone have some more example sentences for “tokoro” (the final usage)?

Seriously, I think Yoshi is the coolest. I want to hang out with him while living in Tokyo this summer.

For example, when you say “I am in the middle of baking a cake” this to me means that right before answering the phone, you were adding ingredients to the cake or something similar. If you were to say simply “I am baking a cake” that sounds more as if you’ve finished adding ingredients to the cake and are simply letting it cook in the oven while doing other things.

Same with “I am in the middle of doing homework”. This means right before answering the phone you were doing some homework. “I am doing homework” implies before picking up the phone you might have been having a coffee or something before continuing to do homework. Your main task is still the homework but you not actually focusing on it intently right now.

I hope that makes some sense

Thank you for great explanation! 　You are correct that when you have a phone call when you are baking a cake, you can use “tokoro” like “ケーキをやいていたところです”. I have a question about English. Can you say “I’m baking a cake” in the same situtaion or use a different expression?

“I’m baking a cake”
“I’m in the middle of baking a cake”

The second phrase, like ところ, indicates a figurative location (unless you’re in the cake…) I think the nuance is that the action isn’t just occuring, you’re entirely wrapped up in it, it’s on-going, even if you broke away from your project to greet guests or answer the phone, you are going to probably go back to that cake baking.

The first line is almost like stating what is literally going on–you’re mixing the batter as we speak, you’re sticking the pan in the oven, etc.

I don’t know how if this is really true, but in my head this is how I understand ところ in this manner.

今はしている –> I am doing it now.
今はしているところ –> I am in a state of doing it now.

Technically, it means the same thing. But the second one seems to emphasize on the state of doing it.

I don’t understand what the difference would be between between
ima ha shiteiru and
ima ha shiteiru tokoro

they both mean, doing now.

Is this right? Am i Crazy?