What does it mean: 'carried on'? Is it an idiom?

[Lirlik]

Test No. errors/inter-14 "Great expections when you are so carried away", question 9

Dave is so carried on with it all that he's put the baby's name down for a very expensive private boys' school.

(a) on
(b) put
(c) down

Test No. errors/inter-14 "Great expections when you are so carried away", answer 9

Dave is so carried away with it all that he's put the baby's name down for a very expensive private boys' school.

Correct entry: away
The error was: (a) on
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What does it mean?
So carried on

[Torsten]

excited; enthusiastic

TOEIC listening, talks: An entrepreneur is talking about how to start a business

[Tung a]

can i have clearer meaning of the word 'carry on' and 'carry away'

[Mister Micawber]

.
Carry on:
a. to manage; conduct.
b. to continue without stopping: Rescue operations were carried on in spite of the storm.
c. to continue to live, work, etc., despite a setback or tragedy; persevere.
d. Informal. to behave in an agitated, foolish, or indiscreet manner.
e. to misbehave or be disruptive; act up.

Carry away:
a. to influence greatly or unreasonably, esp. emotionally; excite; transport: The spectators were carried away by the appeal to their patriotism.
.
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Native English teacher at Mister Micawber's