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People eat popcorn. active
Popcorn is eaten by people. passive
Is there a specific structure/formula for the sentences?

Thanks in advance.
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How to form the passive sentence that corresponds to a given active sentence.

Active: The dog bit the man.

1. Divide into subject, verb, and object.
The dog || bit || the man.

2. Exchange subject and object.
The man || bit || the dog.

3. Add by to the beginning of the last element.
The man || bit || by the dog.

4. Change the verb from its active form to its passive form.
The man || was bitten || by the dog.

Sub-steps of 4.
4a. Determine the tense of the verb: bit: Past.
4b. Form that tense of the verb be: was / were
4c. Use the form that agrees with the subject: The man was
4d. Add the past participle of the original verb: bit: bitten.

The passive is: The man was bitten by the dog.
________________

People eat popcorn.

1. People || eat || popcorn.
2. Popcorn || eat || people.
3. Popcorn || eat || by people.
4a: present 4b. am / is / are 4c. popcorn is 4d. eat: PP: eaten
4. Popcorn || is eaten || by people.

Popcorn is eaten by people.
_______________


Note how this works with sentences with more elements.
The radio operators are sending a signal to the commander.

1. The radio operators || are sending || a signal || to the commander.
2,3. A signal || are sending || to the commander || by the radio operators.
4. are sending : present progressive : am being / is being / are being : signal is being : PP of send > sent
A signal is being sent to the commander by the radio operators.
______________

Students who have difficulty with the last step (4) should practice it in isolation in various tenses. It's a purely mechanical, formula-driven process. To do it, the student must know the forms of be very well, and the past participles of verbs, of course.

chose > was chosen / were chosen
has taken > has been taken / have been taken
sings > is sung / are sung
are giving > is being given / are being given
had known > had been known

CJ
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CJ's explanation is worth printing and keeping. I have a comment about the use of the passive voice.

1. When the identity of the 'doer' of the action is not known. [The sign was knocked down last night.]

2. When the identity of the 'doer' of the action is not imprtant. [The telephone was answered quickly.]

3. When the identity of the 'doer' of the action needs to be kept secret. [Mistakes were made.]

These are only examples of the use of the passive when the agent is not mentioned.
Students: We have free audio pronunciation exercises.
Comments  
Thank you very much, Jim.
You provided some real useful information.

-WA
 Philip's reply was promoted to an answer.
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Thank you, CalifJim.

Why is it seems that when you see some examples of an active to passive transformation case, some parts seem to be left out, giving an impression that it is optional? I think those in parentheses are either allowed to left out or left to give an impression that it is optional.

Your example:

The dog bit the man

The man was bitten (by the dog).
I didn't use any parentheses in my discussion of how to form the passive because I wanted to show how to do it using all the elements of the active structure in the passive structure.
Nevertheless, a sentence does not cease to be passive just because the by phrase is left out. It's still a passive sentence. So sometimes passive sentences are illustrated with parentheses around the by phrase. It means that the sentence is regarded as passive with or without the by phrase.

The usual meaning of parentheses, as you have already guessed, is that the word or words in parentheses are optional.

CJ