Simple subject is the main subject, without the adjective included. Sometimes, there is no adjective, so the complete subject can also be the simple subject.
Example: The smart student got an A on his test.
In the sentence above, the complete noun is smart student. It's describing the student as smart, so it is an adjective. The simple subject is student.
Simple predicate is the verb. Simple predicates NEVER have a helping verb in it. The simple predicate usually comes right after the simple subject.
In the same sentence, the simple predicate is got because the verb is got.
Here is the sentence:
Luckily he spotted Louis in the doorway.
The simple predicate is he. He is the person that spotted Louis in the doorway. Most people would think that the subject is luckily because the sentence starts with it, but the subject isn't always the first word in the sentence. These kind of sentences can trick you.
The simple predicate is spotted. The verb tells what action the subject did. In this sentence, the subject(he) spotted Louis in the doorway.
Simple subject: he
Simple predicate: spotted
he | spotted ↓
Luckily he | spotted Louis in the doorway.
