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To figure out the Independent and dependent clauses in the sentence provided, we first need to simplify the grammar and get to the core meaning of the sentence. If we can find the meaning and restructure the sentence, it will help show you which clause is dependent and which is independent.
Sentence: It is very important more important than the grade that I learn the material.
The meaning of this sentence is: It is important that I learn the material, more important than the grade.
How do we get that meaning from the confusing words above? If we take out "more important that the grade," we are left with "It is very important that I learn the material."
We now have our two clauses:
"It is very important that I learn the material"
and
"more important than the grade"
Which of these clauses can stand on its own as a complete sentence? The answer is "It is very important that I learn the material." That makes this the dependent clause, which means "more important than the grade" the dependent clause.
To relieve the confusion, you have to set the clauses apart in the sentence. The easiest way to do this is to put commas around the dependent clause to set it apart from the independent clause.
The correct way to punctuate the sentence is: It is very important, more important than the grade, that I learn the material.
Now you can easily see the two clauses and understand the meaning of the sentence.