The title of this question is often mistranslated by students into the equation 8 + q = d. My question is how can I explain grammatically where the error in reasoning has occurred? 

Students are taught early on to translate the phrase "8 more than a number" as 8 + n. What is the grammatical difference between the original sentence and that phrase which causes the mistranslation? 

Could it be the presence of the word "quarters" between "more" and "than" and if so, what would be the grammatical function of these words in the original sentence, "He has 8 more quarters than [he has] dimes," as compared to the phrase "8 more than a number"?