You need a pen to write.
You need a pen to write with.
Are there any differences between the two sentences above? Which is more commonly spoken?
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"You need a pen to write" means "You need a pen in order to write". In other words, you can't write without a pen.
"You need a pen to write with" is grammatically correct too but the meaning is different. Now the point is, you are emphasizing the instrument: "You need a pen which you can use to write."
The use of the sentences depends on context, of course.
There are actually two meanings of the first sentence:
1) You need a pen in order to write.
2) You need a pen that is able to write.
The second meaning is less common, but still used:
"I can't get this pen to write!" she said while shaking it.
Your second sentence doesn't have the exact meaning of either of these.