1.

I blanked out your question. What did you say? (blank out: to forget something, perhaps on purpose; to blot something out of memory)
我忘记你的问题了，你刚才问了什么来着？（blank out：忘了某事）

2.

The new manager has been given no detailed instructions about how to train the staff. He just has a blank check. (blank check: freedom to act as one wishes or thinks necessary)
没有人要求也来的经理具体该如何培训员工，他可以自由发挥。（blank check：按自己想法行事的自由）

3.

We looked in the files for an hour, but we drew a blank. (draw a blank: to get no response; to find nothing)
我们在那些文件里搜索了一个小时，一无所获。（draw a blank：毫无回应；一无所获）

4.

Bill: There was a big fight at their house last night, then the neighbors called the police.
Mary: Then what happened?
Bill: Fill in the blanks. (fill in the blank: you can figure out the rest)
比利：昨晚他们在家里打起来了，然后邻居报了警。
玛丽：然后怎么样了？
比利：还能怎么样！猜都能猜到。（fill in the blank：你可以猜到剩下的故事）

5.

After I told her to stop smoking, she just gave me a blank look and kept puffing. (give someone a blank look: to look back at someone with a neutral look on one's face)
我告诉她别抽烟了，她面无表情地看了我一眼，继续“腾云驾雾”。（give someone a blank look：漠然地看着某人）

6.

He knew all his lines in rehearsal, but his mind went blank when he went before an audience. (one's mind went blank: someone's mind has experienced total forgetfulness.)
排练的时候，他对自己的台词倒背如流。但是站在台上，看着台下的观众，他大脑一片空白。（one's mind went blank：脑子一片空白）