问道英语问题判断句子正误Half his money was gone.答案说是对的,可我觉得应该加of,变为Half

问道英语问题
判断句子正误
Half his money was gone.
答案说是对的,可我觉得应该加of,变为Half of his money was gone才对啊,请大家帮忙解答下,谢谢
顺道问下,Half of his money was gone语法上讲也是对的吧?

3.half的用法与all和both相同,既可用作形容词（或称限定词）修饰名词,如 half the year,half the work,half the fruit,亦可用作不定代词,受of短语修饰,如：half of the work,half of the year,half of the fruit.这两种表达形式在意义上没有明显的区别.例如：
① Half (of) the girls are foreigners.这些姑娘有一半是外国人.
② Half (of) the fruit was bad.水果有一半是坏的.
③ Half(of) my friends live in this city.我的朋友有一半住在这个城市.
④ In 1620,about half(of) the USA was covered by forests.在1620年,美国一半的土地被森林覆盖着.
注意：1) half +名词或half of+名词作主语时,谓语动词的单、复数形式由所接名词的单复数形式来决定,名词是中心词（见上例句）.
2） half,half of后面所接的名词前,必须有表示限定含义的冠词、指示代词、物主代词等等（见上例句）.
3) 如果是人称代词,则只能用half of,而且人称代词要用宾格.例如：
① Only half of them came last Sunday.上星期天他们只有一半人来.（不能说：Only half them...或Only half they...)
② Half of you are wrong.你们一半人都错了.（不能说：Half you...)
③ They invited half of us.他们邀请了我们一半人.（不能说：.half us.）
4）在谈论距离、长度和数量时,只能用half,一般不用half of.例如：
①His old house is half a mile down the road.他的旧居在沿着这条路往下走半英里的地方.
②Mr Smith drank half a bottle of whisky last night.史密斯先生昨晚喝了半瓶威士忌酒.
5） half作代词时,后面不跟名词,前面也不使用定冠词.例如：
① We only need half.我们只需要一半.（不能说：We only need the half.）
② I gave her half,and kept half for myself.我给了她一半,自己留了一半.（不能说：I gave the half,...）
4.half也可用作副词.例如：
① I half agree with you.我不完全同意你的意见.
② This meal is only half-cooked.这顿饭做得只有半熟.
5.副词half和not连用,在口语中较为常见.not half 是反语,意为一点也不；非常地；.极了等.例如：
① It is not half bad.(=It is very good.) 很好（很不错）!
② The story is not half interesting.这个故事很有趣.
③ -Do you like Chinese tea?你喜欢喝中国茶吗?
-Oh,not half!噢,喜欢极了!
6.在一本《高中英语解题题典》中有下面一道题（答案是B）：
He cut the cake_________.
A.in halves B.in half
C.into halves D.into half
而在另一本《中学英语错解辨析辞典》中给出了下面这道题（答案是C）：
The arrow split the apple________.
A.in halfs B.into half
C.into halves D.into halves