叉 verb 叉子 noun 勺子=汤匙=汤勺=spoon we usually call it 勺子，not 勺 子在这里相当于助词 　　 (1) 构词后缀。 (2) 加在名词后。如：房子；车子 (3) 加在动词或形容词词素后。如；胖子；瘦子；垫子 (4) 个别量词后缀 http://baike.haosou.com/doc/1254038.html knife=餐刀（for eating)

“子” is a meaningless suffix, but as to whether a noun needs it, you'd better remember the usage of other words in context since I will only explain the case of 叉子 and 勺子 here. 0.“子”makes a noun more informal.(小孩--小孩子) 1.Use the full name 叉子 to refer to a fork(一把叉子), because “叉” also has the meaning of "a cross, ie ×"（错的题打叉//老师在本子上打了一把叉）. However, in some context a fork can be called ”叉“ because of the collocation (the verb can tip you off as in ”打叉“、”画叉” ). “勺” isn't that confusing because it doesn't mean anything else, but it's usually seen in full name.【她端来一碗汤，但是忘了拿勺子；用勺（子)搅拌一下】Without "子" the second sentence sounds more formal, it is more likely to be seen in literary works or medical instructions, etc. 2.Omit “子” in combined words:一只汤勺//一把牛角叉 3.We say“一副刀叉” rather than“一副刀和叉”.

Sorry for the delay. Thank you everyone for your responses. Thank you, Luyi for your very thorough and complete answer.

what about 表叉？

叉 ① verb 用叉子叉食物 ②noun ≈叉子 eg.刀叉means knife and fork