If a person speaks English as a mother tongue and is talking to other such people, everybody can understand "cuppa" instead of "cup of" because their ears are trained to make out the difference. This happens in the same way that Chinese people can easily pick out the difference between 才 （cai) and 在 （zai), while Westerners like me are constantly perplexed. Since you speak English with an accent (unless you are very VERY good) I would suggest using "of". The reason is that "normal" sounds become distorted by the accent and it can be harder to understand by a native speaker if all the original sounds are not present.

You are right that native English speakers sometimes pronounce 'a cup of tea' as əˈcʌpə tiː/. It is very common. They can also pronounce it more formally as əˈcʌp əv tiː/. This is one of the things that makes "native" English difficult for many speakers of English as a second language. Many of my Russian students can understand non-native speakers when they speak English but are unable to understand native speakers for this very reason. It is very good that you are aware of this phenomenon, because it will help you to understand spoken English. If you can learn to imitate it, you will sound more like a native speaker! These simpler pronunciations are called reduced forms. Native speakers tend to stress nouns, verbs, adverbs, and adjectives and to destress function words, like articles, pronouns, and prepositions, etc. It is part of the natural rhythm of the English language. When we pronounce it more formally it sounds like a CUP of TEA....stressing the nouns When we pronounce it less formally it sounds like a cup' tea.....destressing the function word In the cases you mention the pronunciation depends on whether the consonant that comes before the o in "of" is a voiced consonant or a nonvoiced consonant. When the preceding consonant is voiced it sounds like əv . When the consonant is nonvoiced,you do not pronounce the f in "of". Why? Because it is easier to pronounce two voiced sounds together. Nonvoiced. əˈpi sə keik/ .....s is nonvoiced in "piece of cake" əˈcʌpə ti ..... p is nonvoiced in a cup of tea əˈcʌpəl ə things ... l is nonvoiced in a "couple of things" Voiced (the f in "of" is pronounced like the voiced "v".) dʌzənz əv .....the s is voiced as a z sound in "dozens of" han g əv ....the g is voiced in "hang of"

if you are being slangy and slurring the words together ... "a cupla days [a couple of days] is OK, a cuppa tea is OK, "dozens a" doesnt really work, I think it's the trailing s that dictates you should pronounce the v sound, but you can drop the vowel in of and say "dozens'v eggs, same with "hang of". You wont hear hang'a. Ex. "I cant get the hang'v it". In these cases, the 'v is pronounced with an unemphasized short eu sound. A bit difficult to explain in text :(, you need to hear it.

My general advice on this is while it is possible, it's not a good habit to adopt unless you are already very relaxed with speaking. The problem is, by dropping something as casual as "a cuppa tea" into an otherwise perfectly-pronounced sentence, you can sound quite comical to a native speaker. Get very comfortable with the language first, before cutting corners.

Jiao, You can pronounce the "of" that way in any of the phrases, but it is NOT proper pronunciation. Properly, you should pronounce the "of" as a separate word.