"My dad is cleaning the room with a mop."
Translation:אבא שלי מנקֶה את החדר עם סמרטוט.
I once heard a Holocaust survivor tell a group of college students, “I speak seven languages, but I speak them all in Polish.” I think this is a beautiful description of the difficulties of translating, especially when the translation has to bridge a gap between different cultures; different cultures have different sensitivities.
If your goal is to be understood in street Hebrew, you can use עם and –ב interchangeably; people will understand you and some people may even guess where you’re from. But if you want to speak Hebrew in Hebrew, be aware that עם has a tradition of being used for “with” when speaking about people, while –ב is used for “with” when speaking about things or places, and it can equally mean “with” or “in” or have a different English translation depending on the verb it’s used with.
So you would use –ב to say you are eating spaghetti with a fork, and עם to say you are eating spaghetti with a friend. And if you want to say that someone was jealous OF another person, you would use ב, because you would learn that rule at the same time you learn the word for “jealous”. In general, the way prepositions are translated from one language to another is not as consistent as with other parts of speech; the translation that sounds closest to the language you’re starting with may not really be right for the language you’re translating into. A dictionary that gives examples of sentences in the language you are learning can be really helpful with this. One that I like is Multi Dictionary: Bilingual Learners Dictionary; Hebrew-Hebrew-English, English-Hebrew by Edna Lauden, Liora Weinbach, and Miriam Shani, which has sentences for the Hebrew words (not for the English, though). It seems to be published in Israel with funding by several agencies; the ISBN is 965-390-003X. There is also Miloni which is illustrated and geared to children but very nice for adults, too. הצלחה רבה!
I've only ever heard סמרטוט used with the meaning of rag; and, yes, the slight similarity with shmata has always made the word memorable for me. Dictionary says מגב for mop, but admittedly it gives סמרטוט too. In the UK at least, a mop is traditionally made of absorbent strings (or ribbons, or a foam pad) on a stick; a rag is just a schmutter.