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1/2 of 3 and 3/4

3 and 3/4 = 15/4

1/2 x 15/4 = 15/8 = 1 and 7/8 cups

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Q: What is one half of three and three fourths cups of milk?
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How do you put half in a sentence?

It depends on how you are using the word "half". Most of the time it is used as an adjective. If the word is being used as part of a mixed numeral, then the word is preceded by "and a": "I used three and a half cups of flour in the cake." If the word is being used to denote 50% of a single countable item, then you may use "a half" or "half a(n)", but never "a half a(n)": "We will be there in half an hour." "We will be there in a half hour." It is never correct to use "We will be there in a half an hour." If the word is being used to denote 50% of an uncountable or plural countable item, then the word is followed by "the" or "of the": "Jane used up half the napkins during dinner." "Bob lost half of his marbles in the game." Idiomatically, there exists "half and half", which is approximately 50% cream and 50% milk. This is a noun and is used the same way as the word "milk" with nothing extra needed: "I poured half and half in my coffee."