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I think more or less everything is in the title, say I'd like to buy 1000 yen of carrots, would:
Be correct ?
Almost! It would be:
natural: 1000円分の人参（を）お願いします。(You can ommit を, put pause before お願いします）
acceptable: 人参(を)1000円分お願いします。(You can ommit を、put pause before お願いします）
Required, but never shown