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The phrase "over a half of" is correct and usable in written English
You can use it when you want to indicate a quantitative majority. For example, "Over a half of the people in the survey reported feeling anxious about the upcoming election."
Exact(48)
This varied from one third of the group in Laos to over a half of the Thai beer promoters.
Over a half of councils used local welfare funds to subsidise food banks.
We also show that a halvable S 2,2n,v) exists for over a half of possible orders.
"Over a half of our expenditure could be for gas and sulfur-related facilities, not just for oil".
For over a half of American teenagers that say they feel addicted to their smartphone, however, the only solution that will actually work is to go cold turkey and leave their phone at home.
Only a sliver over a half of the Germans, whose leaders have been the prime motor of integration, told pollsters last year that they were in favour of joining the single currency.
Similar(12)
Demand for sustainable products and over a half century of research have led to moderate commercial success of PHA.
A little over a half hour of downtime it looks like.
There has been over a half century of study into how C. neoformans grows at high temperatures.
Chances are you'll end up kicking yourself over a rebound half of the time.
Fusion events may consist of over a half million atoms interacting for hundreds of microseconds.
More suggestions(19)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com