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The phrase "a third of the school" is correct and usable in written English.
It can be used when referring to a portion or fraction of the total number of students or staff within a school.
Example: "A third of the school participated in the science fair this year."
Alternatives: "one-third of the school" or "33% of the school".
Exact(17)
So far more than a third of the school cafeterias' food garbage has been recycled.
Nate, 16, Lower Merion: About three photos go viral each year and a third of the school sees them.
About a third of the school population, or 350,000 students, will get either tutoring or enrichment programs.
About a third of the school districts in Massachusetts already charge middle- and high-school students for busing.
About a third of the school consists of spaces that are at times available to the public, including the performing arts center.
The figures released yesterday showed the total summer enrollment to be 360,984 -- roughly a third of the school system's total of 1.1 million students.
Similar(43)
But about a third of the schools that got millions in School Improvement Grant money saw declines.
Few Liberal Democrats would have campaigned on a policy that threatened to alienate every church and disrupt a third of the schools in the country.
A21 EDUCATION No-Shows for Summer Classes Officials said the opening of summer school in New York City went smoothly, though a check of a third of the schools showed an average of 40percentt of students absent.
Bringing these strands together, the authors determine that, in about a third of the schools, expanded local democratic participation served as a strong lever for introducing systemic change focused on improved instruction.
About a third of the schools (33.1%) had received rainwater tanks.
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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