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The phrase "a like proportion of" is correct and usable in written English.
It can be used when discussing a similar or equivalent ratio or share in a comparative context.
Example: "In the study, a like proportion of participants reported feeling satisfied with the service provided."
Alternatives: "an equivalent share of" or "a similar ratio of".
Exact(1)
We've stampeded ourselves over a cliff into a yearlong primary campaign climaxing next February 5th, when as many as twenty-two states, representing sixty per cent of the nation's population and a like proportion of the two parties' Convention delegates, will hold their primaries all at once.
Similar(58)
While most income variables likely reflect the resources available to the families, a variable like proportion of income from government transfers did not take into account the absolute family income levels which may, in part, be contributing to the different patterns for SGA, spontaneous preterm and postneonatal death.
— MICHAEL D. SHEAR — JOSH HANER DES MOINES — It looks like a similar proportion of evangelical voters is turning out for the caucuses this year, as compared to the four years ago.
Most of the studies measured the outcomes using natural units, like proportion of patients cured, share of children immunized etc.
So in the background population such social factors, like a proportion of non-secured citizens, did not affect our results [ 31].
A previously sequenced wheat BAC clone from the same chromosome 3BL-7 deletion bin [ 5] also found a similar high proportion of gypsy-like LTR-retrotransposons.
Those gamers who have taken pains to uncover the encrypted trysts are probably a high-denominator fraction of the millions who have played the gore-fest; a bit like the proportion of professed "movie buffs" who have actually bothered to sit through all three hours of Citizen Kane.
Like a decent proportion of penalty kicks, it seems, they will be missed.
So we would like a higher proportion of shared ownership homes on the site.
Like a growing proportion of Americans, she said she wanted her body to be cremated.
David is one of over 6,500 rough sleepers in London, and, like a high proportion of them, sticks to the more affluent areas during the day.
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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