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The phrase "a far bigger slice" is correct and usable in written English.
It can be used when discussing a significantly larger portion or share of something, often in a metaphorical sense related to resources, opportunities, or benefits.
Example: "In the new budget proposal, our department is requesting a far bigger slice of the funding to support our initiatives."
Alternatives: "a much larger share" or "a significantly greater portion."
Exact(5)
That's why telecommunications is a far bigger slice of the economy than media.
Sales taxes on clothing and school supplies and fees for bus fare and car registration take up, of course, a far bigger slice of a poor household's budget than they do from the rich.
Tens of millions of people are uninsured by a system that devours a far bigger slice of national output — and that's the sum of all Americans' collective energies — than in any other wealthy society.
But King Abdullah has compensated in part by increasing Shia representation in the Shura Council.A far bigger slice of the population that has been kept to the margins of society, namely women, also got a boost with the appointment of a female deputy minister, the highest-level government post yet to be filled by a woman.
Strict government regulation and omnipresent state involvement in the education marketplace -- combined with powerful unions preventing any one teacher from garnering a far bigger slice of the profit pie, let alone profitably branching out on his or her own -- has insured that wage increases remain relatively constant and predictable.
Similar(55)
A far bigger state sector than England?
A far bigger version of the game is being played on the national stage as a relative handful of Americans receive ever-larger slices of the total national income while most Americans, working harder than ever, receive smaller ones.
Pet cats are a far bigger problem.
2) Second, and a far bigger concern, is the accuracy of estimates from expert opinion.
Catalonia had something of a case for a bigger slice of the cake.
"So the increase is doubly important because it's a bigger slice of a bigger pie".
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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