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The phrase 'fraction of the size' is correct and can be used in written English.
For example, 'The new house was only a fraction of the size of the old one.'.
Exact(60)
"Our company's a fraction of the size of those".
Twitter is also a fraction of the size of Facebook.
In Copenhagen, a city a fraction of the size, you'll pay £160.
The handful that have failed have been a fraction of the size of IndyMac.
He is from Trinidad, which is a fraction of the size of Haiti and Jamaica.
There are already nanotube transistors a fraction of the size of conventional ones.
Now, it is a fraction of the size of both the US and euro-area economies.
It was a fraction of the size of the former festival.
So far, European stimulus efforts are only a fraction of the size of the American package.
His new fund was a fraction of the size, with $2 billion in assets.
In Japan, Suzuki has shown a hybrid city car that is a fraction of the size of a Toyota Prius.
More suggestions(15)
subset of the size
share of the size
particle of the size
component of the size
aliquot of the size
proportions of the size
fraction of the whole
fraction of the weight
fraction of the cost
fraction of the demand
fraction of the ticket
fraction of the percentage
fraction of the innuendo
fraction of the price
fraction of the 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