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Here is my challenge:

According to the proper grammar of English:

My house is TWICE (2X) as big as yours.....Your house is HALF (1/2) as big as mine. CORRECT.

How do I then say that:

My house is ONE AND A HALF (1.5X) times as big as yours.....Your house is 1/1.5?

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    Two-thirds [the size of], last time I did my sums. But maths terms don't often have idiomatic everyday equivalents. 'Scale factor 0.666...' (linear SF?) – Edwin Ashworth May 22 at 16:58
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    @EdwinAshworth is quite right. With your formatting, your example would read, "Your house is TWO-THIRDS (2/3) as big as mine." – Richard Kayser May 22 at 17:02
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    Idiomatically, "My house is ONE AND A HALF (1.5X) times as big as yours." would be "My house is 50% bigger than yours." or "My house is half as big again as yours." – Greybeard May 22 at 17:03
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    @greybead I would say that as "my house is half again as big as yours".... splitting the again away from the half seems wrong to me. – Hellion May 22 at 17:06
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    @Hellion - have a look at Google Ngrams in British English and American English for "half as big again, half again as big" You will see that "half as big again" is far more popular in British English, and "half again as big" is only marginally more popular in American English. ("Half again as big" sounds weird to me :)) – Greybeard May 22 at 17:26
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My house is (2x) twice as big as yours.

My house is (⅓) a third as big as yours.
My house is (½) half as big as yours.

My house is (1⅓x) a third again as big as yours.
My house is (1½x) half again as big as yours.

The use of again after a fractional expression is used to represent that something is of equal size plus the fractional number.

This is the sense of again that's being used:

[Merriam-Webster]
4 : in addition : BESIDES
// Again, there is another matter to consider.

The use of again can come after any fractional representation.


Outside of the particular phrasing in this context, you might hear something like this:

Give me a pint, and then half a pint again.

To paraphrase and analyze the context of its use in house sizes, it means the following:

My house is [the same size] as yours and [this fraction] bigger [in addition].


The use of half again specifically is common enough that it's actually become an idiom:

half again as much/many as
Merriam-Webster
US
—used to say that the size or amount of one thing is 50 percent more than another
// If 100 people were expected and 150 came, half again as many people came as were expected.
// This dress costs half again as much as that one.

Note that the definition includes US, so this could be less common in the UK.

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