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We say, cut it half

Then how do you say when you want to cut, for example, a cake into 3 pieces equally?

Q1) Is it 'cut it one third'?

and what about 4,5 and 6 pieces equally ?

Q2) Is it 'cut it a quarter' , 'cut it one fifth', 'cut it one sixth?'
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1-- Cut it into thirds, fourths or quarters, fifths, sixths.
2-- As above.
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moon7296We say, cut it half
No, we don't. We say, "cut it in half."
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These are the most common in British English:
Cut it in half
Cut it in two OR cut it into two
Cut it into three
Cut it in quarters
Cut it into four
Cut it into five
Cut it into six
etc.

I'm not offering an explanation for this! I'm just giving commonly accepted usage.

[one possible reason why we don't usually say 'cut it into fifths' or 'cut it into sixths' is that the words 'fifths' and 'sixths' are both quite difficult to prononunce - even for native speakers! They would probably come out as 'fiths' or 'sikths']
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Thirds, quarters, sixths etc are plural nouns of the particular fraction, so we cut it into halves, thirds, fifths, sixths etc. "pieces" is plural, so we cut it into pieces (into two pieces, ten pieces etc). "Cut it in sixths" just doesn't sound right does it?

Two, three, five ,six are singular numbers, so we cut it in two, three, four etc. "Half" is a singular term so we "cut it in half".

another example of singular or multiple nou nbs affecting the adjective / adverb is "give me that piece and those pieces"

It is just the way English has evolved from Middle and Old English.

Technically you can;

"Bisect" it - cut it into halves

"Trisect" it - cut it into thirds

"Quarter it" - cut it into quarters

I don't think the terms pentasect, hectasect, septasect, octosect, nanosect or decasect actually exist (they are not in the Windows Spelling Dictionary anyway), so after four pieces go the long route; "Cut it into fifths" etc.