So I know that in Mandarin, 1/2 is 二分之一 or 一半. Is there a similar word to 一半 for 1/3? I mean, instead of 三分之一, something like 一——？
Because the decimal system has been used for a long time in China, there are fewer fractional words. 半 is the only single word, which was used as follows in ancient China.
1/2 one-half 半、中半
1/3 one-third 少半、小半
2/3 two-thirds 太半、大半
1/4 one-fourth, a quarter 弱半
3/4 three-fourths, three quarters 強半
In Chinese fractional system, the denominator is addressed first, and then the numerator.
例如：其亡者三二 (Two-thirds people died)。
三分之一 can only be shortened to 三分一.
The only way to avoid saying 三分一 is using smaller measuring unit. For example: 二十分鐘 instead of 三分一小時; 四分 instead of 三分一尺.
Similarly, 一半 can only be shortened to 半, as in 半小時 (三十分鐘), or 半尺 (六分)
1/4 hour (a quarter of an hour) can be translated to 一刻鐘 or 一刻 instead of 四分一小時 in Chinese.
1/4 hour (a quarter of an hour) can be transliterated to 一個骨 in Cantonese; 3/4 hour (three quarters of an hour) = 三個骨
一比三，三分一，三分之一，一除三： all work!! but of course, is there a half word in English for 1/3? No, there isn't.
English Strictly in Mandarin(Cantonese in written) 1/3 one third 三(3)分之一(1) 1/4 one fourth(quarter) 四(4)分之一(1) 2/5 two fifths 五(5)分之二(2)
See the pattern? Even in written 三分之一, It's common to write "3分之1". Since in Chinese, the number itself doesn't have the plural form, you can ignore the annoying"-s" or"-es".
In accounting, since 一，二，三...etc. The number itself are easily to be modified, so we might use “壹，贰，叁，肆...”, but that's another sotry.
Advanced patterns when it comes to 1(1/3) cases:
English Strictly in Mandarin(Cantonese in written) 1+2/3 one and two thirds 一(1)又三(3)分之2(1) 3+1/4 three and one fourth(quarter) 三(3)又四(4)分之一(1) 4+2/5 four and two fifths 四(4)又五(5)分之二(2)
Hope it helps.