半 / 分之 / 百分之【bàn / fēnzhī / bǎi fēnzhī】

半 means "half". Where it goes depends on whether there's a whole number in front of it.

Half on its own, or with a whole number

Alone, 半 goes before the measure word: 半个苹果 "half an apple". With a whole number, it goes after the measure word: 两个半苹果 "two and a half apples".

• × 一半个小时 → 半个小时
• × 两半个小时 → 两个半小时

半天 and 半年 have no measure word, because 天 and 年 never take one. In speech 半天 also means "ages".

一半: half of something

一半 is a noun, "half (of it)". It works as subject or object, often after the thing being divided.

Fractions: the bottom number first

A fraction gives the denominator, then 分之, then the numerator: 三分之一 is "of three parts, one", a third. English says the top number first.

• × 一分之三 → 三分之一

Percentages

A percentage is a fraction out of a hundred, so it follows the same order: 百分之 + number.

• × 五十百分之 → 百分之五十