Fractions (三分之一) | Chinese (Mandarin) Grammar

Fractions are the place where Chinese and English word order collide head-on. English says the numerator first: "one third," "three quarters." Chinese says the denominator first: the whole is divided into so many parts, then you name how many of them you're taking. The frame is X 分之 Y (X fēn zhī Y), literally "of X parts, Y" — so one third comes out as 三分之一 (sān fēn zhī yī), literally "three-parts-of-one." Reverse your instinct and the rest is mechanical; keep the English order and you'll systematically say the fraction upside down.

The frame: 分之 = "parts of"

Break the pattern into its pieces. 分 (fēn) means "to divide, a part"; 之 (zhī) is the classical particle for "of / 's" (the literary ancestor of modern 的). So 三分之一 parses as 三分 ("three parts") + 之 ("of") + 一 ("one") = "of three parts, one part" = one third. The denominator (the total number of parts) is spoken first because you have to divide the whole before you can pick out a slice of it.

Value	Chinese	Pinyin	Literal
1/3	三分之一	sān fēn zhī yī	of 3 parts, 1
3/4	四分之三	sì fēn zhī sān	of 4 parts, 3
2/3	三分之二	sān fēn zhī èr	of 3 parts, 2
1/2	二分之一	èr fēn zhī yī	of 2 parts, 1
7/10	十分之七	shí fēn zhī qī	of 10 parts, 7
10/100	百分之十	bǎi fēn zhī shí	of 100 parts, 10 (= 10%)

我把蛋糕切成三块，每人吃三分之一。

wǒ bǎ dàngāo qiē chéng sān kuài, měi rén chī sān fēn zhī yī

I cut the cake into three, and we each ate a third. (informal) — 三分之一 = 1/3, denominator (三) first.

这道题四分之三的人都做错了。

zhè dào tí sì fēn zhī sān de rén dōu zuò cuò le

Three quarters of people got this question wrong. (neutral) — 四分之三 = 3/4.

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Say it in the Chinese order out loud: "divide into three — take one." The denominator is the setup (how many parts exist), the numerator is the payoff (how many you take). Whenever you catch yourself starting with the top number, stop and name the bottom number first.

Fractions of a noun: X 分之 Y 的 + noun

To say "two thirds of the students," attach the fraction to the noun with 的, exactly like any quantity: 三分之二的学生. The fraction sits where a number-and-measure phrase would sit.

三分之二的座位已经卖完了。

sān fēn zhī èr de zuòwèi yǐjīng mài wán le

Two thirds of the seats are already sold out. (neutral) — 三分之二的 + noun.

地球表面大约十分之七是海洋。

dìqiú biǎomiàn dàyuē shí fēn zhī qī shì hǎiyáng

About seven tenths of the Earth's surface is ocean. (academic) — 十分之七 = 7/10.

只有五分之二的员工同意加班。

zhǐyǒu wǔ fēn zhī èr de yuángōng tóngyì jiābān

Only two fifths of the staff agreed to work overtime. (neutral) — 五分之二 = 2/5; note the numerator 2 is 二, not 两.

Two details in that last example are worth locking in. First, both the numerator and the denominator use 二 for "two" (五分之二, 二分之一) — a fraction is a pure math value, so it's the digit 二, never the count-word 两. Second, "one half" as a formal fraction is 二分之一; in ordinary speech people just say 一半 (see 半 / 一半).

口语里说一半，写公式的时候写二分之一。

kǒuyǔ li shuō yíbàn, xiě gōngshì de shíhou xiě èr fēn zhī yī

In speech you say 'yíbàn'; in a formula you write 'èr fēn zhī yī'. (neutral) — same value, two registers.

Percentages, mixed numbers, and asking "what fraction"

Percentages are just fractions with 百 (100) as the denominator: 10% = 百分之十 (bǎi fēn zhī shí), "of a hundred parts, ten." The denominator-first logic is identical, which is why 百分之 always leads with 百. The full treatment is on the percentages page.

今年的房租涨了百分之五。

jīnnián de fángzū zhǎng le bǎi fēn zhī wǔ

Rent went up five percent this year. (neutral) — 百分之五 = 5%, the 百-denominator fraction.

For a mixed number — a whole plus a fraction — join them with 又 (yòu, "and"): 二又四分之一 = "two and one quarter." This register is mathematical or written.

计算结果是二又四分之一。

jìsuàn jiéguǒ shì èr yòu sì fēn zhī yī

The result of the calculation is two and a quarter. (academic) — 二又四分之一 = 2¼, joined by 又.

To ask "what fraction," use 几 in both slots: 几分之几 (jǐ fēn zhī jǐ).

你能算出阴影部分是整个图形的几分之几吗？

nǐ néng suàn chū yīnyǐng bùfèn shì zhěnggè túxíng de jǐ fēn zhī jǐ ma?

Can you work out what fraction of the whole figure the shaded part is? (neutral) — 几分之几 asks for the fraction.

For "how many times" rather than a part-of-a-whole (double, triple), Chinese switches to a different word, 倍 — see multiples with 倍. And for fine-grained values that aren't clean fractions, you'll want decimals (三点五 = 3.5).

Common Mistakes

1. Using English order (numerator first). 一分之三 doesn't mean 1/3 — it literally means 3/1, i.e. three.

❌ 一分之三

Reversed — for 1/3, this parses as 'of 1 part, 3' = 3, not a third. One third is 三分之一 (denominator first).

✅ 三分之一

sān fēn zhī yī

one third (1/3).

2. Dropping 分之. Without the frame, the two numbers are just two numbers.

❌ 三一杯水

Incomplete — for 'a third of a cup' you must keep 分之: 三分之一杯水.

✅ 三分之一杯水

sān fēn zhī yī bēi shuǐ

a third of a cup of water.

3. Using 两 in a fraction. A fraction is a math value, so "two" is the digit 二.

❌ 五分之两

Incorrect — the numerator 'two' in a fraction is 二: 五分之二 (2/5).

✅ 五分之二

wǔ fēn zhī èr

two fifths (2/5).

4. Reversing a percentage. Percentages are 百-denominator fractions — 百 leads.

❌ 十分之百

Reversed — ten percent (10%) is 百分之十 ('of 100 parts, 10'), with the denominator 百 first.

✅ 百分之十

bǎi fēn zhī shí

ten percent (10%).

Key Takeaways

Chinese fractions are denominator-first: X 分之 Y = "of X parts, Y" = Y/X. So 三分之一 = 1/3, 四分之三 = 3/4 — the exact reverse of English.
分之 is the fixed frame: 分 = "divide into parts," 之 = classical "of" (= 的).
Attach to a noun with 的: 三分之二的学生 (two thirds of the students).
A fraction is a math value, so 二 (never 两): 五分之二, 二分之一.
Percentages are the same pattern with 百: 百分之十 = 10%. Mixed numbers join with 又: 二又四分之一 = 2¼. Ask "what fraction" with 几分之几.

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