余数 (yú shù) — remainder (in arithmetic); complement (in number theory or modular arithmetic)

Definition

Strict mathematical term for the remainder left after division — the leftover amount when one integer does not divide evenly into another (e.g., 10 ÷ 3 leaves 余数 1).

noun
remainder (in arithmetic)complement (in number theory or modular arithmetic)
Easily confused

Examples

  • ，余数。
    Shí chú yǐ sān, yú shù shì yī.
    Ten divided by three, the remainder is one.
  • 余数。
    Zhè dào tí de yú shù shì wǔ.
    The remainder in this problem is five.
  • ，余数。
    Zài mó yùn suàn zhōng, yú shù bù néng dà yú chú shù.
    In modular arithmetic, the remainder cannot be larger than the divisor.

Origin

Compound word
构词法gòucífǎ
偏正piānzhèngModifier + head

The first part narrows down the second: it says what kind of thing the head is.

余yúremaining
数shùnumber

余 (remaining) and 数 (number) form the number left after division.

Characters in this word

Most characters — around four in five — are built this way: one part hints at the meaning, the other at the pronunciation.

This origin belongs to the traditional form 餘; 余 is its simplified writing.

Meaning part形符xíngfú
食食shí
Sound part声符shēngfú
余
余yú餘Yú
Same sound today

The traditional form 餘 pairs 食 (food) with 余 as its sound part; the simplified 余 is a later abbreviation.

Open 余 →

Most characters — around four in five — are built this way: one part hints at the meaning, the other at the pronunciation.

This origin belongs to the traditional form 數; 数 is its simplified writing.

Meaning part形符xíngfú
攴攴pū
Sound part声符shēngfú
婁
婁lóu數shù(r)
The sound has drifted apartThe sound part was a clue two thousand years ago — it often still helps, but not always.

The traditional form 數 pairs 攴, the meaning part, with 婁, the sound part; the simplified 数 is a shorthand.

Open 数 →

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