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Grammar detail: mathematical notation

mathematical notation
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This article shows how to express simple arithmetic as well as more complex mathematical formulas in Japanese.
Arithmetic
When reading out a formula, the operators are read as follows:
+たす
-ひく
xかける
÷わる
=は (read わ)
For example, 3 x 2 = 6 would be read さんかけるにはろく.
More examples:
くわ
える
なる
Add 5 to 3 and you have 8.
じょう
- to the power of
さん
さん
じょう
にじゅうなな
27
である
3 to the third power is 27.
Odd and even numbers
3
even number  (see also: 奇数)
(click the word for examples and links)
2
odd number  (see also: 偶数)
(click the word for examples and links)
Sequences
4
noun
arithmetic progression; arithmetic sequence  (see also: 等差級数; mathematics)
(click the word for examples and links)
4 6
noun
arithmetic series  (see also: 等差数列)
(click the word for examples and links)
Fractions and parts
中 can be used to illustrate a part of a whole. For example:
  • ろくにん
    6人
    ちゅう
    ごにん
    5人
    いしゃ
    医者
    five out of six doctors
The most common way to indicate a part of something is X
ぶん
の Y. For example:
わたし
ケーキ
よんぶん
4分
いち
べた

I ate a quarter of a cake.
Ratios
Ratios are expressed in the form 〜
たい
〜. For example:
その
がっぺい
合併
いちたいいち
1対1
おこな
われた

The merger was implemented on an equal basis.
クラス
だんじょひ
男女比
だんせい
男性
たい
じょせい
女性
2
たい
さん
3

The ratio of males to females in the class is 2:3.
Averages
しち
じゅう
10
じゅうろく
16
へいきん
平均
じゅういち
11
である
The average of 7, 10, and 16 is 11.
Key mathematical terms
3
noun
decimal point; radix point
(click the word to view an additional 1 form, examples and links)
1
noun
denominator  (mathematics)
(click the word for examples and links)
1
1. numerator
2. molecule
(click the word to view an additional 1 meaning, examples and links)

Note: this article is a work in progress! If you need help with something not covered here, please let us know via the feedback link.
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Kanji used in this grammar

ジョウ   load; power   の to board   のせる to load on   
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チュウ   ジュウ   なか middle   
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ジン   ニン   ひと person   
イ    doctor   
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シャ   もの person, someone   
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ブン   ブ   フン   わける to divide, to distinguish   わかる to understand   わかれる to be divided   わかつ to share, distribute   
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タイ   ツイ    vis-a-vis   
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カ   くわえる to add to   くわわる to join, to be added to   
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シ   わたくし    わたし I, myself   
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ショク   ジキ    food   たべる to eat   く to eat   
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ゴウ   ガッ   カッ   あ to fit, come together   あわす to match   あわせる to unite, join   
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ヘイ   あわせる to combine, put together, unite   
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コウ   ギョウ   アン   ゆ    い to go   おこな to take place   
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ダン   ナン   おとこ male, man   
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ジョ   ニョ   ニョウ   woman; female   おんな woman   め woman   
ヒ   くらべる to compare   
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セイ   ショウ    sex, gender, nature, disposition   
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ヘイ   ビョウ   たい flat   ひら ordinary; flat   
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キン    level; average   
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