# Math

##### 數學

In our fifth and final Numbers lesson, we will learn some basic arithmetic, as well as a few situations which appear far less frequently in practice than the ones in previous lessons, yet must be covered nevertheless.

##### 第

## ㄉㄧˋ

1. Ordinal numbers

Ordinal numbers are the way we say what order things go in. In English, we usually use #1, #2, #3; or 1st, 2nd, 3rd; to represent ordinals. Chinese has several ways to represent ordinals as well; the most common is to simply put 第 in front of one of the counting numbers you already know.

#1 | 第一 |

#2 | 第二 |

#3 | 第三 |

The full phrase adds the noun in question, with the appropriate measure word. It’s almost the same as the full version of a counting phrase.

1st person | 第一個人 | 1 person | 一個人 |

2nd person | 第二個人 | 2 people | 兩個人 |

3rd person | 第三個人 | 3 people | 三個人 |

Aside from the fact that 第 requires 二 instead of 兩, the only difference is the 第 in front. In addition, both grammar patterns can omit the noun in context.

1st person | 第一個 | 1 person | 一個 |

2nd person | 第二個 | 2 people | 兩個 |

3rd person | 第三個 | 3 people | 三個 |

Sometimes, the 第 phrase can appear without a measure word, whereas a counting phrase must always have one.

1st person | 第一 | 1 person | 一個 |

2nd person | 第二 | 2 people | 兩個 |

3rd person | 第三 | 3 people | 三個 |

A few examples of ordinals without counters or nouns:

我 | 考試 | 得 | 第一 |

I | test | get | #1 |

我考試得第一！

My test was the high score!

第一 | 請 | 先 | 洗 | 手 |

#1 | please | before | wash | hands |

第一，請先洗手。

First, please wash your hands.

Just as in English, ordinal words like 第一 and 第二 (first and second) can have multiple meanings.

我 | 昨天 | 買 | 了 | 我 | 第一 | 輛 | 車 |

I | yesterday | buy | -ed | I | #1 | (counter for cars) | car |

我昨天買了我第一輛車。

Yesterday, I bought my first car.

這 | 是 | 我 | 第一 | 次 | 吃 | 龍蝦 |

this | is | I | #1 | time | eat | lobster |

這是我第一次吃龍蝦。

This is my first time eating lobster

我 | 以第一 | 名的 | 成績 | 畢業 |

I | first | place’s | rank | graduate |

我以第一名的成績畢業。

I graduated first in my class.

開會 | 的 | 第一 | 個 | 小時 | 在 | 討論 | TPS | 報告 |

meeting | ’s | first | (counter) | hour | at | discuss | Testing Procedure Specification | report |

開會的第一個小時在討論TPS報告。

For the first hour of the meeting, we discussed TPS reports.

That said, many nouns do not require a 第 when used as an ordinal.

她 | 是 | 我 | 二 | 妹 |

she | is | I | two | little sister |

她是我二妹。

She is my second youngest sister.

餐館 | 在 | 五 | 樓 |

restaurant | at | five | floor |

餐館在五樓。

The restaurant is on the 5th floor.

Now lets do some math!

##### 加減乘除 等於

## ㄐㄧㄚ ㄐㄧㄢˇ ㄔㄥˊ ㄔㄨˊ ㄉㄥˇㄩˊ

2. Arithmetic

Basic math in Chinese is pretty simple. The word for “arithmetic” literally means “add-subtract-multiply-divide” ~~ or more accurately, “plus-minus-times-divided *into*”.

加減乘除 (ㄐㄧㄚ ㄐㄧㄢˇ ㄔㄥˊ ㄔㄨˊ)** ~ arithmetic**

加 (ㄐㄧㄚ)** ~ plus**

減 (ㄐㄧㄢˇ)** ~ minus**

乘 (ㄔㄥˊ)** ~ multiplied by, times**

除 (ㄔㄨˊ)** ~ divided into***

等於 (ㄉㄥˇ ㄩˊ)** ~ equals**

The operation “divided into” is, of course the *opposite* of “divided by”. “Two *divided into* four” is the same as “four *divided by* two” (4÷2). Just as in English, the second way is the common one.

除以 (ㄔㄨˊ ㄧˇ)** ~ divided by**

So then, the four operations would look like this:

二加二等於四 | 2 + 2 = 4 |

四減二等於二 | 4 – 2 = 2 |

二乘二等於四 | 2 × 2 = 4 |

四除以二等於二 | 4 ÷ 2 = 2 |

It will take a bit of practice before you are good enough at math that shopkeepers will stop using the calculator to show you prices; so any time you have a spare moment, use it to count things you see, read numbers out loud, or say basic math problems in Chinese.

##### 負 零下

## ㄈㄨˋ ㄌㄧㄥˊㄒㄧㄚˋ

3. Negative Numbers

To make a number negative, simply stick a 負 in front of it.

五 | 減 | 十 | 等於 | 負 | 五 |

five | minus | ten | equals | negative | five |

五減十等於負五。

Five minus ten equal negative five.

Just as in English, sometimes “negative” is substituted with “below zero”.

外面 | 是 | 零 | 下 | 十二 | 度 |

outside | is | zero | below | twelve | degrees |

外面是零下十二度。

It’s -12º outside.

##### 點

## ㄉㄧㄢˇ

4. Decimals

Yes, this is the same “dot” we used to say what time it is. To read a decimal, first say the integer, then 點, and then say the remaining numbers individually.

一百二十三 | 點 | 四五六 |

one hundred twenty-three | point | four, five, six |

一百二十三點，四五六

one hundred twenty-three, point four-five-six (123.456)

##### 分之

## ㄈㄣ ㄓ

5. Fractions

Fractions in Chinese are a little weird, because you have to say them backwards.

三 | 分 | 之 | 一 |

three | parts | ’s | one |

三分之一

one third (1/3)

五 | 分 | 之 | 三 |

five | parts | ’s | three |

五分之三

three fifths (3/5)

Just as English always reads 1/2 as “one half” (and never “one second”); Chinese always reads 1/2 as 一半 (never 二分之一).

Also just as in English, if there is a 100, 1000, etc. in the denominator (the bottom number), the “one” can be omitted.

(一)百 | 分 | 之 | 十五 |

(one) hundred | parts | ’s | fifteen |

(一)百分之十五

Fifteen (one) hundredths (15/100)

(Also) Fifteen percent (15%)

Finally, once more as in English, decimals can be read aloud as if they were fractions.

### Numerals

.747 = 747/1000

### English

Seven hundred forty-seven thousandths

### Chinese

一千分之七百四十七

But now we’re getting into math teacher stuff.

##### 趴

## ㄆㄚ

6. Percent

There are two main ways to say a percent in Chinese. The first is to read the number as a fraction of one hundred, using 百分之 .

百分之八十五

85%

The second, much simpler way is to replace the percent symbol with 趴.

八十五趴

85趴

85%

By the way, if you see a sign at the store that says 85趴, it means 85% **of** the original price, NOT 85% **off**!

We’re almost there! Next lesson, we will finally finish off the Numbers section once and for all, by learning how to state inequalities, and make basic comparisons in Chinese!