When followed by a counter starting with a は—column syllable, the counter voices to a 'b' sound:

なん + はい becomes なんばい

As mentioned in the section on counting, the numerical orders in Japanese are technically counters too, with their own set of pronunciations:

Note that 一百 isn't used unless it needs to be stressed that it's one hundred, rather than some other factor of a hundred. Also note that quite obviously "ten hundred" doesn't exist. Instead this is 千, 1000.

The counter for a thousand has an irregular pronunciation for 3, and the question counter:

Again, unless the factor 1 needs to be stressed, 千 rather than 一千 is used. And again, there is no "ten thousand", there is the counter 万 instead.

The highest "low order" order counter, 万 stands for ten thousand. Because it is the highest "low order" order counter, it is used in combination with 10, 100 and 1000 to indicate a hundred thousand, a million and ten million respectively. 100 million is a new counter, おく億.

The biggest "useful" number, 億 is still a realistically large number in, for instance, prices for houses, luxury yachts or fancy sports cars. The pronunciation is wholly unremarkable:

While slightly ridiculous, there are counters for 10 to the power minus 21, which is the truly insignificant number 0.0000000000000000000001, up to the incredibly huge number 10 to the power 68, or 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Now, while for normal purposes these are of course ridiculous numbers, they're quite useful for science. The list of all available counters, plus their western abbreviated counterparts, is as follows:

The measures for mega (M), giga (G), peta (P) and exa (E) are missing from this set because these correspond to 10 to the powers 6, 9, 15 and 18 respectively, none of which are divisible by 4.

For orders higher than 48, there is a curious problem where in the rigid counting system the order keeps going up by 4, so that the five terms refer to 10 to the power 52, 56, 60, 64 and 68 respectively, but can also stand for older Japanese numbers, in which case they refer to 10 to the power 56, 64, 72, 80 and 88 respectively. While it is unlikely you will ever hear about these numbers ever again, these numbers have a very high trivia factor:

The first counter in this list isn't actually a counter, but an ordinal prefix. It's quite frequently used, so it's important you've learned it, and it's relatively easy to wrap your head around: if some counter statement says "... somethings", then prefixing 第 to it will create the statement "the ...th something" or "something (number) ...":

このほん本が１７か課があります。

"This book has 17 chapters."

第１～１０課はやす易くて, 第１１～１７課はむず難しいです。

"Chapters 1 through 10 are easy, chapters 11 through 17 are hard."

When you want to count cylindrical objects like pencils, bottles, or arms, 本 is used. As a noun this word means "book" or "origin", but as a counter it obviously means something completely different. The pronunciations for this counter are:

An example of its use is counting bottles of cola on the table:

何本ありますか。

"How many bottles are there?"

テーブルのうえ上にコーラが三本あります。

"There are 3 bottles of cola on the table."

Interestingly, phone calls can also be counted using this counter, the "logic" behind this being that telephone horns used to also be cylindrical (think of the classical phone with a rotary number dial).

This counter is used for counting bound objects like books, magazines, notebooks and the like. The pronunciations are:

And an example of use would be:

ほんだな本棚に五冊のほん本があります。

"There are 5 books on the bookshelf."

(In this sentence, 本 is used as a normal noun, not a counter.)

This counter is used to count volumes in a series of bound volumes. For instance, a twenty volume encyclopedia comprises ２０巻 worth of books. The difference between 巻 and 冊 is that 冊 only means bound volume. A stack of reading material consisting of a magazine, a newspaper, a novel and a text book on Japanese consists of 四冊, but since these are each completely different works, the stack does not consist of 四巻.

This counter is used to count sections in a (text) book, or lessons in a lesson programme. On its own, 課 technically means "division", but is understood within the context of something educational, so mostly translates to chapter, lesson, section, or even (educational) department.

This counter is used to count sheet-like things, such as sheets of paper, plates, planks, or even things like folded up T-shirts. The pronunciations are:

And an example of use would be:

このおお大きなほん本は何枚ですか。

"How many pages (literally: sheets) is this big book?"

This counter is used to count cups of drink, such as glasses of wine, cups of tea, glasses of beer and the like. The pronunciations are:

An example of use would be:

あか赤ワインを二杯とビールを一杯()くだ下さい。

"2 glasses of red wine and 1 glass of beer please."

Note that 一杯 can mean two things: as a counter statement it means "one cup [of something]". However, it can also be used as a quantifier, in which case it means "plenty" or "full", depending on the context. When used to mean "one cup", the pronunciation drops in pitch on "っぱい", whereas when it is used to mean "full", the pronunciation has a rising pitch on "っぱい".

This counter is used to count mechanical or electrical machinery of all sizes. This would include things like cars, televisions, pianos, cameras, sewing machines, and the like.

An example of use would be:

ともだち友達のヒロシは三台のコンピューターがあるんだって。

"(My) friend Hiroshi said he had three computers."

This counter is used to count floors or levels of a building, and has a special pronunciation for 3:

An example of use would be:

しんしつ寝室は二階にあります。

"The bedrooms are on the second floor."

For floors underground, the prefix ちか地下 (literally meaning "underground") is added to this counter:

In addition, there are also two useful words to know when it comes to floors, being さいじょうかい最上階, meaning "top floor" and ちゅうにかい中二階 meaning "mezzanine" (a 'floor' between first and second floor).

This is a general purpose counter used to count "numbers of [something]", such as the number of eggs needed for a specific recipe, or the number of bricks in a wall. The pronunciations are:

And example of use would be:

たまご卵を何個()い入れていいですか。

"How many eggs should (I) add?"

This counter is a typical fall-back counter when you do not know the proper counter for something, although with the note that it only makes sense for things that can be measured in units, or instances. So eggs and bricks are fine, people or thoughts are not.

This is a special general counter for counting items. Because this counter creates statements such as "I will have four [items]", it's typically omitted in translation because it doesn't indicate what kind of items are counted at all, merely that they are being counted. The pronunciations for this counter, as mentioned in the counting section, are what make this particle special, since it uses the native Japanese pronunciations for 1-9, and has a special question word:

Important to note is that 十 doesn't actually have つ as counter at all. Also, the question word for this counter can be used not just to ask "how many items", but also "how many years [of age]" someone is, although this only applies to the age of young children, as the counter only really goes up to 10. For children that are older, as well as adolescents and adults, the regular question word なんさい (何才 / 何歳), which is the question word for the counter for years of age, is used instead.

An example of use would be:

二つのオレンジがのこ残りました。

"There were 2 oranges left."

This counter is used for ¥, the Japanese currency. This counter has special pronunciations for 4 and 9, and also has a special question word:

An example sentence would be:

このペンは五十円でした。

"This pen was 50 yen."

Note the different readings よえん instead of "よんえん" and くえん instead of "きゅうえん". Also note that the question word for "how many yen" is actually the question word meaning "how much", and is remarkably similar to くらい in that it can be used to refer to either quantity, duration or frequency. Thus, the question いくらよ読みますか, "how much do you read?", can mean three different things, reflected in the possible answers to it:

にしゅうかん二週間にいっさつ一冊読みます。

"(I) read 1 book every 2 weeks."

いちにち一日ににじかん二時間読みます。

"(I) read 2 hours a day."

あんまり読ませんよ。

"Oh, (I) don't really read that much."

Of course, in the context of currency いくら is always understood as meaning "how much (money)".

Other major currency counters are ドル, the (US) dollar, ユーロ, the euro (€), and ポンド, the (British) pound.

Traditional Japanese houses, or traditional rooms in apartment buildings or flats in Japan (called わふうしつ和風室, literally 'Japanese style room'), are never counted in terms of square feet or meters, but in terms of how many tatami mats, たたみ畳, it will fit. This unit of measure is one of the 'common knowledge' units of surface measure, so it's generally a good idea to know it. The size of tatami mats depends on the region, ranging from 0.955 meter by 1.91 meter in the Kyoto area to only 0.88 meter by 1.76 meter in the Tokyo area. Thus, a 六畳 room may be bigger or smaller, depending on where in Japan you find it.

The counting table is fairly simple, with a different reading for 9:

Typically, however, there are only three counts for 畳, namely the common room dimensions for Japanese style rooms: 四畳()はん半 (four and a half), 六畳 and 八畳. When indicating actual counts of individual tatami mats, such as when purchasing replacement mats or for outfitting several rooms, the counter 枚 is used instead. The reason for this is that rather than indicating surface measure, you are now counting flat, sheet-like objects, which must of course be counted using the counter for flat, sheet-like objects.

This counter is used to count small animals. "Small" should not be taken too literally, as this counter applies to cats, squirrels, mice, or fish just as it does to great Danes (a particularly huge kind of dog) or even moderately sized alligators.

The pronunciations are:

An example sentence would be:

ねずみ一匹でもはい入れないはずです。

"Not even a single mouse should be able to get in (here)."

This kanji means "wings" when pronounced はね, and as a counter is used to count birds. As a peculiarity, this counter can also be used to count rabbits (although 匹 is more common these days), because of an interesting bit of Japanese history: from the 6th century until the mid-19th century, Japanese people were — by decree — forbidden to eat several kinds of meat between April and October. However, birds and adult fish could still be eaten, so in order to be able to eat meat anyway, people started calling certain animals by different names, referring to them as birds of fish. Boars, for instance, became "land whales" (whales still being considered fish at the time, rather than the mammals we now know them to be), and rabbits became "birds" on account of their floppy ears, so these animals were counted using the counters that applied to these animals instead. This practice lasted until 1872, when the Meiji restoration embraced a number of Western views and customs, and eating meat was allowed all year round again after a more than 1300 year period of decreed abstinence. That said, rabbits can of course also be counted using 匹.

The pronunciations for this counter are wholly unremarkable:

A fun example sentence for this counter is a classic:

庭には二羽の鶏がいる。

"There are 2 chickens in the garden."

The pronunciation for this sentence is "にわにわにわのにわとりがいる", which is always a good reason to use this sentence whenever appropriately possible.

This kanji on its own means "head", and for reasons about as inexplicable as why 本 is used for cylindrical objects, 頭 is used to count large animals such as sheep, cows, horses, elephants, giraffes, salt water crocodiles (which are astoundingly huge), etc. The pronunciations are:

An example sentence would be:

一頭のうま馬がみ見えます。

"(I) can see 1 horse."

It should be noted that there are special pronunciations for 1 person and 2 people, using the reading り, but that 3 and up are all counted using the pronunciation にん:

An example sentence would be:

あの二人はふうふ夫婦ですか。

"Are those two (people) over there a (married) couple?"

The polite counter for people, as used by, for instance, waiters or receptionists, is めい名, which has a very polite counterpart: めいさま名様. However, don't use these counters unless you find yourself serving patrons in a restaurant or something similar. For normal counting of people, stick with 人.

As a counter for occurrences, this counter is principally used only for counting once, twice and thrice. For something that occurs more than three times, かい回 is used instead.

Aside from being used for occurrence, 度 is also used to count degrees Celsius, and geometric degrees (such as a 90 degree angle, or GPS degrees). The pronunciations are:

Example sentences would be:

もう一度()い言ってくだ下さいませんか。

"Could you please say that one more time?"

きょう今日はあつ暑いねえ。何度でしょう。

"It's hot today, don't you think? I wonder what temperature (literally: how many degrees) it is."

This particle is also a noun on itself, pronounced たび, which is used as a nominaliser for turning clauses into occurrences, which will be explained in the next chapter, in the nominalisers section.

While strictly speaking not genuinely related to counters, a special note for this counter involving the indicator 今, meaning "now" and read as こん, should be added: こんど今度 can either mean "now", or "next time":

今度はなん何だ。

"Oh, now what?"

また今度！

"(See you) next time!"

Where 度 is used for once, twice and thrice, 回 can be used for any number of occurrences. The pronunciations are:

An example sentence would be:

もう三回してみちゃったよ。

"(I) already tried (and failed) three times..."

The same oddity for 度 exists, when pairing 回 with こん今:

こんかい今回はなん何だ。

"Oh, now what?"

今回にしましょう。

"Let's do (that) next time."

This counter is used to indicate a number in a ranking. This counter has a different pronunciation for 9, so the pronunciations are:

An example sentence would be:

わたし私は三番です。

"I'm (up) third."

The first count in this series, 一番, is the same 一番 that is used in the adjectival superlative in Japanese, since it literally means "first" and thus also means "most".

This counter is used to count issues, such as magazine or newspaper issues, or number in a series, such as room numbers on a floor, or the number of a limited series prototype car. Like 番, it has a different pronunciation for 9, so the pronunciations are:

An example sentence would be:

りょうしん両親は１７号にす住んでいます。

"My parents live at number seventeen."

The combination of 番 and 号, ばんごう番号, is used to indicate a ranked "number", such as a phone number, registration number or product serial number, where the number doesn't particularly indicate a rank on its own, but does sit at a particular position in the greater list of all numbers of its category.

It can also be used to change the number from an absolute value, such as "17 Thornhill Street" to a position in an ordered list, such as "the 17th house after you turn left":

両親は１７号に住んでいます。

"My parents live at number seventeen."

両親は１７番号に住んでいます。

"My parents are the seventeenth door."

In the second sentence, "seventeenth" is understood to be from some kind of (contextually obvious) reference point, like the start of the block, or from the floor's staircase.

This is technically not a counter, but can be added to rank counters to indicate ordinality — that is, it indicates an item's position in some ordered set. Being very specific: adding 目 to a counter changes the count from a cardinal number to ordinal number.

For instance, it can be used in combination with 日 to create the counter 日目, changing the meaning from "... days" or "day ... of the month" to "the ...th day (relative to some arbitrary time)":

みっか三日にホテルでと泊まった。

"We stayed at the hotel for three days."

みっかめ三日目にホテルで泊まった。

"We stayed at a hotel on the third day."

It's also frequently combined with 番 to create the counter ばんめ番目, which changes the meaning from a number in a ranking, to number of appearance. For instance, a runner with the back number "214" could be the first person to start in a relay, in which case the runner himself would be indicated using 214番のランナー (or 214号のランナー) but would also be the 一番目のランナー, because he's the first runner.

Another example of this difference can be shown in the context of waiting for a bus:

このていりゅうじょ停留所から５番のバスにの乗ってくだ下さい。

"Please take the no. 5 bus at this bus stop."

この停留所から５番目のバスに乗って下さい。

"Please take the fifth bus at this bus stop."

Counting seconds in Japanese uses 秒, for which the pronunciations are:

An example sentence would be:

何秒かかりますか。二十秒か、はんぷん半分か。

"How long will it take? 20 seconds, half a minute?"

Moving from seconds to minutes, the counter for minutes has different pronunciations for 3, 4, and the question word:

An example sentence would be:

いま今さんじ三時五分()まえ前です。

"It's now 5 minutes to 3."

Also, the measure "half minute" (as used in the example sentence for seconds) is はんぷん半分, using the same pronunciation as for 三 and 何.

Don't confuse clock hours with durational hours. Clock hours are things like "three o' clock" and "seven in the evening". Durational hours are "it took 3 hours" or "I went home after waiting an hour". This counter is for the first category and indicates the hours of the day:

Note the pronunciations for 4 and 9, both being the short pronunciations. An example sentence would be:

何時ですか。

"What time is it?"

The indicators for a.m. and p.m. are ごぜん午前 and ごご午後 in Japanese, indicating whether a time is before or after the "hour of the horse", which corresponds to the period from 11 a.m. to 1 p.m. according to the classical Chinese system. These are prefixed to the time:

いま今午後三時です。

"It is 3 p.m."

午前九時にあ会おう。

"Let us convene at 9 a.m."

To make the "useful words" list complete, midday is しょうご正午, and midnight is れいじ零時.

By adding the durational particle かん間 — literally "interval" — to the counter 時, we get the durational counter for hours. The difference between clock time and duration is striking:

何時ですか。

"What time is it?"

何時間ですか。

"How long is it?"

This difference is also very important for actual counting statements. Quite often, people starting with Japanese will mix up 時 and 時間, creating sentences such as the following:

三時間です。

"It's three hours long."

When they really mean to say 三時です, "it's 3 o' clock". Similarly, they might say:

二時()にべんきょう勉強しました。

"(I) studied at 2 o' clock."

while meaning to say 二時間に勉強しました, "I studied for two hours".

Moving up from hours to days, we reach a rather interesting counter. As explained before, this counter is special in several ways. Firstly, counting 1 to 10 days uses the counter 日 in its pronunciation か, paired with native Japanese readings for the numbers. 14 and 24, too, use 日 pronounced as か, but use a mixed Chinese/Japanese reading for the number, and "20 days" has its own special word. The rest of the days are counted using 日 in its pronunciation にち, with Chinese read numbers:

The reading for 一日 differs depending on what it's used to mean: ついたち refers to the first day of the month, but the reading いちにち is also possible, in which case it refers to a single day in duration (including 'my day' in, for instance, "my day consists of doing ..."). Also, for every other number under 32, 日 refers to both day of the month and length of duration in days. Any number above 31 automatically only means "days of duration", since months only go up to the 31st at best. Because of this, 34, 44, etc. have the pronunciation ～よ(ん)にち instead of ～よっか.

An example sentence would be:

ふつか二日いっぱく一泊と泊まった。

"(We) stayed 2 days and one night."

In this sentence a counter that won't be treated separately, はく泊, is used which means "nights of stay".

There are two question words regarding dates; we can be either use いつ, which means "when", or we can use the counter question word なんにち何日. We can also ask about the length of duration in days, for which we can use two question words too: どのぐらい, for approximate duration, and 何日, for exact duration.

Aside from being able to count days, it's also good to be able to name the immediate past and future days:

You may sometimes head the word ほんじつ本日 being used to mean "today" (or, less frequently, "yesterday" or "tomorrow"). However, this word is only used when there is some contextual day that is tied to a specific date. The word 本日 literally means "the day in question", and can be taken to mean "today" (or "yesterday" or "tomorrow") only when the event's "day in question" coincides with "today" (or "yesterday" or "tomorrow").

Increasing the scale further, we reach weeks, indicated with 週. Like 時, 週 on its own just refers to the yearly week, with 週間 referring to length of duration as measured in weeks. The pronunciations are:

An example sentence would be:

ことし今年のまつ祭りは十八週です。

"This year's festival is in week 18."

The words for the immediate past and future weeks are:

Like 時, 週 has to be followed by 間 to turn it into a durational counter:

しけん試験はおよそ二週間です。

"The exams are in about two weeks."

Like 時 and 週, 月 alone refers to month of the year. While western languages typically have named months, the Japanese — not too long ago in fact — gave up on named months in favour of the Chinese system of numbered months, resulting in:

The names of the months have been added here to stress that these are not so much numbered months, but calendar months. Remember them as such! Also note that there are specific readings for April, July and September. You can't use another reading for the number for these words — these "counts" are very much fixed in the Japanese language as nouns. The question word for month of the year is なんがつ何月.

The words for the immediate past and future months are:

And finally, in the interest of satisfying human curiosity, the old names for the months are:

When read as つき, and paired with the native Japanese readings for numbers, this counter expresses duration in terms of lunar months, and is typically only used for indicating 1 to 3 months of duration. This is a slightly poetic counter, but is also used in formal writing to indicate the 1-3 month durational range:

While — like 時 and 週 — 月 on its own means "month of the year", the suffix 間 cannot be used to turn 月 into a durational counter. Instead, the prefix ヶ is used, but be careful: this is not the katakana ケ, but actually a simplified kanji form of 箇. You can tell this difference by looking at the size of the kanji: ヶ月 (かげつ) vs. ケ月 — the katakana ケ is much bigger than the simplified version of 箇. Why exactly this kanji got simplified to this deceptive form is not entirely clear, but it has, which means you'll need to be able to recognise it as a counter. The standard contractions occur in the pronunciations:

An example sentence would be:

三ヶ月にがいこく外国にいます。

"I will be abroad for three months."

Once more, there is the distinction between years in an era, 年, and years of duration, 年間. The pronunciations for 年 are:

An example sentence would be:

このほん本はめいじ明治十年の本です。

"This book is from 1877."

(The 明治 era ran from 1868 to 1912, so with 1868 being the first year, the 10th year of the Meiji era is 1877 — more on this later, in the section on time and dates)

The words for the immediate past and future years are:

年生 — Scholar year

Once more, adding 間 turns the counter into a durational counter:

三年間チャンピオンのざ座をまも守った。

"(He) kept with his title (literally: 'seat') as champion for three years."

The one thing 年 cannot be used for is to indicate years of age. For this, two special counters are used: 歳 and its simpler counterpart 才. While simpler, it's generally not a good idea to use it in every instance where writing age is required; because it is simpler, using it is a sign that you're not quite good enough at kanji yet to write the "real" kanji form. The pronunciations are the same as for any other さ-counter:

The reading くさい for 九歳, while technically possible, should be avoided, since it sounds identical to くさ臭い, meaning "smelly/stinky". Also note that there is a special word for twenty years of age, はたち, just like there is a special word for twenty days, はつか.

An example sentence would be:

とう父さんはあした明日六十一歳になります。

"My father will turn 61 tomorrow."

There is a special counter that is used for the ages 20 through 90, being じ路, and using native Japanese numbers (with 十 pronounced そ), although typically only 30 through 60 are actively used:

In addition to these counts, there are numerous terms and titles associated with virtually each age, but listing all of these goes well beyond the scope of this book.

As mentioned in the particle section on も, this word doesn't mean two different things in Japanese, but merely gets translated with two different words depending on whether it's followed by a positive or negative verb.

いつもそんなこと事ばかりい言っている。

literally: "(You)'re always saying only those kind of things."

meaning: "(You)'re always saying the same thing."

いつもしないのに、どうしてわ分かるんですか。

"Why is it (you) know (how to do it) when (you) never do it (in the first place)?"

When indicating something happens 'most of the time', or 'usually', たいてい is used. There's not much else to say about it other than that it's usually used in combination with a positive verb form:

たいていしちじ七時にお起きます。

"(I) usually get up at 7."

We've already covered this adverb by virtue of it being the adverbial form of よい. In a quantifying role, it signifies a frequent occurrence of whatever verb it's being used with:

よくおよ泳ぎます。

"(I) often swim."

This adverb actually comes from the the 五段 verb 余る, meaning "to be left over", and is the counterpart to よく. It is typically only be used when followed by a negative verb or verbal adjective:

こうちゃ紅茶はあんまりす好きじゃありません。

"(I) don't like (red) tea very much."

There is no real difference between あまり and あんまり, but the latter sounds slightly more emphatic.

This quantifier only works when followed by a positive verbal adjective:

これはとてもやす安いですね。

"This is very cheap isn't it?"

This quantifier can be emphatically intensified by sticking a っ in, to form とっても:

とってもたの楽しかったよ。

"That was really, really fun."

The kanji form should already give it away, but when activities are performed from time to time, 時々 is used:

時々みんなでえいが映画をみ見にい行きます。

"We all go to the cinema together from time to time."

The construction 時々 may frequently be found written as ときどき instead. The choice on whether to use a kanji or kana form depends mostly on intended style. In literary material the kanji form is preferred, while in informal writing the kana form is used more.

Like あまり, this quantifier is usually followed by a negative verb or verbal adjective:

全然()かま構いませんよ。

"(I) don't mind at all."

However, it derives its negative meaning only from these verbals — there is no rule that says this word cannot be used with affirmative verbals instead, in which case it translates to "completely". Like the こそあど+(で)も words, the meaning of 全然 itself is merely this "complete"-ness, connoting "not at all" only because it is paired with a verbal negative.

Like とても, this quantifier only works when followed by positive verbals:

これはかなりたか高いんですね。

"This is rather expensive, isn't it?"

Like あまり and ぜんぜん, this quantifier is typically followed by a negative verb:

これはさっぱりわ分かりません。

"(I) don't understand this at all."

However, on its own さっぱり just means "clean" or "neatly", again highlighting the fact that most quantifiers associated with a negative quantity only do so thanks to the negative verb form.

Literally, this quantifier means "in small part", and is usually followed by a positive verb:

少しま待てばいいかな。

literally: "Waiting for a little while is okay, isn't it?"

meaning: "Could (we) wait for just a bit?"

にほんご日本語は少しわ分かります。

"I understand Japanese a little (bit)."

This quantifier can be followed by either a positive verb or verbal adjective in normal statements, or by negative verbs and verbal adjectives when used in the form of a question. When used in a negative question, the full sentence actually connotes a positive, as can be seen in the following examples:

ちょっとさむ寒くないですか。

"Isn't it a little cold?"

ちょっとある歩きませんか。

"Shall (we) take a little walk?"

Used with a positive, there is nothing remarkable to note:

これはちょっとたか高いですね。

"This is a bit expensive, don't you agree?"

Mentioned in the counter section for 杯, this quantifier can only be used with positive verbs:

あいにく、ほんじつ本日はよやく予約で一杯です。

"(I)'m sorry, but today is fully booked."

Remember that this is only a quantifier if pronounced with the っぱい part in raised pitch. If pronounced with the っぱい part in a lower pitch, it means "one cup (of something)".

Used as the comparative for adjectives, as well as comparative for verb actions, this quantifier can only be used with positive verbs and verbal adjectives:

まだた足りないみたいね。ざいりょう材料をもっとい入れて。

"It looks like it's still not enough. (Please) add in (even) more (of the) ingredients."

This quantifier is only used with positive verbal adjectives:

かのじょ彼女はどんなモデルよりでもずっときれいだ。

"She's much prettier than any model."

This word actually translates to a wide spectrum of words, because of what it's composed of: the mimesis ず paired with と. This mimesis represents a straight, through and through somethingness, so that it can be translated as "very much", "completely", and even "forever", depending on the context.

This quantifier means "all" or "wholly" by virtue of its literal meaning "all parts":

おかね金をほとんどぜんぶ全部つか使ってしまった。

"(I)'ve spent almost all my money."

Beginning students will often mistakenly use this quantifier when meaning すべ全て, which means "every(thing)" rather than "all", or vice versa, so make sure you picked the right one.

This quantifier is usually paired with positive verbs (and should not be confused with ぜんぶ全部):

ほんだな本棚にあるほん本を全てよ読んでしまった。

"(I)'ve (sadly) read every book on (my) shelves."

Addition is the root of all things maths related. The idea of addition is a childishly simple one: you have something, you get more, you have more. The mathematical part of this concept is to determine how much more you have, and for this we need three things: numbers, something that states addition, and something that marks an outcome. Luckily (though not unexpectedly) Japanese has all three of these. Numbers we have already seen plenty of, the outcome marker is simply です, and the verb that we use for addition is た足す.

いち一足すよん四はご五です。

"One plus four is five."

In this use, 足す acts remarkably western in that even though 足す is used in 連体形, and should thus be attributive, 一足す四 does not say "a one-added four", but merely says "one plus four" (this is also the case for the verb used for subtraction).

We can also use 足す on its own, for such obvious things as:

にじゅうえん二十円をた足せば、ちょうどにする。

"If (you) add 20 yen, that'll make it (a) round (number)."

Where ちょうど is a nice little word meaning 'exact' or 'precise'. In this sentence, it is interpreted as "round number", because in the context of numbers, a precise number corresponds to a 'clean' number, which can either be a round number, or a number without a decimal fraction.

For subtraction, ひ引く instead of 足す is used:

さんびゃく三百引くごじゅうさん五十三はにひゃくよんじゅうなな二百四十七です。

"300 minus 53 is 247."

Division in Japanese is done in the same way as in western maths, but the phrasing is somewhat confusing if you don't pay attention: in western maths, the number that results from 3 × ⅕ is pronounced "three fifths". In Japanese, this 'factor, then denominator' order is the reverse, so instead of saying "three fifths", in Japanese you say "five's three":

ごぶん五分のさん三。

literally: "three five-parts"

"⅗"

This uses the genitive の to link 三, 3, as genitivally belonging to 五分, ⅕.

One thing to note here is that in this use, 分 is pronounced ぶん, and this is the reason why the counter series for minutes has an oddity for three, where ふん becomes ぷん instead of ぶん:

A final simple operation is multiplication, which uses the noun ばい倍. This is actually a rather interesting word, because on its own it means "two fold", such as in for instance:

もんだい問題が倍になった。

"(Our) problems doubled."

Interestingly, this noun can also be used in combination with other numbers (except of course the number 1) to indicate any random multiplication:

ごばい五倍のしち七はさんじゅうご三十五です。

"7 times 5 is 35."

Here, the literal statement is "the five-fold of seven is 35".

This is basic multiplication, but there's also another word that's used for the x-fold for one through ten involving the counter 重, which is pronounced in various different ways this role:

You may have noticed that this is perhaps the most bizarre counter series the language has; the counter has three different possible readings, has a mix of possible native Japanese and Chinese readings for the numbers, and the native reading used for 10 is very rare one, not to mention the question word uses 幾 instead of 何.

Needless to say, this counter series is "special". In fact, it's so special that it's a mainly literary counter for "-fold", where it depends on the context which reading is used. In eloquent language, え is more likely, and in technical literature, じゅう will be used more.

There are two special words for squaring (x²) and cubing (x³), へいほう平方 and りっぽう立方, used to indicate squared and cubed units respectively. For instance, when indicating something is 500 square kilometres, one would say:

500平方キロ(メートル)です。

"(It) is 500 square kilometres."

Or, if one wanted to say a particular vehicle has a 12 cubic meter interior, one could say:

なかみ中身は12立方メートルです。

"The interior fits 12 cubic meters."

Going beyond squares or cubes, and raising numbers to an arbitrary power in Japanese uses the counter じょう乗, and is used in the following way:

しち七のさんじょう三乗はさんびゃくよんじゅうさん三百四十三です。

"7 to the power 3 is 343."

The inverse of this operation is taking the root of some power, which is done with the "counter" じょうこん乗根, which is just the counter for raising power paired with the noun for 'root':

よんじゅうきゅう四十九のにじょうこん二乗根はしち七です。

"The square root of 49 is seven."

And that's it, that's all the mathematics you will probably care to know how to work with, so let's leave the numbers as what they are and move on to the next chapter, which deals with more general language patterns.