Mark Spahn writes:

On page 33 of the (British) textbook

Personally, when referring to division I always say "divide

In a division expression like

Looking up what "into" means in a division context, I find in

Another point to note is that "into", like "plus", is what in math is called a "dyadic infix operator"; that is, it occurs between two numbers and operates on them to produce another number. Compare:

3 plus 21 is 24 3 + 21 = 24There is an operator symbol (found on all calculators) for each of the four operators "plus", "minus", "times", and "divided by", but there are no signs to denote the

3 minus 21 is -18 3 - 21 = -18

3 from 21 is 18 3 ? 21 = 18

3 times 21 is 63 3 x 21 = 63

3 divided by 21 is 1/7 3/21 = 1/7

3 into 21 is 7 3 ? 21 = 7

The corresponding Japanese expressions are 加減乗除 = addition, subtraction, multiplication, division (加法, 減法, 乗法, and 除法, or 足し算, 引き算, 掛け算, and 割り算).

The results of these operations are called the sum (和), difference (差), product (積), quotient (商).

3 plus 4 is 7 3 + 4 = 7 3 足す 4 は 7Let's check these readings with native speakers. In particular, how are schoolkids taught to read "3 + 4 = 7"? And I hope someone will sit down one day and write a short article about the wording that goes through the mind of a Japanese while doing arithmetic. For example, the operation 3 x 3 = 9 seems to be memorized with the wording "サザン[三三]が九" (三省堂国語辞典, 第5版, entry "さ【三】").

8 minus 6 is 2 8 - 6 = 2 8 引く 6 は 2

6 from 8 is 2 6 ? 8 = 2 6 ? 8 は 2

3 times 4 is 12 3 x 4 = 12 3 掛ける 4 は 12

24 divided by 6 is 4 24/6 = 4 24 割る 6 は 4

6 into 24 is 4 6 ? 24 = 4 6 ? 24 は 4

I wonder whether short mental wordings like this make it easier to do arithmetic fast than wordings like "3 times 3 is nine". (Is it even possible to do arithmetic without imagining a pronunciation? Do abacists think of words as they manipulate their beads, or would that just slow them down?)

(September 1, 2003)