Given the following expression:

5 (+-×÷%) 4

You would say "5 plus 4," "5 minus 4," "5 times 4," "5 divided by 4," and "5 mod(ulo) 4" respectively.

As far as I know, "divided by" does not have any shorthand form in the same way the above examples do.

  • 1
    "5 by 4" actually indicates multiplication in common usage (or, more properly, the dimensions of the sides of an object or matrix). The percentage sign is commonly used as the modulo operator in computer languages. By the same token, though, division is expressed by a virgule (/) rather than a division sign (÷) in those same languages.
    – bye
    Commented Feb 20, 2011 at 16:49
  • @Jasper I included it because I'm into computer programming and it fit along with my examples. "5 mod 4" is how one would say it informally, but the correct phrasing is "5 modulo 4."
    – Corey
    Commented Feb 20, 2011 at 17:26
  • Isn't "by" also usually used to read a differential-- "dy/dx" > "dy by dx" doesn't strictly mean "dy over/divided by dx". Commented Feb 20, 2011 at 17:32
  • The way you phrase your question is fallacious. Might want to edit it. Also, the way it's phrased it identifies itself as too broad or vague, according to the FAQ. I'm just saying ...
    – Robusto
    Commented Feb 20, 2011 at 18:37
  • In your example phrases, plus, minus, times and modulo are not verbs. Commented Feb 20, 2011 at 18:54

4 Answers 4


Perhaps alternatives suffice to the extent that no great pressure exists to shorten "divided by"?

"5 over 4"?

"five fourths"?

  • 14
    No, it doesn't -- it merely describes the statement as if it were written in fractional notation rather than as if it were written using the division sign (÷).
    – bye
    Commented Feb 20, 2011 at 16:44
  • 2
    I almost always use "over." I also use "in(to)" sometimes, but that usually takes people a minute to figure out. Everyone I've worked homework problems with understands "over," though.
    – kitukwfyer
    Commented Feb 20, 2011 at 17:27
  • 6
    @jae: It most certainly does not. Unfortunately the state of understanding of mathematics is so poor, that people think division, fractions, ratio, odds are all different things. They are not.
    – Orbling
    Commented Feb 20, 2011 at 17:40
  • 2
    don't worry jae, I had the same connotation in mind. native germans speaker as well.
    – Femaref
    Commented Feb 20, 2011 at 19:10
  • 5
    @Martijn: the pronunciation I’m familiar with is "a choose b". I’m sure there are other options, though!
    – PLL
    Commented Feb 21, 2011 at 13:35

What about "per"? While not usually used in the same context as plus, minus, etc., it does mean "divided by".

  • 4
    As in 5 per 4 as an example for 5/4? That doesn't sound right, and most native english speakers wouldn't understand you. Commented Feb 20, 2011 at 21:41
  • 1
    It works for rates (which also involve division). Five miles in four hours is the same as five-fourths of a mile per hour (1.25 MPH). In that case, 1.25 miles per hour sounds much better than 1.25 miles over one hour (or 1.25 miles divided by one hour) even though they are both technically correct.
    – Adam
    Commented Feb 21, 2011 at 0:34
  • @advs89 But that's reserved pretty exclusively for dimensional analysis, and not actual division. You never simplify a "per" expression; you just cancel things which appear in both numerator and denominator. You wouldn't say "the ship was moving at 32 miles divided by hours" because that's not really accurate. In other words, you'll divide a number of miles by a number of hours, but you aren't actually dividing the units themselves. Commented Oct 20, 2015 at 17:46

Invert the question/problem

4 into 5 goes 1.2 was the way I was brought up...

  • This is why division tables are sometimes colloquially called "gazindas". "4 gazinda 12 three times, 4 gazinda 16 four times, ..."
    – mmyers
    Commented Feb 21, 2011 at 15:10

I would use "5 by 4" in a generic setting like @Jasper mentioned. @Stan's point is valid, however in a matrix setting we're usually specific, like "A five by four matrix". From what I've seen/heard/experienced, "5 times 4" is the colloquial norm for multiplication and "5 by 4" is the colloquial norm for division.

  • 6
    I don't think I'd interpret "by" as division unless there was a form of "divide" earlier in the sentence. The result of dividing 5 by 4 is...
    – Marthaª
    Commented Feb 20, 2011 at 17:21
  • The problem with by is that it's also used for material dimensions sans units. It would depend on the context, of course, but it could cause unnecessary confusion. In a purely mathematical discussion, there would likely be no problem, but when discussing applied mathematics in engineering or design, it's hard to tell where the pure numbers end and the materials begin.
    – bye
    Commented Feb 20, 2011 at 17:25
  • 1
    Unfortunately “by” is very ambiguous — I’ve heard it used by some people to mean multiplication, by others to mean division.
    – PLL
    Commented Feb 20, 2011 at 17:44
  • 1
    This is a varieties-of-English thing. In India, "five by four" means "five divided by four", except in dimensions like "a nine-by-four room". Commented Feb 20, 2011 at 18:55
  • 1
    This implies multiplication not division. Commented Feb 20, 2011 at 21:42

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