Poll: Asking for a friend – what do you understand by "6x4"

A big chunk of wood.

Before looking at the full question I started with a timber size. Then thought it might represent an area. Within the context of the full question I suppose it is:

a) An Area or b) Six, four copies of

but the little automated arithmetic unit at the back of my brain keeps "shouting" 24.

Another new IPv6 transition mechanism?

It reminds me of the 6to4 translation for IPv4 connectivity for IPv6 hosts.

My first thought: a small rectangle (width: 6px, height:4px)

The context has to be very particular for me not to consider this to be exactly 24 (natural number, not real number) without intermediate representation. I assume we're working over the ring of integers here. In that case, 6x4 is only ever not instantly 24 when it's part of an expression of similar terms (say, 6x1 + 6x2 + 6x3 + 6x4) in which a pattern is being expressed.

If you're not working over the usual ring, though, intuition goes out the window and I think of it as "six-but-not-six blob four-but-not-four". That's because in a module sense, it is 6 (element of ring) times (arbitrary multiplication operation) 4 (element of module).

6 wheels out of which 4 are driving wheels.

A grid of 6x4 cells, or a generic thing of 6 units by 4 units.

I may have done too much math to give a useful answer. 6 x 4 is the number which is the result of multiplying 6 and 4, here written with the 6 first, but probably not for any particular reason. It doesn't seem like any arrangement of lots or copies of anything, but all the listed arrangements of lots and copies are instances of it. Some other instances that are nothing like the suggested answers are "the area of a rectangle with dimensions 6 and 4" or "the amount of torque you get if you apply 6 Newtons to the end of a 4 meter arm"

Because it's not in an obviously maths context, I read it as "Six by Four", the first association in my mind for that is cars - 4 x 4 being four wheel drive, so I guess 6 x 4 would be a six wheeled vehicle with 4 driven wheels.

Standard photo size (6 inches by 4 inches) - or at least some form of note card/postcard/paper size.

I read it as six by four, as in the size of a photograph in inches.

Standard dimensions for photographic prints, pre digital cameras.

I thought of 4x6, the photo size.

First association - wood (mighty big as well)

Second association - 6 wheeled vehicle, 4 wheels driven (possibly because of the recent Top Gear with the Mercedes 6x6).

There are two options for "six, four copies of".

I see this as an area with six units along one side and four units along the next side.

I'd read "6 x 4" as "multiply 6 by 4" which I'd see as "6 + 6 + 6 + 6" and the same as six x four.

I am not sure what you mean by "lots" or "copies".

It can mean any of the things on your poll, and many not on your poll, except for "Six lots of four", that one doesn't make sense to me.

But that term has MANY meanings - without the context (arithmetic? wood? cars? IPv6? matrix?) it's impossible to say.

6 inches wide by 4 inches tall.

Multiplication would be 6 * 4 or 6 × 4, not 6 x 4.

Maybe this is the designer in me speaking, but I immediately thought of width x height.

Six sets of four reps each. But that's a really weird routine. I recommend 3-4 sets of 8-12 reps for most people.

As others have mentioned, a grid of 6 columns by 4 rows, like the resolution of a display.

How about: "The multiplicative ring operation of ℤ on the elements (((((1+1)+1)+1)+1)+1) and (((1+1)+1)+1)."

As a mathematician with a slight focus on algebra when I see such terms the questions that come to my mind are rather: Which ring am I working on, has it finite characteristics, is one of these numbers a ring element and the other an Element of ℤ [1]? It is always funny to see how your focus changes your perception :)

[1] For example 4 could be an element of the finite field with 5 elements GF(5). Then I would interpret 6x4 as 4+4+4+4+4+4, because 6 is not an element of GF(5) and I thus cannot plug it into the multiplication operation of GF(5).

I see 6x4 either as the dimensions of a surface, or as some kinds of informal coordinate (like "the 4th episode of the 6th season of a tv show).

The ordinary language expression "six times four" [and a wasted opportunity to use Polish notation]. After that "24" and I don't mean some picture of countable things but just the abstraction called "24".

Even after reading the poll answers none of the this-or-that options even prompt an image of a grouping. What makes algebraic notation useful is that it abstracts away the need to model the calculation further in most cases. There's no need to ponder "x lots of y or y lots of x". That's good because "lots" and "of" are more muddied. concepts than "times". My fourth grade teacher could explain "times" by giving examples of timesing. Examples of lotsing and ofing are harder to come by.

A plank of wood? i.e. six by four