Decimals as factors

[JeffM]

Yeah exactly. So if you take the 2 out of the 1 and 1.4, and re-writing as 2(0.5+0.7) you're not taking out a common factor as defined in arithmetic context?

I would say that "factor" is a whole number when discussing number theory, which used to be called the "higher arithmetic." I would also agree that in a number of contexts, say in "factoring a polynomial," what is usually intended by factor is an integer or a rational number. But I think the general meaning in mathematics is that a factor is a component of a product. Within different contexts, it may have a more restricted meaning, but it will always mean at least that. And sometimes it will mean nothing more than that. I recognize that that is a rather unsatisfactory state of affairs, but language has fuzzy borders.

Arguments about the meaning of words always comes down to how they are commonly used: a rose by any other name would smell as sweet.

 

[Steven G]

2(0.5+0.7) means two times what is inside the bracket. You don't need to think of the 2 as being factored out.

Suppose you bought two toothbrushes and two candy bars. One way to compute the sum is to add the cost of a toothbrush and the cost of a candy bar and then multiple that sum by 2.

Now if you want to think of the 2 being out in 2(0.5+0.7) you can certainly do that.

Since 2(0.5+0.7) = 2*0.5 + 2*0.7 = 1+1.4
You can now factor out 2 from (1+1.4) and get 2(0.5+0.7).
Why would you do that? To find the cost, for example, of one toothbrush (0.5) and the cost of one candy bar (0.7)

 

[lookagain]

In the expression xy, x is a factor of y and y is a factor of x.

Here are the words I would choose here:

In the expression xy, x is a factor with y, and y is a factor with x. In the product xy, x is a factor of it, and y is a factor of it.

 

[JeffM]

Here are the words I would choose here:

In the expression xy, x is a factor with y, and y is a factor with x. In the product xy, x is a factor of it, and y is a factor of it.

Better.