Is "divide into" in this sentence equivalent to "be divided by"?

Question

When the beats divide into twos, the music is said to be in simple time;

Source: The AB Guide to Music Theory, page 19, in the last paragraph

But I don't understand why is the 3/4 time signature also in simple time, since 3 can not be divided by two.

In this answer it says that:

idiomatic alternative...
divide 2 into 4, giving the answer 2

And in this definition:

(of a number) be contained in a number without a remainder.
"3 divides into 15"

Then I guess that "divide 2 into 4 without a remainder" amounts to "2 divides into 4", and hence "the beats divide into twos" means "twos can be divided by the beats with no remainder". But does that statement make sense?

Answer 1

You are misunderstanding the use of "divide into" in the music example.

In common 4/4 time, the beats can be divided into 2. This is not because 4 is divisible by 2, but because each individual beat has two quavers in it. In 3/4 this is the same. Each beat has 2 quavers in it.

In compound time, the beats cannot be divided into 2. 6/8, for example, has 2 beats, each beat with 3 quavers.

The sentence is saying that the individual beats can be divided into two, not the number of beats in a bar.

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The meaning of "divide into" in this sentence is the same, you just applied it to the wrong thing.