Just curious as to why you can multiply straight across and it works. Why does multiplying the two parts, and two wholes works. I can see that it does work but am not sure what exactly is going on that does make it work.
My assumption is the following:
When multiplying 4/2 • 6/3
You are really saying 4 ÷ 2 • 6 ÷ 3
that can then be flipped to say 4 • 1/2 • 6 • 1/3
Multiplication can be done in any order. Multiplying by 1/2 and 1/3 is the same as multiplying by 1/6 or in other words dividing by 6 (this would be multiplying the denominators).
Also because multiplying can be done in any order you can multiply the 4 and 6 (numerators).
So you would then have the product of the numerators (24) times the product of the denominators (1/6) which si the same as 4/6 or 4÷6
I was just hoping there was an easier way to explain this.