# Thread: This kind of scenario (DIVISION help).

1. ## This kind of scenario (DIVISION help).

I need your insight on this matter again.
Can you explain why 2/5/2 cancels out the 2 and only leaves 1/5. I mean, if you write it down it would look like
2
__
5
__
2

You cancel out the twos and get left with 1over 5.
I don't really get this unless the following is the explanation:
2 .....1
__ x __
5 ..... 2

And that's how 2 and 2 cancel out because they are both divisible by themselves and they become 1.
But shouldn't it be something like
2 ..... 2
__ x __ ?
1...... 5

But then how would you get the answer of .20 if it was solved in this manner? So this is definitely wrong but isn't this supposed to be how it looks like?

Now I don't know whether that is right or wrong but I'd appreciate it if you could explain on that.
~
Another one like the above. The inverse of csc, sec, and cot is just one over sin, cos, and tan respectively.
This might be a very elementary question, but I need the answer to it if you do know; since I don't know the answer.
So cot = 1/tan
In turn that means 1/sin/cos
or
1
__
sin
__
cos
.
Now look back at the case of 2/5/2. This is where I'm confused. And I'm already past this law. I'm just reviewing. But suddenly seeing the 2/5/2 pop up, I actually became really confused.

Can you explain to me why
1
__
sin
__
cos

is not equal to

1 ...... 1
__ x ___
sin .. .cos

so to get the cancellation if ever that 1 was a cosine to actually simulate the 2/5/2 expression?
Thanks to anyone who's willing to help and reply.

This is the proper forum I believe since the latter still boils down to the concept of the former and I need to understand the former before the latter would make sense.

2. ## Re: This kind of scenario (DIVISION help).

Originally Posted by RandomInquirer
I need your insight on this matter again.
Can you explain why 2/5/2 cancels out the 2 and only leaves 1/5. I mean, if you write it down it would look like
2
__
5
__
2

...
Hello,

the confusion is caused by the writing of the fraction:

2/5/2 could be (2/5)/2
or
2/5/2 could be 2/(5/2)

In both cases: You divide by multiplying with the reciprocal. That means:

(2/5)/2 = (2/5) * (1/2) = 1/5

or

2/(5/2) = (2/1) * (2/5) = 4/5

You wrote:
So cot = 1/tan
In turn that means 1/sin/cos

Set paranthese
1/(sin(x)/cos(x)) and multiply with the reciprocal:

(1/1) * (cos(x)/sin(x)) = 1 * cot(x)