# Thread: What's wrong in it

1. ## What's wrong in it

Please tell me where I am mistaking in the following problem

1/5 < 3/5 (1)
therefore 1 x 5 < 3 x 5
and 5 < 15

but 1/5 = -1/-5 (2)

therefore from 1 and 2

-1/-5 < 3/5
therefore -1 x 5 < 3 x -5
and -5 < -15

but we know that this is not the case.
So please tell me where have I mistaken.

2. Originally Posted by uspatange
Please tell me where I am mistaking in the following problem

1/5 < 3/5 (1)
therefore 1 x 5 < 3 x 5
and 5 < 15

but 1/5 = -1/-5 (2)

therefore from 1 and 2

-1/-5 < 3/5
therefore -1 x 5 < 3 x -5
and -5 < -15

but we know that this is not the case.
So please tell me where have I mistaken.
When you multiply (or divide) both sides by a negative you reverse the "sense" of the inequality. So
$\frac{-1}{-5} < \frac{3}{5}$

$-5 \cdot \frac{-1}{-5} > -5 \cdot \frac{3}{5}$

$-1 > -3$

-Dan

3. Originally Posted by topsquark
When you multiply (or divide) both sides by a negative you reverse the "sense" of the inequality.
You can prove this by addition.

Is -5 < -3?

Rather than multiply by -1 and reverse the inequality, add 5 and then add 3 (resist the temtation to simplfy everything.)

-5 < -3