how do I determine when the negative sign will be to the left of the entire fraction or next to the numerator or denominator

Question

How do I determine when the negative sign will be to the left of the entire fraction or next to the numerator or denominator?

 

REVIEWING FOR PRE-ALGEBRA

Answer 1

It is quite simple.

Look at the numerator and the denominator.

If exactly one of them is negative, you can move the minus sign to the front of the fraction.

  –2        2            2
 —– =  ——  = –  —–
   5       –5            5

If both are negative, then the minus signs cancel.

–2       2
—– = —–
–5       5

Answer 2

      3             3              3          15           45               17
–  ——  ×  3 ——  =  –  ——  ×  ——  =  – ——  =  – 1 ——
      7             4               7          4            28               28
or      
– 3/7 × 15/4
    
     1                        6         - 3        - 18              18             3
1 ——  ×  (– 3)  =  ——  ×  ——  =  ———  =  –  —— = – 3 ——
     5                        5           1           5                5              5 
or 
6/5 × (-3/1) 

Answer 3

A fraction with a negative sign in front of it is the same as a fraction with a negative sign in front of the numerator, or a fraction with a negative sign in front of the denominator.

For example:

-(1/2) = (-1)/2 = 1/(-2)

This is true because a negative one can be factored out from any negative number, similar to the way that a positive one can be factored out of any positive number.

For example:

-6 = -2 x 3     OR     -6 = -1 x 2 x 3

6 = 2 x 3       OR      6 =  1 x 2 x 3