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

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

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Roman C. | Masters of Education Graduate with Mathematics ExpertiseMasters of Education Graduate with Mathe...
4.9 4.9 (331 lesson ratings) (331)
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

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
0

      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) 

Andy Z. | Economics and Math TutorEconomics and Math Tutor
5.0 5.0 (16 lesson ratings) (16)
0

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

Comments

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

Clarification: -3/7 * 15/4=-3*15/7.4=Negative 45/28 WHERE THE NEGATIVE SIGN IS NEXT TO THE FRACTION

6/5/-1/3=6/5*-3/1=-18/5 WHERE THE NEGATIVE SIGN IS NEXT TO 18....WHY IS THE NEGATIVE SIGN NEXT TO THE FRACTION IN THE FIRST EXAMPLE AND IT IS NEXT TO THE NUMERATOR 18 IN THE SECOND FRACTION...

I HAVE BEEN OUT OF SCHOOL A WHILE SO PLEASE FORGIVE IF I AM NOT UNDERSTANDING

THANK YOU

It's okay. There is no need to apologize :)

Let's try again...

Negative 45/28 is the same as -45/28 which is also the same as 45/-28. Thus, it does not matter where the - sign is (in front, numerator, or denominator). The difference is simply preferences and continuity. Most of the time the negative is put in front of the entire fraction. This is apparently what mathematicians have agreed upon as the "normal" way of writing a negative faction.