Find two fractions with the same denominator, one positive and one negative, whose difference is 2/3

Question

I must show all my work

It helps me study better when I do that

Answer 1

Hi Bill.

If the difference is 2/3, then the denominators were both 3

 

So any two fractions with the same denominator of 3 which, whose numerators when subtracted gives you 2 will work.

 

 a  - b        2

---  ---  =  ----

 3    3         3

 

One has to be positive and the other negative, so   if a=1 and b=-1, then 

 

 1       (-1)      1 +  1      2

---  -  ---    = ---   --- = --- 

 3        3         3     3      3

 

 

 

so one possible answer is that one fraction is (1/3)  

and the other fraction is -(1/3)

Answer 2

If there is freedom to pick any denominator, then pick 3.  Then the fractions can be:

 

m/3, -n/3, with both m and n positive, and m - (-n) = 2.  That way,

 

m/3 - (-n/3) = (m + n)/3 = 2/3

 

Now find two positive numbers that add up to 2:  1 + 1 = 2 works

 

Then the fractions are 1/3 and -1/3.

 

Test: 1/3 - (-1/3) = 2/3