Why did they use 2. I don’t understand where the 2 would come from being that neither fraction can be reduced by it.

Question

First problem: -7/8 + (-1/2) ... I solved this by -7•2/8•2 + -1•8/2•8 = -14/16 + -8/16 which gave me -22/16 . But when I was given the problem 6/3 + (-1/6) they didn’t multiply the numerator and denominator by the opposite denominator. Instead they multiplied by 2. Why ?

Answer 1

So, Christina, the easiest way to find the common denominator is to multiply each by the other denominator, like you did.

 

However, in your first problem, the common denominator is 8, or 2(2)(2).

 

-7/8 +(-1/2)

 

Since -7/8 is already 2(2)(2), it can stay as -7/8.

 

-1/2 is missing 2(2), or 4. -1(4)/2(4) = -4/8

 

-7/8 + (-4/8) = -11/8 (if you reduce -22/16, you get -11/8).

 

So, let's look at 6/3 + (-1/6). The common denominator is 6, or 2(3).

 

36/18 - 3/18 = 33/18 = 11/6

 

Or, 12/6 + (-1/6) = 11/6

 

Make sense?