What is -1.111... as mixed fraction

Step-by-step explanation:

When you are changing a repeating decimal to a fraction, there is a trick you have to know.  2 actually.  Put the decimal right before the repeating starts and right after the repeating starts.  This one is a bit tricky since the decimal is after a 1, and 1 is what is repeating.  So let's leave that one as is and simply say that

x = -1.11111

Now let's move the decimal right after the second one.  To do that you have to multiply by 10.  So we then can say that

10x = -11.11111

For this problem, we will disregard the negative til the end because it just makes things confusing.

Subtract the smaller equation from the larger:

  10x = 11.111111

-    1x =   1.111111

and get

9x = 10

Divide both sides by 9 to get 10/9 which is 1 1/9 as a mixed fraction.  Let's check it first to see if we're correct, then we'll throw the negative sign back on.  

10/9 on your calculator gives you 1.111111111 repeating, so now that we know we are correct, the mixed fraction is

-1 1/9