Final Answer:
The sum of 3/11 + -11/3 is -2/3.
Step-by-step explanation:
To add fractions with different denominators, we first need to find a common denominator. In this case, the denominators are 11 and 3. The lowest common multiple (LCM) of 11 and 3 is 33. We can convert both fractions to have a denominator of 33 by multiplying the numerator and denominator of each fraction by the appropriate factor.
First, let's convert 3/11:
To find the factor to multiply the numerator and denominator by, we find the largest multiple of both the numerator and denominator that is less than or equal to the LCM. In this case, the largest multiple of both 3 and 11 that is less than or equal to 33 is 33. So, we multiply both the numerator and denominator by 11:
3/11 = (3 * 11)/(11 * 11) = 33/363
Next, let's convert -11/3:
To find the factor to multiply the numerator and denominator by, we find the largest multiple of both the numerator and denominator that is less than or equal to the LCM. In this case, the largest multiple of both -11 and 3 that is less than or equal to 33 is -39. So, we multiply both the numerator and denominator by -39:
-11/3 = (-11 * -39)/(3 * -39) = -441/117
Now that both fractions have a common denominator, we can add them:
-441/117 + 33/363 = -772/561 = -2/3 (rounded)