Question

evaluate the expression shown below and write your answer as a fraction or mixed number in simplest form.
$-\frac{8}{11} - \frac{1}{12}$

Explanation:

Step1: Find a common denominator

The denominators are 11 and 12. The least common denominator (LCD) of 11 and 12 is \(11\times12 = 132\) since 11 and 12 are coprime.

Step2: Rewrite the fractions with the LCD

For \(-\frac{8}{11}\), multiply numerator and denominator by 12: \(-\frac{8\times12}{11\times12}=-\frac{96}{132}\)
For \(-\frac{1}{12}\), multiply numerator and denominator by 11: \(-\frac{1\times11}{12\times11}=-\frac{11}{132}\)

Step3: Subtract the fractions

Now we have \(-\frac{96}{132}-\frac{11}{132}\). When subtracting fractions with the same denominator, we subtract the numerators: \(\frac{-96 - 11}{132}=\frac{-107}{132}\)

Answer:

\(-\frac{107}{132}\)