Question

Evaluate the expression shown below and write your answer as a fraction or mixed number in simplest form.

− 2/7
​
− 10/11

Answer 1

To evaluate the expression \(-\frac{2}{7} - \frac{10}{11}\), we first need to find a common denominator for the fractions. The denominators are 7 and 11. The least common multiple (LCM) of 7 and 11 is 77.

Next, we convert each fraction to have the common denominator of 77.

1. Convert \(-\frac{2}{7}\) to an equivalent fraction with a denominator of 77:
\[
-\frac{2}{7} = -\frac{2 \times 11}{7 \times 11} = -\frac{22}{77}
\]

2. Convert \(-\frac{10}{11}\) to an equivalent fraction with a denominator of 77:
\[
-\frac{10}{11} = -\frac{10 \times 7}{11 \times 7} = -\frac{70}{77}
\]

Now we can combine the two fractions:
\[
-\frac{22}{77} - \frac{70}{77} = -\frac{22 + 70}{77} = -\frac{92}{77}
\]

We can simplify the fraction \(-\frac{92}{77}\). Since 92 and 77 have no common factors other than 1, \(-\frac{92}{77}\) is already in simplest form.

Thus, the final answer is:
\[
-\frac{92}{77}
\]

Or, converted into a mixed number:
\(-\frac{92}{77} = -1 \frac{15}{77}\).

So, the answer can be expressed as:
\[
-\frac{92}{77} \quad \text{or} \quad -1 \frac{15}{77}
\]