Question

Find the difference.



711−(−1311)\frac{7}{11}-\left(-\frac{13}{11}\right)
11
7
​
−(−
11
13
​
)

Answer 1

To find the difference, we will evaluate both expressions step-by-step.

1. Evaluating the first expression:

\[
711 - (-1311)
\]

This simplifies to:

\[
711 + 1311 = 2022
\]

2. Evaluating the second expression:

\[
\frac{7}{11} - \left(-\frac{13}{11}\right)
\]

This simplifies to:

\[
\frac{7}{11} + \frac{13}{11} = \frac{7 + 13}{11} = \frac{20}{11}
\]

Now we have two results:

- The result of the first expression is \(2022\).
- The result of the second expression is \(\frac{20}{11}\).

Next, we need to find the difference between these two results:

\[
2022 - \frac{20}{11}
\]

To combine the integer \(2022\) and the fraction \(\frac{20}{11}\), we convert \(2022\) into a fraction with a common denominator of \(11\):

\[
2022 = \frac{2022 \times 11}{11} = \frac{22242}{11}
\]

Now, we have:

\[
\frac{22242}{11} - \frac{20}{11} = \frac{22242 - 20}{11} = \frac{22222}{11}
\]

Thus, the difference is:

\[
\frac{22222}{11}
\]

If desired, you can also convert this fraction into a decimal or mixed number:

\[
\frac{22222}{11} \approx 2020.181818181818 \quad (or \quad 2020 \frac{2}{11})
\]

The final answer is:

\[
\frac{22222}{11}
\]