Question

Find the difference.



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



Leave answer in fraction form

Answer 1

To calculate the expression \( 711 - (-1311) \) and \( \frac{7}{11} - \left(-\frac{13}{11}\right) \), let's break it down step by step.

1. **Calculating \( 711 - (-1311) \)**:
\[
711 - (-1311) = 711 + 1311
\]
Now, add the two numbers:
\[
711 + 1311 = 2022
\]

2. **Calculating \( \frac{7}{11} - \left(-\frac{13}{11}\right) \)**:
\[
\frac{7}{11} - \left(-\frac{13}{11}\right) = \frac{7}{11} + \frac{13}{11}
\]
Since the fractions have the same denominator, we can add the numerators:
\[
\frac{7 + 13}{11} = \frac{20}{11}
\]

Now, we have the two results:
- \( 711 - (-1311) = 2022 \)
- \( \frac{7}{11} - \left(-\frac{13}{11}\right) = \frac{20}{11} \)

The final difference can be expressed as:
\[
2022 - \frac{20}{11}
\]

To perform this subtraction, we need to express \( 2022 \) in terms of the same denominator (11):
\[
2022 = \frac{2022 \cdot 11}{11} = \frac{22242}{11}
\]

Now, we can subtract:
\[
\frac{22242}{11} - \frac{20}{11} = \frac{22242 - 20}{11} = \frac{22222}{11}
\]

Thus, the final answer is:
\[
\frac{22222}{11}
\]