To calculate the expression \( 711 - (-1311) \) and \( \frac{7}{11} - \left(-\frac{13}{11}\right) \), let's break it down step by step.
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Calculating \( 711 - (-1311) \): \[ 711 - (-1311) = 711 + 1311 \] Now, add the two numbers: \[ 711 + 1311 = 2022 \]
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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: \[ \frac{22222}{11} \]