Introduction:
To find the rational number that should be added to -7/11 in order to get 4/7, we need to determine the difference between these two fractions. By finding the difference, we can identify the numerator and denominator of the rational number that needs to be added.

Step 1: Finding the difference:
To find the difference between -7/11 and 4/7, we need to have a common denominator for both fractions. The least common denominator (LCD) is the smallest multiple of the denominators, which in this case is 77.

Step 2: Converting the fractions:
To convert -7/11 and 4/7 into fractions with a common denominator, we multiply the numerator and denominator of each fraction by the appropriate factor to obtain fractions with the same denominator.

-7/11 = (-7 * 7) / (11 * 7) = -49/77
4/7 = (4 * 11) / (7 * 11) = 44/77

Step 3: Finding the difference:
Now that both fractions have a common denominator, we can find the difference by subtracting -49/77 from 44/77.

44/77 - (-49/77) = 44/77 + 49/77 = (44 + 49) / 77 = 93/77

Step 4: Simplifying the rational number:
The difference between -7/11 and 4/7 is 93/77. However, to find the rational number that needs to be added to -7/11, we need to simplify this fraction.

To simplify 93/77, we divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 93 and 77 is 1, so we can simplify the fraction to its simplest form.

93/77 = 93/77

Conclusion:
Therefore, the rational number that needs to be added to -7/11 in order to get 4/7 is 93/77.