Final answer:
The missing number that makes the equation (4/16) + (7/8) = 11_() correct is 1/8, as the simplified and combined fraction equals 9/8, or 1 1/8.
Step-by-step explanation:
To solve this equation (4)/(16) + (7)/(8) = 11_(), we first need to simplify the fractions and find a common denominator. The fraction 4/16 can be simplified to 1/4 because 4 is a common factor of both the numerator and the denominator. To add this to 7/8, we must have a common denominator. If we multiply the numerator and denominator of 1/4 by 2, we get 2/8, which can be added to 7/8. So the equation would look like this: 2/8 + 7/8 = 9/8.
Since 9/8 is greater than 1, we can convert it to a mixed number. 9/8 is equivalent to 1 1/8. Therefore, the sum of 1/4 (which was simplified from 4/16) and 7/8 is equal to 1 1/8. So, the missing number that makes the equation correct is 1/8.
The final step is to make sure this makes sense. Indeed, when we add 1/4 (or 2/8) to 7/8, we get 9/8, which is 1 1/8, confirming that our solution is reasonable.