Write the answer as a mixed number when necessary:
The goal is to calculate the sum of two fractions with the same denominator: \(\frac{17}{4} + \frac{11}{4}\). Both fractions share the denominator 4, which makes the addition straightforward by summing their numerators.
To add the fractions, we combine the numerators over the common denominator:
\[\frac{17}{4} + \frac{11}{4} = \frac{17+11}{4} = \frac{28}{4}\]
Next, we simplify the fraction \(\frac{28}{4}\) by performing the division:
\[\frac{28}{4} = 7\]
Since the division results in a whole number, there is no fractional part remaining. Therefore, the sum is simply 7.
In daily life, this type of addition is common when working with measurements. For instance, if you have two lengths of wood measuring \(\frac{17}{4}\) inches and \(\frac{11}{4}\) inches, adding them together gives you a total length of \(\frac{28}{4} = 7\) inches. Understanding how to sum and simplify fractions is a foundational skill in carpentry, cooking, and many other practical tasks where materials are divided into segments.