To determine how much Brianna grew in total during the two years, we need to add the growth from each year.
When Brianna was 15, she grew \( \frac{7}{8} \) of an inch. When she was 16, she grew \( \frac{1}{4} \) of an inch.
First, we need to find a common denominator to add these fractions. The denominators are \( 8 \) and \( 4 \). The least common denominator (LCD) is \( 8 \).
Now, we can convert \( \frac{1}{4} \) to have a denominator of \( 8 \):
\[ \frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8} \]
Now, we can add the two fractions:
\[ \frac{7}{8} + \frac{2}{8} = \frac{7 + 2}{8} = \frac{9}{8} \]
The total growth over the two years is \( \frac{9}{8} \) inches.
This fraction can also be expressed as a mixed number:
\[ \frac{9}{8} = 1 \frac{1}{8} \]
Therefore, Brianna grew a total of \( \frac{9}{8} \) inches or \( 1 \frac{1}{8} \) inches during those two years.
Final answer:
\[ \frac{9}{8} \text{ inches or } 1 \frac{1}{8} \text{ inches} \]