Answer:
David increased by \( \frac{1}{8} \) of an inch over the summer, which is equivalent to \( 0.125 \) inches.
Step-by-step explanation:
To find out how much David increased over the summer, we need to calculate the difference in height between when he finished his first year of high school and when he returned after the summer.
David's height at the end of his first year of high school: \( 71 \frac{9}{16} \) inches
His height after returning from summer break: \( 73 \frac{7}{16} \) inches
To find the increase, we subtract his initial height from his height after the summer:
\[ \text{Increase} = \text{Height after summer} - \text{Height at end of first year} \]
\[ \text{Increase} = 73 \frac{7}{16} - 71 \frac{9}{16} \]
To subtract fractions, we need a common denominator. Since both fractions already have the same denominator (16), we can directly subtract the numerators:
\[ \text{Increase} = 73 \frac{7 - 9}{16} \]
\[ \text{Increase} = 73 \frac{-2}{16} \]
Now, we can simplify the fraction:
\[ \text{Increase} = 73 \frac{-1}{8} \]
To convert the fraction to a mixed number, we divide the numerator (-1) by the denominator (8):
\[ \text{Increase} = 73 - \frac{1}{8} \]
\[ \text{Increase} = 73 - 0.125 \]
\[ \text{Increase} = 72.875 \]
So, David increased by \( \frac{1}{8} \) of an inch over the summer, which is equivalent to \( 0.125 \) inches.
