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Reggie's parents keep a chart on the wall where they mark how much Reggie grows each year. When Reggie was $15$, he grew $1$ inch and when he was $16$, he grew $\frac{4}{5}$ of an inch. In total, how much did Reggie grow in during those two years?$\newline$Write your answer as a fraction or as a whole or mixed number.$\newline$$\_\_\_\_$ inches