She needs to run 4 3/8 miles
Explanation:[tex]\begin{gathered} \text{Given:} \\ 4\frac{5}{8}\text{ + r = 9} \end{gathered}[/tex]To solve for r, first we need to convert the mixed fraction to improper frction. Then we will subtract the fraction from both sides of the equation
[tex]\begin{gathered} 4\frac{5}{8}\text{ = 37/8} \\ \\ \frac{37}{8}\text{ + r = 9} \\ \\ \text{substract }\frac{37}{8}\text{ from both sides:} \\ \frac{37}{8}\text{ -}\frac{37}{8}\text{+ r = 9}-\frac{37}{8} \\ \text{r = 9 }-\frac{37}{8} \\ \text{LCM is 8} \\ r\text{ = }\frac{8(9)\text{ - 37}}{8} \end{gathered}[/tex][tex]\begin{gathered} r\text{ = }\frac{72-37}{8} \\ r\text{ = 35/8} \\ r\text{ = 4}\frac{3}{8} \end{gathered}[/tex]She needs to run 4 3/8 miles
