Rachel has $\frac{7}{15}$ of her project done. If she can finish $\frac{7}{45}$ of her project each day, how many more days will it take her to complete it? $\newline$ It will take her _________more days.

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Q. Rachel has

\frac{7}{15}

of her project done. If she can finish

\frac{7}{45}

of her project each day, how many more days will it take her to complete it?

\newline

It will take her _________more days.

Determine Remaining Fraction: Determine the fraction of the project Rachel has left to complete. $\newline$ Rachel has completed $\frac{7}{15}$ of her project. To find out how much she has left to do, we subtract the completed fraction from the whole ( $1$ ). $\newline$ Remaining fraction of the project = $1 - \left(\frac{7}{15}\right)$
Calculate Remaining Fraction: Calculate the remaining fraction of the project. $\newline$ Remaining fraction of the project = $1 - \left(\frac{7}{15}\right)$ $\newline$ = $\left(\frac{15}{15}\right) - \left(\frac{7}{15}\right)$ $\newline$ = $\left(\frac{15 - 7}{15}\right)$ $\newline$ = $\frac{8}{15}$
Determine Daily Completion Rate: Determine how much of the project Rachel can complete each day. $\newline$ Rachel can complete $\frac{7}{45}$ of the project each day.
Calculate Number of Days: Calculate the number of days it will take Rachel to finish the remaining project. $\newline$ To find the number of days, divide the remaining fraction of the project by the daily completion rate. $\newline$ Number of days = $(\text{Remaining fraction of the project}) / (\text{Daily completion rate})$ $\newline$ Number of days = $(8/15) / (7/45)$
Perform Division: Perform the division to find the number of days. $\newline$ Number of days = $(\frac{8}{15}) / (\frac{7}{45})$ $\newline$ To divide by a fraction, we multiply by its reciprocal. $\newline$ Number of days = $(\frac{8}{15}) \times (\frac{45}{7})$
Simplify Multiplication: Simplify the multiplication to find the number of days. $\newline$ Number of days = $(\frac{8}{15}) \times (\frac{45}{7})$ $\newline$ = $(8 \times 45) / (15 \times 7)$ $\newline$ = \frac{ $360$ }{ $105$ }
Simplify Result: Simplify the result to get the number of days. $\newline$ Number of days = $\frac{360}{105}$ $\newline$ = $\frac{24}{7}$ $\newline$ Rachel will need $\frac{24}{7}$ days to complete her project.