To solve for \( r \) in the equation \( F = P(1 + \frac{r}{100}) \), follow these steps:

### Step 1: Isolate the term containing \( r \)
Start by dividing both sides of the equation by \( P \) to get rid of \( P \) on the right side:
\[
\frac{F}{P} = 1 + \frac{r}{100}
\]

### Step 2: Subtract 1 from both sides
Subtract 1 from both sides to isolate the fraction with \( r \):
\[
\frac{F}{P} - 1 = \frac{r}{100}
\]

### Step 3: Multiply both sides by 100
Multiply both sides of the equation by 100 to solve for \( r \):
\[
r = 100\left(\frac{F}{P} - 1\right)
\]

### Final Answer
\[
r = 100 \left(\frac{F - P}{P}\right)
\]

Let me know if you need more details or have any questions!

### Related Questions:
1. How would you solve the equation if it included compounding, such as \( F = P(1 + \frac{r}{100})^n \)?
2. What is the relationship between \( F \), \( P \), and \( r \) in the context of simple interest?
3. How does the formula \( F = P(1 + \frac{r}{100}) \) relate to percentage increase calculations?
4. Can you express \( r \) in terms of \( F \), \( P \), and another parameter, say time \( t \)?
5. What happens to the value of \( r \) if \( F = 2P \)?

### Tip:
When solving equations, isolating the variable of interest (in this case, \( r \)) by systematically undoing operations is key to finding the solution.

Discover how to solve for the interest rate (r) in the linear equation F = P(1 + r/100). This step-by-step guide covers key algebraic concepts and percentage calculations, suitable for students in Grades 8-10.

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