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To solve the problem of making \( b \) the subject of the formula given by:

\[
s = \frac{a}{a + b}
\]

we can follow these steps:

1. **Multiply both sides by \( a + b \)** to eliminate the fraction:

\[
s(a + b) = a
\]

2. **Expand the left-hand side**:

\[
sa + sb = a
\]

3. **Move all terms involving \( b \) to one side** and the terms involving \( a \) to the other side:

\[
sb = a - sa
\]

4. **Factor out \( a \) on the right-hand side**:

\[
sb = a(1 - s)
\]

5. **Solve for \( b \) by dividing both sides by \( s \)**:

\[
b = \frac{a(1 - s)}{s}
\]

Thus, the formula with \( b \) as the subject is:

\[
b = \frac{a(1 - s)}{s}
\]

Would you like more details on any step or have any questions? Here are some related questions for further practice:

1. If \( s = 0.5 \) and \( a = 10 \), what is the value of \( b \)?
2. How would the formula change if \( s = \frac{a + b}{a} \)?
3. If \( b = 0 \), what would \( s \) be in terms of \( a \)?
4. Derive a formula for \( a \) in terms of \( s \) and \( b \).
5. How does the value of \( b \) change as \( s \) approaches 1?

**Tip:** Always double-check your algebraic manipulations, especially when rearranging formulas to solve for a different variable.

Make b be the subject of the formula: s = a / (a + b).

Learn how to rearrange the formula s = a / (a + b) to make b the subject. This problem involves key algebraic concepts like fraction manipulation and formula rearrangement. Suitable for students in Grades 9-12.

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