To simplify the expression \( 100 \times \left(1 - \frac{a - b}{a}\right) \), we can proceed as follows:

1. Start with the expression:
   \[
   100 \times \left(1 - \frac{a - b}{a}\right)
   \]

2. Distribute the division within the parentheses:
   \[
   = 100 \times \left(1 - \frac{a}{a} + \frac{b}{a}\right)
   \]

3. Simplify \(\frac{a}{a}\) to \(1\):
   \[
   = 100 \times \left(1 - 1 + \frac{b}{a}\right)
   \]

4. Combine terms within the parentheses:
   \[
   = 100 \times \frac{b}{a}
   \]

5. This gives us:
   \[
   = \frac{100b}{a}
   \]

So, the simplified form of the expression is:
\[
\frac{100b}{a}
\]

Would you like further details or have any questions?

### Related Questions
1. How would this simplify if \( b = 0 \)?
2. How does this expression change if you replace \(a\) with another variable?
3. What if you wanted to maximize \( \frac{100b}{a} \) for specific values of \(a\) and \(b\)?
4. How would this be useful in a real-world percentage change calculation?
5. Could we apply similar steps to simplify \(100 \times \left(1 - \frac{c - d}{c}\right)\)?

**Tip:** When simplifying, look for terms that cancel, such as \(\frac{a}{a} = 1\).

Discover how to simplify the expression 100 × (1 - (a - b) / a) in a step-by-step algebraic solution. Learn key simplification techniques and apply them to percentage calculations. Suitable for students in Grades 8-10.

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