m = (z.f - g) / (z.f) * 100

formula to calculate z

To isolate \( z \) in the equation \( m = \frac{z.f - g}{z.f} \times 100 \), follow these steps:

1. Start with the given equation:
   \[
   m = \frac{z.f - g}{z.f} \times 100
   \]

2. Divide both sides by 100 to simplify:
   \[
   \frac{m}{100} = \frac{z.f - g}{z.f}
   \]

3. Rewrite the right side of the equation:
   \[
   \frac{m}{100} = 1 - \frac{g}{z.f}
   \]

4. Rearrange to isolate the fraction involving \( z \):
   \[
   \frac{m}{100} - 1 = -\frac{g}{z.f}
   \]

5. Simplify the left side:
   \[
   \frac{m - 100}{100} = -\frac{g}{z.f}
   \]

6. Multiply both sides by -1 to clear the negative sign:
   \[
   \frac{100 - m}{100} = \frac{g}{z.f}
   \]

7. Multiply both sides by \( z.f \):
   \[
   z.f \times \frac{100 - m}{100} = g
   \]

8. Divide both sides by \( \frac{100 - m}{100} \) to solve for \( z.f \):
   \[
   z.f = \frac{g \times 100}{100 - m}
   \]

9. Finally, divide both sides by \( f \) to solve for \( z \):
   \[
   z = \frac{g \times 100}{f (100 - m)}
   \]

Thus, the formula to calculate \( z \) is:
\[
z = \frac{g \times 100}{f (100 - m)}
\]

Would you like further details or have any questions?

Here are some related questions that might interest you:

1. How can you derive a similar formula if the variable \( f \) was not present?
2. What are common mistakes to avoid when isolating variables in an equation?
3. How can you verify the accuracy of your derived formula?
4. How does the formula change if \( m \) is in percentage format?
5. What happens to the value of \( z \) if \( m \) approaches 100?
6. Can you apply this formula to a real-world problem? If so, how?
7. How does altering \( g \) affect the value of \( z \)?
8. What mathematical concepts are important for understanding this derivation?

**Tip:** Always double-check your algebraic manipulations to avoid mistakes in isolating variables.

Learn how to calculate variable z using the percentage formula with a step-by-step solution. This problem involves isolating variables in equations and applying percentage calculations effectively. Suitable for advanced high school students and beyond.

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