The price of one share in the stock market increases by 10% the first six months of a year and then falls by 40% in the last six months. What is the total change (in %) over the year for this share?

*(Give your answer in percentage, without the “%” symbol, and round your answer to the nearest unit)*

Let's calculate the total change in percentage over the year.

1. **Initial Price:** Let the initial price of the share be \( P \).

2. **After the first 6 months (10% increase):**
   \[
   \text{Price after increase} = P \times (1 + 0.10) = 1.1P
   \]

3. **After the next 6 months (40% decrease):**
   \[
   \text{Price after decrease} = 1.1P \times (1 - 0.40) = 1.1P \times 0.60 = 0.66P
   \]

4. **Total change over the year:**
   \[
   \text{Total change} = \frac{\text{Final Price} - \text{Initial Price}}{\text{Initial Price}} \times 100 = \frac{0.66P - P}{P} \times 100 = \frac{-0.34P}{P} \times 100 = -34\%
   \]

The total change over the year is \(-34\%\).

Would you like more details or have any questions about this solution? Here are five related questions:

1. How does compound interest differ from simple percentage increases?
2. What is the significance of the order of percentage changes?
3. How do you calculate the net percentage change over multiple periods?
4. How would the calculation change if the decrease happened first?
5. What would be the final percentage change if the increase was 50% and the decrease was 40%?

**Tip:** When dealing with percentages, order and the starting point significantly affect the final outcome.

Learn how to calculate the total percentage change in a stock price over a year with a detailed explanation. This problem involves calculating percentage changes over two periods: a 10% increase in the first six months followed by a 40% decrease in the last six months. Suitable for students in Grades 7-9.

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