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To solve part (a) of the problem, we need to determine the maximum value of \( a + b \) given the constraints:

- \( a \) can be either 4 or 5.
- \( b \) can be either 1 or 2.

Let's evaluate all possible combinations of \( a \) and \( b \) to find the maximum value of \( a + b \):

1. If \( a = 4 \) and \( b = 1 \), then \( a + b = 4 + 1 = 5 \).
2. If \( a = 4 \) and \( b = 2 \), then \( a + b = 4 + 2 = 6 \).
3. If \( a = 5 \) and \( b = 1 \), then \( a + b = 5 + 1 = 6 \).
4. If \( a = 5 \) and \( b = 2 \), then \( a + b = 5 + 2 = 7 \).

The maximum value of \( a + b \) is:

\[
\boxed{7}
\]

Would you like to go through the other parts (b) to (h) as well, or do you have any questions about this part?

Here are some related questions:
1. How would you find the minimum value of \( a + b \)?
2. What are the steps to determine the maximum value of \( ab \)?
3. How can you calculate the minimum value of \( a - b \)?
4. What method would you use to determine the maximum value of \( \frac{a}{b} \)?
5. How do you find the maximum value of \( a^2 - b^2 \)?

**Tip:** Always list all possible combinations when dealing with maximum or minimum problems to ensure you cover all scenarios!

In this question the value of a is either exactly 4 or 5, and the value of b is either exactly 1 or 2. Work out: a) the maximum value of a + b.

Explore how to calculate the maximum and minimum values for expressions involving two variables a and b, with detailed examples. This problem involves basic arithmetic operations like addition, subtraction, multiplication, and division, suitable for Grades 6-8 students.

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