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The image contains a set of math exercises labeled "Activity 1: Divide and Conquer." It asks for the ratio of the second number to the first number for each of the following number pairs:

1. \( -2 \) and \( 8 \)
2. \( 3 \) and \( 9 \)
3. \( 1 \) and \( -2 \)
4. \( -5 \) and \( -10 \)
5. \( 12 \) and \( 4 \)
6. \( -9 \) and \( -7 \)
7. \( 1^a \) and \( 1 \)
8. \( x^2 \) and \( x^a \)
9. \( 1 \) and \( 2^0 \)
10. \( 8xr \) and \( 8xr \)

Let me solve each ratio for you.

The ratio of the second number to the first number is calculated by dividing the second number by the first number. Let's compute them one by one.It looks like some of the pairs contain algebraic expressions rather than numbers, so I'll handle those separately. Let's go through the number pairs first:

1. \( -2 \) and \( 8 \): \( \frac{8}{-2} = -4 \)
2. \( 3 \) and \( 9 \): \( \frac{9}{3} = 3 \)
3. \( 1 \) and \( -2 \): \( \frac{-2}{1} = -2 \)
4. \( -5 \) and \( -10 \): \( \frac{-10}{-5} = 2 \)
5. \( 12 \) and \( 4 \): \( \frac{4}{12} = \frac{1}{3} \)
6. \( -9 \) and \( -7 \): \( \frac{-7}{-9} = \frac{7}{9} \)

Now for the algebraic expressions:

7. \( 1^a \) and \( 1 \): For any \( a \), \( 1^a = 1 \), so the ratio is \( \frac{1}{1} = 1 \).
8. \( x^2 \) and \( x^a \): The ratio is \( \frac{x^a}{x^2} = x^{a-2} \).
9. \( 1 \) and \( 2^0 \): Since \( 2^0 = 1 \), the ratio is \( \frac{1}{1} = 1 \).
10. \( 8xr \) and \( 8xr \): The ratio is \( \frac{8xr}{8xr} = 1 \).

Here are the final ratios:

1. \(-4\)
2. \(3\)
3. \(-2\)
4. \(2\)
5. \(\frac{1}{3}\)
6. \(\frac{7}{9}\)
7. \(1\)
8. \(x^{a-2}\)
9. \(1\)
10. \(1\)

Would you like more details or have any questions?

### Related Questions:
1. How do you simplify algebraic expressions involving powers like \(x^a/x^2\)?
2. What is the general method to find the ratio of two numbers?
3. What happens when dividing two negative numbers?
4. How do we handle ratios involving variables or powers?
5. What is the significance of the ratio \(1/1\)?

**Tip:** When calculating ratios, always check if both numbers are positive, negative, or zero, as that will affect the final sign and value.

Find the ratio of the second number to the first number for each given pair in the list: -2 and 8, 3 and 9, 1 and -2, -5 and -10, 12 and 4, -9 and -7, 1^a and 1, x^2 and x^a, 1 and 2^0, 8xr and 8xr.

Learn how to find the ratio of two numbers or algebraic expressions. This guide provides step-by-step solutions for a variety of number pairs and algebraic expressions, covering important concepts like ratios and exponentiation. Suitable for students in Grades 8-10.

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