The image shows a list of numbers and some equations that need to be completed using pairs of numbers from that list. The task is to fill in the blanks with the appropriate numbers so that the equations are correct.

List of Numbers:

• $-24$, $-12$, $3$, $-4$, $6$, $2$, $48$, $-8$

Equations to Complete:

1. $\_\_\_$ ÷ $8 = \_\_\_$
2. $\_\_\_$ × $2 = \_\_\_$
3. $\_\_\_$ ÷ $-6 = \_\_\_$
4. $\_\_\_$ ÷ $-8 = \_\_\_$
5. $\_\_\_$ ÷ $4 = \_\_\_$

Step-by-Step Solutions:

1. Equation 1: $\_\_\_$ ÷ $8 = \_\_\_$

   • Look for a number in the list that, when divided by $8$, gives a result also found in the list.
   • Possible solution: $\frac{48}{8} = 6$.
   • So, the answer is $48$ ÷ $8 = 6$.

2. Equation 2: $\_\_\_$ × $2 = \_\_\_$

   • Look for a number in the list that, when multiplied by $2$, gives a result also found in the list.
   • Possible solution: $\frac{6}{2} = 3$.
   • So, the answer is $3$ × $2 = 6$.

3. Equation 3: $\_\_\_$ ÷ $-6 = \_\_\_$

   • Look for a number in the list that, when divided by $-6$, gives a result also found in the list.
   • Possible solution: $\frac{-24}{-6} = 4$.
   • So, the answer is $-24$ ÷ $-6) = 4$.

4. Equation 4: $\_\_\_$ ÷ $-8 = \_\_\_$

   • Look for a number in the list that, when divided by $-8$, gives a result also found in the list.
   • Possible solution: $\frac{-24}{-8} = 3$.
   • So, the answer is $-24$ ÷ $-8) = 3$.

5. Equation 5: $\_\_\_$ ÷ $4 = \_\_\_$

   • Look for a number in the list that, when divided by $4$, gives a result also found in the list.
   • Possible solution: $\frac{-24}{4} = -6$.
   • However, $-6$ is not on the list. So, let's try another combination.
   • $\frac{-12}{4} = -3$.
   • Again, $-3$ is not on the list. A correct combination would be $\frac{-12}{-4} = 3$.
   • But as none of these seem to match well, this might be a typographical error or trick problem.

Summary of Solutions:

1. $48$ ÷ $8 = 6$
2. $3$ × $2 = 6$
3. $-24$ ÷ $-6$ = 4
4. $-24$ ÷ $-8) = 3$
5. $-12$ ÷ $-4$ = 3

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Would you like more details or have any questions?

Follow-up Questions:

1. What does it mean to divide a negative number by another negative number?
2. Can you find other pairs in the list that satisfy the equations?
3. How do you approach solving division problems with negative numbers?
4. How can you check your answers in multiplication and division equations?
5. What is the significance of understanding the order of operations in these problems?

Tip:

When working with negative numbers, remember that dividing or multiplying two negative numbers gives a positive result!