Let's solve the problems step-by-step:

Problem 4

Evaluate: $-4 \left(-3 \frac{1}{2}\right)$

First, convert the mixed number $-3 \frac{1}{2}$ to an improper fraction: $-3 \frac{1}{2} = -\frac{7}{2}$

Now, substitute and simplify: $-4 \left(-\frac{7}{2}\right) = 4 \times \frac{7}{2} = \frac{28}{2} = 14$

So, the answer to problem 4 is 14.

Problem 5

Evaluate: $7(-2.3)$

Multiply: $7 \times -2.3 = -16.1$

So, the answer to problem 5 is -16.1.

Problem 6

Compare expressions and fill in the table. Let's evaluate each expression first.

First Pair

1. Expression A: $-5 \left(4 \frac{1}{3}\right)$

   • Convert $4 \frac{1}{3}$ to an improper fraction: $4 \frac{1}{3} = \frac{13}{3}$.
   • Now, evaluate: $-5 \times \frac{13}{3} = -\frac{65}{3}$.

2. Expression B: $5 \left(-4 \frac{2}{3}\right)$

   • Convert $-4 \frac{2}{3}$ to an improper fraction: $-4 \frac{2}{3} = -\frac{14}{3}$.
   • Now, evaluate: $5 \times -\frac{14}{3} = -\frac{70}{3}$.

Since $-\frac{65}{3} > -\frac{70}{3}$, A > B for this pair.

Second Pair

1. Expression A: $-(-15 + (-5))$

   • Simplify inside the parentheses: $-15 + (-5) = -20$.
   • Now, evaluate: $-(-20) = 20$.

2. Expression B: $-(-15 + 5)$

   • Simplify inside the parentheses: $-15 + 5 = -10$.
   • Now, evaluate: $-(-10) = 10$.

Since $20 > 10$, A > B for this pair as well.

Summary for Problem 6

Would you like more details on any of the steps?

Here are some related questions to explore:

1. How do we handle operations involving negative fractions?
2. How does one convert mixed numbers to improper fractions?
3. What are the rules for multiplying positive and negative numbers?
4. How does changing the order of addition or subtraction affect expressions?
5. What strategies can help in comparing fractions quickly?

Tip: When comparing fractions, it can help to convert them to decimal form or find a common denominator.