Let's solve each problem step by step.

### **6. \( 23 + 25 - 48 \)**

1. **Addition**: Start by adding the first two numbers.
   \[
   23 + 25 = 48
   \]
2. **Subtraction**: Now subtract 48 from the result.
   \[
   48 - 48 = 0
   \]

**Final Answer**: \( \mathbf{0} \)

---

### **7. \( (2)(3)(4) \)**

1. **First Multiplication**: Multiply the first two numbers.
   \[
   2 \times 3 = 6
   \]
2. **Second Multiplication**: Multiply the result by the third number.
   \[
   6 \times 4 = 24
   \]

**Final Answer**: \( \mathbf{24} \)

---

### **8. \( (-8)(-7) \)**

1. **Multiplication of Negative Numbers**: Multiply the two negative numbers. The rule is that multiplying two negatives gives a positive.
   \[
   (-8) \times (-7) = 56
   \]

**Final Answer**: \( \mathbf{56} \)

---

### **9. \( (-1)(2)(-4) \)**

1. **First Multiplication**: Multiply \(-1\) and \(2\).
   \[
   (-1) \times 2 = -2
   \]
2. **Second Multiplication**: Now multiply the result by \(-4\).
   \[
   -2 \times (-4) = 8
   \]

**Final Answer**: \( \mathbf{8} \)

---

### **10. \( \left(\frac{4}{5}\right)\left(\frac{2}{3}\right) \)**

1. **Multiply the Numerators**: Multiply the top numbers (numerators) together.
   \[
   4 \times 2 = 8
   \]
2. **Multiply the Denominators**: Multiply the bottom numbers (denominators) together.
   \[
   5 \times 3 = 15
   \]
3. **Form the Fraction**: Combine the results.
   \[
   \frac{8}{15}
   \]

**Final Answer**: \( \mathbf{\frac{8}{15}} \)

---

Would you like to explore further or ask about a specific step?

Here are some related questions:
1. What is the importance of order in arithmetic operations?
2. How can negative numbers be interpreted in multiplication?
3. What is the significance of multiplying by 1 in an equation?
4. How do you add fractions with different denominators?
5. Can you always simplify the fraction after multiplication?

**Tip:** When solving problems with multiple steps, always keep track of signs (positive/negative) and ensure to follow the correct order of operations.

Explore step-by-step solutions to arithmetic problems including addition, subtraction, multiplication of integers, and fraction multiplication. Learn fundamental arithmetic concepts with detailed explanations and examples. Suitable for middle school students.

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