6. The steps your friend took to divide two mixed numbers are shown. $$ \begin{aligned} 3 \frac{3}{5} \div 1 \frac{1}{2} & =\frac{18}{5} \times \frac{3}{2} \ & =\frac{27}{5} \ & =5 \frac{2}{5} \end{aligned} $$ What should your friend change in order to divide the two mixed numbers correctly? A. Find a common denominator of 5 and 2. B. Multiply by the reciprocal of $$ \frac{18}{5} $$. C. Multiply by the reciprocal of $$ \frac{3}{2} $$. D. Rename $$ 3 \frac{3}{5} $$ as $$ 2 \frac{8}{5} $$. 7. A company ordering parts receives a charge of $$ \$ 25 $$ for shipping and handling plus $$ \$ 20 $$ per part. Which equation represents the cost $$ c $$ (in dollars) of ordering $$ p $$ parts? F. $$ c=25+20 p $$ G. $$ c=20+25 p $$ H. $$ p=25+20 c $$ I. $$ p=20+25 c $$

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UpStudy AI · Accepted Answer

Let's address both questions one by one:

---

### **Question 6**

**Problem:**  
Your friend attempted to divide two mixed numbers:

$$
\begin{aligned}
3 \frac{3}{5} \div 1 \frac{1}{2} & =\frac{18}{5} \times \frac{3}{2} \
& =\frac{27}{5} \
& =5 \frac{2}{5}
\end{aligned}
$$

However, the correct procedure for dividing by a fraction is to **multiply by its reciprocal**.

**Error Analysis:**  
- **Incorrect Step:** $$ 3 \frac{3}{5} \div 1 \frac{1}{2} = \frac{18}{5} \times \frac{3}{2} $$  
  - Instead of multiplying by $$ \frac{3}{2} $$, you should multiply by its reciprocal $$ \frac{2}{3} $$.

**Correct Procedure:**  
$$
\frac{18}{5} \div \frac{3}{2} = \frac{18}{5} \times \frac{2}{3} = \frac{36}{15} = \frac{12}{5} = 2 \frac{2}{5}
$$

**Conclusion:**  
To divide correctly, **multiply by the reciprocal of the second fraction**.

**Correct Answer:**  
**C. Multiply by the reciprocal of $$ \frac{3}{2} $$.**

---

### **Question 7**

**Problem:**  
A company charges a flat fee of \$25 for shipping and handling plus \$20 for each part ordered.

**Objective:**  
Formulate an equation representing the total cost $$ c $$ based on the number of parts $$ p $$.

**Solution:**  
The total cost $$ c $$ consists of:
- A fixed fee: \$25
- A variable fee: \$20 per part

Thus, the equation is:
$$
c = 25 + 20p
$$

**Correct Answer:**  
**F. $$ c = 25 + 20p $$**

---

**Summary of Answers:**  
- **Question 6:** **C. Multiply by the reciprocal of $$ \frac{3}{2} $$.**
- **Question 7:** **F. $$ c = 25 + 20p $$**
**Question 6:** Your friend should multiply by the reciprocal of $$ \frac{3}{2} $$ instead of $$ \frac{3}{2} $$ itself. **Question 7:** The cost $$ c $$ is represented by $$ c = 25 + 20p $$.

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