11. Divide. Draw a number line to show your work. \( 2 \div \frac{1}{3}=\square \)

To solve the division problem \( 2 \div \frac{1}{3} \), we can follow these steps: 1. **Understand the Division of a Fraction**: Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the expression as: \[ 2 \div \frac{1}{3} = 2 \times 3 \] 2. **Perform the Multiplication**: Now we can calculate: \[ 2 \times 3 = 6 \] So, \( 2 \div \frac{1}{3} = 6 \). Next, let's represent this on a number line: - We start at 0 and mark the number 2. - Since we are dividing by \(\frac{1}{3}\), we can think of this as how many \(\frac{1}{3}\) units fit into 2. - Each \(\frac{1}{3}\) unit can be represented on the number line, and we can count how many of these fit into 2. Now, let's draw the number line and indicate the points: 1. Mark the points for 0, \(\frac{1}{3}\), \(\frac{2}{3}\), 1, \(\frac{4}{3}\), \(\frac{5}{3}\), 2, 3, etc. 2. Count how many \(\frac{1}{3}\) segments fit into 2. I'll create the number line representation now. ### Number Line Representation - **0** | **1/3** | **2/3** | **1** | **4/3** | **5/3** | **2** | **3** - **0** | **1** | **2** | **3** | **4** | **5** | **6** From 0 to 2, we can see that there are 6 segments of \(\frac{1}{3}\) (i.e., \(0, \frac{1}{3}, \frac{2}{3}, 1, \frac{4}{3}, \frac{5}{3}, 2\)). Thus, the final answer is: \[ 2 \div \frac{1}{3} = 6 \]