Each friend received \( b \) cookies. How many cookies did each friend receive? Complete the tape diagram to represent the word problem. Start by labeling the total.

To represent the word problem **"Each friend received \( b \) cookies. How many cookies did each friend receive?"** using a tape diagram, follow these steps: ### 1. **Understand the Problem** - **Total Cookies**: This is the entire amount of cookies being distributed. - **Number of Friends**: Let's denote the number of friends as \( f \). - **Cookies per Friend**: Each friend receives \( b \) cookies. ### 2. **Draw the Tape Diagram** A tape diagram visually represents the total quantity divided into equal parts. Here's how to construct it: #### **Step-by-Step Guide:** 1. **Draw a Large Rectangle (Total):** - Draw a horizontal rectangle to represent the **Total Cookies**. - Label this rectangle as **Total Cookies** or simply **Total**. ``` ---------------------------- | Total | ---------------------------- ``` 2. **Divide the Rectangle into Equal Parts:** - Since each friend receives \( b \) cookies, divide the **Total** rectangle into \( f \) equal parts (where \( f \) is the number of friends). - Each part represents the cookies received by one friend. ``` ---------------------------- | | | | | | b | b | b | ... | | | | | | ---------------------------- ``` *(Each segment labeled "b" represents the number of cookies one friend receives.)* 3. **Label Each Part:** - Label each divided section with \( b \) to indicate that each friend gets \( b \) cookies. ### 3. **Final Tape Diagram Example** Assuming there are **3 friends**, the tape diagram would look like this: ``` Total Cookies ---------------------------- | b | b | b | ---------------------------- Friend1 Friend2 Friend3 ``` Here: - **Total Cookies** = \( b + b + b = 3b \) - Each **\( b \)** represents the number of cookies one friend receives. ### 4. **Interpretation** - The **Total** is divided equally among the friends. - If you know the number of friends (\( f \)), the equation can be written as: \[ \text{Total Cookies} = f \times b \] - If you need to find the total number of cookies when each friend receives \( b \) cookies, multiply the number of friends by \( b \). ### 5. **Visual Representation Without Specific Numbers** If the number of friends isn't specified, the tape diagram will show the **Total** divided into equal sections labeled \( b \): ``` Total Cookies ---------------------------- | b | b | b | ... | ---------------------------- ``` Each **\( b \)** still represents the number of cookies per friend, and the number of sections corresponds to the number of friends. ### 6. **Summary** - **Total Cookies** is the entire length of the tape. - Each **\( b \)** represents the portion of the total given to one friend. - The number of sections (each labeled \( b \)) corresponds to the number of friends. This visual aid helps in understanding how the total is distributed equally among friends.