Part B A customer wants to know how many \( \frac{1}{4} \)-cup servings of cereal there are in the box of cereal. - Write an expression to find the number of \( \frac{1}{4} \)-cup servings of cereal that are in the box of cereal. - Use a model to find the number of \( \frac{1}{4} \)-cup servings of cereal that are in the box of cereal. Show your work. - How can you use the relationship between multiplication and division to find the number of \( \frac{1}{4} \)-cup servings of cereal that are in the box of cereal? Enter your answers in the space provided. Show all your work to support your answers.

To solve the problem, we need to determine how many \( \frac{1}{4} \)-cup servings are in a box of cereal. Let's break this down step by step. ### Step 1: Write an Expression Let \( C \) represent the total amount of cereal in the box (in cups). The expression to find the number of \( \frac{1}{4} \)-cup servings in the box can be written as: \[ \text{Number of servings} = C \div \frac{1}{4} \] ### Step 2: Use a Model to Find the Number of Servings To find the number of \( \frac{1}{4} \)-cup servings, we can use the expression derived above. Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, we can rewrite the expression as: \[ \text{Number of servings} = C \times 4 \] This means that if we know the total amount of cereal \( C \) in cups, we can simply multiply it by 4 to find the number of \( \frac{1}{4} \)-cup servings. ### Example Calculation Let's assume the box of cereal contains \( C = 2 \) cups of cereal. We can calculate the number of \( \frac{1}{4} \)-cup servings as follows: \[ \text{Number of servings} = 2 \times 4 = 8 \] So, there are 8 servings of \( \frac{1}{4} \)-cup in a 2-cup box of cereal. ### Step 3: Relationship Between Multiplication and Division The relationship between multiplication and division can be used to find the number of servings by recognizing that: \[ C = \text{Number of servings} \times \frac{1}{4} \] If we know the total amount of cereal \( C \) and we want to find the number of servings, we can rearrange this equation to: \[ \text{Number of servings} = C \div \frac{1}{4} \] This shows that dividing the total amount of cereal by the size of each serving gives us the number of servings. ### Summary 1. The expression to find the number of \( \frac{1}{4} \)-cup servings is \( C \div \frac{1}{4} \) or \( C \times 4 \). 2. If \( C = 2 \) cups, then the number of servings is \( 8 \). 3. The relationship between multiplication and division allows us to find the number of servings by dividing the total amount of cereal by the size of each serving.