2. Consider the problem: How many liters of water fit in the water dispenser? a. Write a multiplication equation and a division equation for the question. b. Find the answer and explain your reasoning. If you get stuck, consider drawing a diagram. c. Check your answer using the multiplication equation. 9.3: Amount in One Group Write a multiplication equation and a division equation and draw a diagram to represent each situation. Then, find the answer and explain your reasoning. 1. Jada bought $$ 3 \frac{1}{2} $$ yards of fabric for $$ \$ 21 $$. How much did each yard cost? 2. $$ \frac{4}{9} $$ kilogram of baking soda costs $$ \$ 2 $$. How much does 1 kilogram of baking soda cost? $$ 1 \frac{1}{5} $$ bottles with 3 liters of water. How many liters of water fill 1 bottle? 3.

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Let's break down the problems step by step.

### Problem 2: Water Dispenser

#### a. Write a multiplication equation and a division equation for the question.

Let $$ x $$ be the number of liters of water that fit in the water dispenser.

- **Multiplication Equation:** If we know how many bottles of water fit in the dispenser and how many liters each bottle holds, we can express it as:
  $$
  \text{Number of bottles} \times \text{Liters per bottle} = x
  $$

- **Division Equation:** If we know the total amount of water and how many liters fit in each bottle, we can express it as:
  $$
  x \div \text{Liters per bottle} = \text{Number of bottles}
  $$

#### b. Find the answer and explain your reasoning.

Assuming we have a specific number of liters and bottles, let's say the dispenser holds $$ 12 $$ liters and each bottle holds $$ 3 $$ liters.

1. **Using the multiplication equation:**
   $$
   \text{Number of bottles} = \frac{12}{3} = 4
   $$
   So, the dispenser can hold $$ 4 $$ bottles of water.

2. **Using the division equation:**
   $$
   12 \div 3 = 4
   $$
   This confirms that $$ 4 $$ bottles fit in the dispenser.

#### c. Check your answer using the multiplication equation.

Using the multiplication equation:
$$
4 \times 3 = 12
$$
This confirms that the total amount of water in the dispenser is indeed $$ 12 $$ liters.

---

### Problem 9.3: Amount in One Group

#### 1. Jada bought $$ 3 \frac{1}{2} $$ yards of fabric for $$ \$ 21 $$. How much did each yard cost?

**a. Write a multiplication equation and a division equation.**

Let $$ y $$ be the cost per yard.

- **Multiplication Equation:**
  $$
  y \times 3.5 = 21
  $$

- **Division Equation:**
  $$
  21 \div 3.5 = y
  $$

**b. Find the answer and explain your reasoning.**

To find $$ y $$:
$$
y = \frac{21}{3.5}
$$

Calculating $$ y $$:
$$
y = 21 \div 3.5 = 6
$$
So, each yard costs $$ \$ 6 $$.

**c. Check your answer using the multiplication equation.**
$$
6 \times 3.5 = 21
$$
This confirms that the total cost is $$ \$ 21 $$.

---

#### 2. $$ \frac{4}{9} $$ kilogram of baking soda costs $$ \$ 2 $$. How much does 1 kilogram of baking soda cost?

**a. Write a multiplication equation and a division equation.**

Let $$ z $$ be the cost per kilogram.

- **Multiplication Equation:**
  $$
  z \times \frac{4}{9} = 2
  $$

- **Division Equation:**
  $$
  2 \div \frac{4}{9} = z
  $$

**b. Find the answer and explain your reasoning.**

To find $$ z $$:
$$
z = \frac{2}{\frac{4}{9}} = 2 \times \frac{9}{4} = \frac{18}{4} = 4.5
$$
So, 1 kilogram of baking soda costs $$ \$ 4.5 $$.

**c. Check your answer using the multiplication equation.**
$$
4.5 \times \frac{4}{9} = 2
$$
This confirms that the cost for $$ \frac{4}{9} $$ kilogram is indeed $$ \$ 2 $$.

---

#### 3. $$ 1 \frac{1}{5} $$ bottles with 3 liters of water. How many liters of water fill 1 bottle?

**a. Write a multiplication equation and a division equation.**

Let $$ w $$ be the liters per bottle.

- **Multiplication Equation:**
  $$
  w \times 1.2 = 3
  $$

- **Division Equation:**
  $$
  3 \div 1.2 = w
  $$

**b. Find the answer and explain your reasoning.**

To find $$ w $$:
$$
w = \frac{3}{1.2}
$$

Calculating $$ w $$:
$$
w = 3 \div 1.2 = 2.5
$$
So, each bottle holds $$ 2.5 $$ liters of water.

**c. Check your answer using the multiplication equation.**
$$
2.5 \times 1.2 = 3
$$
This confirms that $$ 1 \frac{1}{5} $$ bottles hold $$ 3 $$ liters of water.
**Problem 2: Water Dispenser** - **a. Equations:** - Multiplication: Number of bottles × Liters per bottle = Total liters - Division: Total liters ÷ Liters per bottle = Number of bottles - **b. Answer:** - If the dispenser holds 12 liters and each bottle holds 3 liters, then: - 12 ÷ 3 = 4 bottles - 4 × 3 = 12 liters - **c. Check:** - 4 × 3 = 12 liters (Confirmed) **Problem 9.3: Amount in One Group** 1. **Jada's Fabric:** - **a. Equations:** - Multiplication: Cost per yard × Yards = Total cost - Division: Total cost ÷ Yards = Cost per yard - **b. Answer:** - $$ \$6 $$ per yard - **c. Check:** - 6 × 3.5 = 21 (Confirmed) 2. **Baking Soda:** - **a. Equations:** - Multiplication: Cost per kg × Fraction of kg = Total cost - Division: Total cost ÷ Fraction of kg = Cost per kg - **b. Answer:** - \$4.5 per kg - **c. Check:** - 4.5 × (4/9) = 2 (Confirmed) 3. **Water Bottles:** - **a. Equations:** - Multiplication: Liters per bottle × Number of bottles = Total liters - Division: Total liters ÷ Number of bottles = Liters per bottle - **b. Answer:** - 2.5 liters per bottle - **c. Check:** - 2.5 × 1.2 = 3 (Confirmed)

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