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Let's break down the problem:

1. The bakery has **72 half-gallons** of milk.
2. It takes **1 2/3 cups** (which equals \( \frac{5}{3} \) cups) of milk to make one cake.
3. It is given that **1 cup = \(\frac{1}{8}\) half-gallon = 0.125 half-gallons**.

### Step-by-step calculation:

1. First, let's convert the milk required for one cake (1 2/3 cups) into half-gallons:
   \[
   \frac{5}{3} \text{ cups} \times 0.125 \text{ half-gallons per cup} = \frac{5}{3} \times 0.125 = 0.2083 \text{ half-gallons}
   \]
   So, it takes **0.2083 half-gallons** of milk to make one cake.

2. Now, let's figure out how many cakes the bakery can make with 72 half-gallons of milk:
   \[
   \frac{72 \text{ half-gallons}}{0.2083 \text{ half-gallons per cake}} \approx 345.6
   \]
   Since the bakery can only make whole cakes, we round down to 345 cakes.

### Final answer:
The bakery can make **345 cakes**.

Let me know if you'd like further explanation or have any questions!

### Related Questions:
1. How many cups of milk are there in 72 half-gallons?
2. What if each cake required 2 cups of milk? How many cakes could be made?
3. If the bakery had 100 half-gallons of milk, how many cakes could it make?
4. How would the result change if the milk requirement was 1 1/4 cups per cake?
5. How many cakes can be made with 50 half-gallons of milk?

### Tip:
Always make sure to convert units consistently, especially when mixing fractions and decimals!

A bakery has 72 half-gallons of milk. It takes 1 2/3 cups of milk to make a cake. Note that 1 cup = 1/8 half-gallon = 0.125 half-gallon. How many cakes can the bakery make?

This problem involves converting between cups and half-gallons to determine how many cakes a bakery can make with 72 half-gallons of milk when each cake requires 1 2/3 cups of milk. Learn how to solve this step-by-step, with detailed unit conversions.

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