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The problem presented is as follows:

Adesh has \( 7 \frac{2}{3} \) gallons of milk. He uses:
- \( 2 \frac{1}{6} \) gallons to make muffins.
- \( 3 \frac{1}{3} \) gallons to make cakes.

We are tasked with determining how many gallons of milk Adesh has left. We will:
1. Subtract the amount of milk used for muffins and cakes from the total amount of milk he started with.
2. Write an expression to represent the situation and evaluate it.

### Step 1: Convert the mixed numbers to improper fractions
- \( 7 \frac{2}{3} = \frac{23}{3} \)
- \( 2 \frac{1}{6} = \frac{13}{6} \)
- \( 3 \frac{1}{3} = \frac{10}{3} \)

### Step 2: Subtract the amounts used
We need to subtract the sum of the milk used for muffins and cakes from the total.

\[
\text{Milk left} = \frac{23}{3} - \left( \frac{13}{6} + \frac{10}{3} \right)
\]

### Step 3: Combine the fractions
First, find a common denominator for the fractions. The least common denominator (LCD) between 3 and 6 is 6.

- \( \frac{23}{3} = \frac{46}{6} \)
- \( \frac{10}{3} = \frac{20}{6} \)

Now, we can add the fractions:

\[
\frac{13}{6} + \frac{20}{6} = \frac{33}{6}
\]

### Step 4: Subtract the total used from the total milk

\[
\frac{46}{6} - \frac{33}{6} = \frac{13}{6}
\]

### Step 5: Convert the improper fraction back to a mixed number
\[
\frac{13}{6} = 2 \frac{1}{6}
\]

Thus, Adesh has **2 \(\frac{1}{6}\)** gallons of milk left.

Would you like further details, or do you have any questions?

### Here are 5 related questions you can explore:
1. How would the problem change if Adesh used \(4 \frac{1}{2}\) gallons for cakes?
2. What if Adesh started with \(10\) gallons of milk instead of \(7 \frac{2}{3}\)?
3. Can you express the total milk used as a decimal instead of a fraction?
4. How much milk would Adesh have left if he used \(5 \frac{1}{4}\) gallons in total for both cakes and muffins?
5. How can you use this same method to solve problems with other ingredients?

### Tip: When working with fractions, always check for a common denominator before adding or subtracting.

Adesh has 7 2/3 gallons of milk. He uses 2 1/6 gallons to make muffins and 3 1/3 gallons to make cakes. How many gallons of milk does Adesh have left?

Learn how to solve a fraction word problem involving mixed numbers. Adesh has 7 2/3 gallons of milk and uses some for muffins and cakes. Find out how much milk is left using fraction subtraction. Suitable for students in Grades 5-7.

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