To solve the expression \( 7 \frac{1}{3} + 2 \frac{1}{2} - 3 \frac{1}{6} \), we'll first convert the mixed numbers into improper fractions, then perform the arithmetic.

### Step 1: Convert mixed numbers to improper fractions

\[
7 \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{22}{3}
\]
\[
2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}
\]
\[
3 \frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{19}{6}
\]

### Step 2: Find a common denominator

The least common denominator (LCD) of 3, 2, and 6 is 6. We will convert all fractions to have a denominator of 6.

\[
\frac{22}{3} = \frac{22 \times 2}{3 \times 2} = \frac{44}{6}
\]
\[
\frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}
\]
\[
\frac{19}{6} \text{ remains } \frac{19}{6}
\]

### Step 3: Perform the addition and subtraction

Now, we can add and subtract the fractions:
\[
\frac{44}{6} + \frac{15}{6} - \frac{19}{6} = \frac{44 + 15 - 19}{6} = \frac{40}{6}
\]

### Step 4: Simplify the result

\[
\frac{40}{6} = \frac{20}{3}
\]

### Step 5: Convert the improper fraction back to a mixed number

\[
\frac{20}{3} = 6 \frac{2}{3}
\]

So, the final answer is \( 6 \frac{2}{3} \).

Would you like more details on any part of this solution?

Here are five related questions to try:

1. How do you convert an improper fraction to a mixed number?
2. How would you add \( 5 \frac{3}{4} + 2 \frac{1}{3} \)?
3. What is the difference between \( 8 \frac{1}{5} \) and \( 6 \frac{2}{3} \)?
4. How do you find the least common denominator of three fractions?
5. How do you simplify fractions after adding or subtracting them?

**Tip:** Always convert mixed numbers to improper fractions when adding or subtracting them to simplify the process.

Learn how to solve the expression 7 1/3 + 2 1/2 - 3 1/6 by converting mixed numbers to improper fractions and using the least common denominator (LCD) method. Suitable for students in Grades 5-7.

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