Simplify the complex fraction as much as possible. Leave your answer as a proper fractio or a mixed number. 2/3 - 1/2 / 1/2 + 1/3 =

Let's simplify the complex fraction:

\[
\frac{\frac{2}{3} - \frac{1}{2}}{\frac{1}{2} + \frac{1}{3}}
\]

### Step 1: Simplify the numerator
We need to subtract the fractions in the numerator:

\[
\frac{2}{3} - \frac{1}{2}
\]

Find a common denominator between 3 and 2, which is 6:

\[
\frac{2}{3} = \frac{4}{6}, \quad \frac{1}{2} = \frac{3}{6}
\]

Now, subtract:

\[
\frac{4}{6} - \frac{3}{6} = \frac{1}{6}
\]

So the numerator is \( \frac{1}{6} \).

### Step 2: Simplify the denominator
We need to add the fractions in the denominator:

\[
\frac{1}{2} + \frac{1}{3}
\]

Find a common denominator between 2 and 3, which is 6:

\[
\frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}
\]

Now, add:

\[
\frac{3}{6} + \frac{2}{6} = \frac{5}{6}
\]

So the denominator is \( \frac{5}{6} \).

### Step 3: Divide the fractions
Now, divide the simplified numerator by the simplified denominator:

\[
\frac{\frac{1}{6}}{\frac{5}{6}} = \frac{1}{6} \times \frac{6}{5} = \frac{1 \times 6}{6 \times 5} = \frac{1}{5}
\]

### Final Answer:
The simplified complex fraction is:

\[
\frac{1}{5}
\]

---

Would you like any further details or clarifications?

Here are five related questions to practice:

1. Simplify \( \frac{\frac{3}{4} - \frac{1}{5}}{\frac{2}{5} + \frac{1}{4}} \).
2. Simplify \( \frac{\frac{5}{6} + \frac{2}{9}}{\frac{7}{8} - \frac{1}{3}} \).
3. How would you simplify \( \frac{\frac{7}{12}}{\frac{5}{8}} \)?
4. Solve \( \frac{\frac{3}{5} - \frac{2}{7}}{\frac{4}{9} + \frac{3}{7}} \).
5. What is \( \frac{\frac{4}{9} + \frac{1}{6}}{\frac{3}{8} - \frac{1}{4}} \)?

**Tip**: Always find the least common denominator when adding or subtracting fractions.

Simplify the complex fraction as much as possible. Leave your answer as a proper fraction or a mixed number. 2/3 - 1/2 / 1/2 + 1/3 =

Simplify the complex fraction 2/3 - 1/2 divided by 1/2 + 1/3 with a step-by-step solution. This problem highlights key concepts in adding and subtracting fractions and dividing complex fractions. Suitable for students in Grades 6-8.

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