Simplify the complex fraction as much as possible. leave your answer as a proper fraction or a mixed number. 5/8 - 1/4 / 5/8 + 1/1 =

We need to simplify the complex fraction:

\[
\frac{\frac{5}{8} - \frac{1}{4}}{\frac{5}{8} + \frac{1}{1}}
\]

### Step 1: Simplify the numerator
We start with the numerator: 

\[
\frac{5}{8} - \frac{1}{4}
\]

To subtract these fractions, we need a common denominator. The common denominator between 8 and 4 is 8.

Rewrite \(\frac{1}{4}\) as \(\frac{2}{8}\):

\[
\frac{5}{8} - \frac{2}{8} = \frac{3}{8}
\]

### Step 2: Simplify the denominator
Now, simplify the denominator:

\[
\frac{5}{8} + \frac{1}{1}
\]

Rewrite \(\frac{1}{1}\) as \(\frac{8}{8}\):

\[
\frac{5}{8} + \frac{8}{8} = \frac{13}{8}
\]

### Step 3: Combine the numerator and denominator
Now, the complex fraction is:

\[
\frac{\frac{3}{8}}{\frac{13}{8}}
\]

When dividing fractions, we multiply by the reciprocal:

\[
\frac{3}{8} \div \frac{13}{8} = \frac{3}{8} \times \frac{8}{13} = \frac{3}{13}
\]

Thus, the simplified result is:

\[
\boxed{\frac{3}{13}}
\]

Would you like more details, or have any questions?

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Here are 5 related questions for further practice:
1. Simplify \(\frac{\frac{7}{10} - \frac{3}{5}}{\frac{7}{10} + \frac{2}{2}}\).
2. Simplify \(\frac{\frac{4}{9} + \frac{2}{3}}{\frac{4}{9} - \frac{1}{1}}\).
3. Simplify \(\frac{\frac{5}{6} - \frac{1}{2}}{\frac{5}{6} + \frac{3}{3}}\).
4. Simplify \(\frac{\frac{9}{12} - \frac{3}{4}}{\frac{9}{12} + \frac{5}{5}}\).
5. Simplify \(\frac{\frac{2}{7} + \frac{1}{7}}{\frac{2}{7} - \frac{1}{1}}\).

**Tip:** When simplifying complex fractions, remember that dividing by a fraction is equivalent to multiplying by its reciprocal.

Learn how to simplify the complex fraction (5/8 - 1/4) / (5/8 + 1/1) with this step-by-step guide. This problem covers key concepts such as fraction subtraction, addition, and division using reciprocals, suitable for students in Grades 6-8.

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