Evaluate the expression shown below and write your answer **as a fraction** in simplest form.

start fraction, start fraction, 9, divided by, 8, end fraction, minus, 0, point, 7, 5, divided by, start fraction, 2, divided by, 7, end fraction, end fraction


Let's evaluate the expression given:

\[
\frac{\frac{9}{8} - 0.75}{\frac{2}{7}}
\]

### Step 1: Convert the decimal to a fraction
\( 0.75 \) can be expressed as \( \frac{3}{4} \).

So, the expression becomes:
\[
\frac{\frac{9}{8} - \frac{3}{4}}{\frac{2}{7}}
\]

### Step 2: Subtract the fractions in the numerator
To subtract \( \frac{9}{8} - \frac{3}{4} \), we need a common denominator. The common denominator between 8 and 4 is 8. Convert \( \frac{3}{4} \) to \( \frac{6}{8} \) so the subtraction can be done:
\[
\frac{9}{8} - \frac{6}{8} = \frac{3}{8}
\]

Now the expression simplifies to:
\[
\frac{\frac{3}{8}}{\frac{2}{7}}
\]

### Step 3: Simplify the complex fraction
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{3}{8} \times \frac{7}{2} = \frac{3 \times 7}{8 \times 2} = \frac{21}{16}
\]

### Step 4: Ensure the fraction is in simplest form
The fraction \( \frac{21}{16} \) is already in its simplest form.

So, the final answer is \( \frac{21}{16} \).

Would you like further clarification or details on this problem? Here are some related questions that might interest you:

1. How do you find a common denominator when adding or subtracting fractions?
2. How do you convert a fraction to its simplest form?
3. How do you multiply and divide fractions?
4. What are some techniques to quickly convert decimals to fractions?
5. What steps should be followed to evaluate complex fractional expressions?

**Tip:** Always convert all components of an expression to fractions before performing operations, especially when dealing with decimals and mixed operations.

Learn how to evaluate the complex fraction (9/8 - 0.75) / (2/7) step-by-step. This problem covers fractions, including operations and converting decimals to fractions. Suitable for students in Grades 6-8.

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