To solve the expression \( \frac{3}{2} \times \frac{4}{13} \div \frac{9}{13} \), follow these steps:

### Step 1: Rewrite the division as multiplication
When dividing by a fraction, you multiply by its reciprocal. So, we rewrite the expression:

\[
\frac{3}{2} \times \frac{4}{13} \times \frac{13}{9}
\]

### Step 2: Multiply the numerators and the denominators
Now multiply the fractions straight across:

Numerators: \( 3 \times 4 \times 13 = 156 \)  
Denominators: \( 2 \times 13 \times 9 = 234 \)

So, the expression becomes:

\[
\frac{156}{234}
\]

### Step 3: Simplify the fraction
To simplify, find the greatest common divisor (GCD) of 156 and 234, which is 78:

\[
\frac{156}{234} = \frac{156 \div 78}{234 \div 78} = \frac{2}{3}
\]

### Final Answer:
\[
\frac{2}{3}
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. Simplify \( \frac{5}{7} \times \frac{8}{9} \div \frac{3}{4} \).
2. What is \( \frac{6}{11} \times \frac{12}{13} \div \frac{9}{13} \)?
3. Solve \( \frac{5}{8} \times \frac{3}{4} \div \frac{15}{16} \).
4. Simplify \( \frac{7}{9} \times \frac{14}{27} \div \frac{28}{81} \).
5. What is \( \frac{2}{5} \times \frac{10}{11} \div \frac{8}{11} \)?

**Tip**: When dividing fractions, always multiply by the reciprocal of the divisor to simplify the operation!

Learn how to solve the fraction expression 3/2 x 4/13 ÷ 9/13 with a step-by-step solution. This problem demonstrates multiplying and dividing fractions, including simplifying the final result. Suitable for students in Grades 6-8.

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