To solve \( \frac{31}{2} \div \frac{23}{4} \), follow these steps:

1. Rewrite the division of fractions as multiplication by the reciprocal:
   \[
   \frac{31}{2} \div \frac{23}{4} = \frac{31}{2} \times \frac{4}{23}
   \]

2. Multiply the numerators and denominators:
   \[
   = \frac{31 \times 4}{2 \times 23} = \frac{124}{46}
   \]

3. Simplify \( \frac{124}{46} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
   \[
   = \frac{124 \div 2}{46 \div 2} = \frac{62}{23}
   \]

So, the result is:
\[
\frac{62}{23}
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How would you divide two mixed numbers?
2. What is the result if you multiply \( \frac{31}{2} \) and \( \frac{23}{4} \) instead?
3. How do you simplify fractions efficiently?
4. How does changing a fraction’s denominator affect its value?
5. Can you explain the concept of reciprocals in division?

**Tip:** To divide fractions, remember to multiply by the reciprocal.

Learn how to divide fractions with the example 31/2 divided by 23/4, including step-by-step simplification using the reciprocal method. This solution covers fraction division, reciprocal concepts, and fraction simplification. Perfect for students in Grades 6-8.

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