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To solve the division of fractions problem \( \frac{5}{2} \div \frac{8}{9} \), we can follow these steps:

### Step 1: Rewrite as Multiplication
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:
\[
\frac{5}{2} \div \frac{8}{9} = \frac{5}{2} \times \frac{9}{8}
\]

### Step 2: Multiply the Fractions
Now, multiply the numerators and the denominators:
\[
\frac{5 \times 9}{2 \times 8} = \frac{45}{16}
\]

### Step 3: Simplify the Fraction
In this case, \( \frac{45}{16} \) is already in its simplest form because 45 and 16 have no common factors other than 1.

### Final Answer
\[
\frac{5}{2} \div \frac{8}{9} = \frac{45}{16}
\]

Would you like further explanation on any part of this process?

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Here are five related questions to expand your understanding:

1. How do you multiply fractions?
2. What is the reciprocal of a fraction, and why is it used in division?
3. How do you simplify a fraction to its lowest terms?
4. How would you solve if the problem was \( \frac{5}{2} \times \frac{8}{9} \) instead of division?
5. What if the problem involved mixed numbers instead of improper fractions?

**Tip:** Always simplify your answer when dealing with fractions to make sure it is in its lowest terms.

What is \( \frac{5}{2} \div \frac{8}{9} \)? Give your answer as a fraction in its lowest terms.

Learn how to solve the fraction division problem \( \frac{5}{2} \div \frac{8}{9} \) with a step-by-step solution. This guide explains key concepts such as reciprocal multiplication and fraction simplification, suitable for students in Grades 7-8.

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