Understanding the Problem
To solve the expression \( \frac{6}{25} \div \frac{9}{10} \), we will use the method of multiplying by the reciprocal. The reciprocal of a fraction is obtained by flipping the numerator and the denominator.

Step 1: Rewrite the Division as Multiplication
- The expression \( \frac{6}{25} \div \frac{9}{10} \) can be rewritten as:
\[
\frac{6}{25} \times \frac{10}{9}
\]

Step 2: Multiply the Fractions
- Now, multiply the numerators and the denominators:
\[
\text{Numerator: } 6 \times 10 = 60
\]
\[
\text{Denominator: } 25 \times 9 = 225
\]
- This gives us:
\[
\frac{60}{225}
\]

Step 3: Simplify the Fraction
- To simplify \( \frac{60}{225} \), we need to find the greatest common divisor (GCD) of 60 and 225.
- The GCD is 15. Now, divide both the numerator and the denominator by 15:
\[
\frac{60 \div 15}{225 \div 15} = \frac{4}{15}
\]

Final Answer
- Therefore, the value of \( \frac{6}{25} \div \frac{9}{10} \) is:
\[
\frac{4}{15}
\]
This solution demonstrates the process of dividing fractions by converting to multiplication, multiplying, and simplifying.

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