Answer :
To solve the problem [tex]\frac{5}{9} \cdot \frac{12}{25}[/tex], we need to multiply two fractions. The process of multiplying fractions is straightforward as follows:
Multiply the Numerators: Multiply the top numbers (numerators) of both fractions.
[tex]5 \times 12 = 60[/tex]Multiply the Denominators: Multiply the bottom numbers (denominators) of both fractions.
[tex]9 \times 25 = 225[/tex]Form the New Fraction: The product of the numerators becomes the numerator of the new fraction, and the product of the denominators becomes the denominator of the new fraction.
[tex]\frac{60}{225}[/tex]Simplify the Fraction: Lastly, simplify the fraction by finding the greatest common divisor (GCD) of 60 and 225, which is 15, and divide both the numerator and denominator by this number:
[tex]\frac{60 \div 15}{225 \div 15} = \frac{4}{15}[/tex]
Therefore, the answer to [tex]\frac{5}{9} \cdot \frac{12}{25}[/tex] is [tex]\frac{4}{15}[/tex]. This is the simplified form of the result. When working with fractions, always make sure to simplify your answer if possible.