To solve the division of the two fractions [tex]\(\frac{3}{4} \div \frac{13}{5}\)[/tex], we follow these steps:
1. Rewrite the Division as Multiplication by the Reciprocal:
[tex]\[
\frac{3}{4} \div \frac{13}{5} = \frac{3}{4} \times \frac{5}{13}
\][/tex]
Dividing by a fraction is equivalent to multiplying by its reciprocal.
2. Multiply the Numerators and Denominators:
[tex]\[
\frac{3}{4} \times \frac{5}{13} = \frac{3 \times 5}{4 \times 13} = \frac{15}{52}
\][/tex]
3. Convert the Fraction to a Decimal:
To find the decimal form of [tex]\(\frac{15}{52}\)[/tex], we divide 15 by 52.
[tex]\[
\frac{15}{52} \approx 0.28846153846153844
\][/tex]
Therefore, the solution to [tex]\(\frac{3}{4} \div \frac{13}{5}\)[/tex] is approximately [tex]\(\boxed{0.28846153846153844}\)[/tex].
