To solve the problem of multiplying the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{16}{9}\)[/tex], follow these detailed steps:
1. Numerator Calculation:
- Multiply the numerators of both fractions:
[tex]\[
3 \times 16 = 48
\][/tex]
2. Denominator Calculation:
- Multiply the denominators of both fractions:
[tex]\[
4 \times 9 = 36
\][/tex]
3. Form the New Fraction:
- The result of multiplying the two fractions is:
[tex]\[
\frac{48}{36}
\][/tex]
4. Simplify the Fraction:
- To simplify [tex]\(\frac{48}{36}\)[/tex], find the greatest common divisor (GCD) of 48 and 36. The GCD of 48 and 36 is 12.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{48 \div 12}{36 \div 12} = \frac{4}{3}
\][/tex]
Thus, the simplified result of the multiplication [tex]\(\frac{3}{4} \times \frac{16}{9}\)[/tex] is [tex]\( \frac{4}{3} \)[/tex].
The best answer for the question is:
A. [tex]\( \frac{4}{3} \)[/tex]
