To solve the problem of multiplying the fractions [tex]\(\frac{3}{4} \times \frac{16}{9}\)[/tex], let's go through the steps methodically:
1. Multiply the numerators:
The numerator of the first fraction is 3, and the numerator of the second fraction is 16.
[tex]\[
3 \times 16 = 48
\][/tex]
So, the numerator of the product is 48.
2. Multiply the denominators:
The denominator of the first fraction is 4, and the denominator of the second fraction is 9.
[tex]\[
4 \times 9 = 36
\][/tex]
So, the denominator of the product is 36.
3. Form the resulting fraction:
Combining the results from steps 1 and 2, we get:
[tex]\[
\frac{48}{36}
\][/tex]
4. Simplify the fraction:
To simplify [tex]\(\frac{48}{36}\)[/tex], we divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 48 and 36 is 12.
[tex]\[
\frac{48 \div 12}{36 \div 12} = \frac{4}{3}
\][/tex]
Thus, the simplified form of the product of [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{16}{9}\)[/tex] is [tex]\(\frac{4}{3}\)[/tex].
The answer is:
A. [tex]\( \frac{4}{3} \)[/tex]
