Let's solve the problem of multiplying the two fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{16}{9}\)[/tex].
Step 1: Multiply the numerators together:
[tex]\[ 3 \times 16 = 48 \][/tex]
Step 2: Multiply the denominators together:
[tex]\[ 4 \times 9 = 36 \][/tex]
Now we have the fraction [tex]\(\frac{48}{36}\)[/tex].
Step 3: Simplify [tex]\(\frac{48}{36}\)[/tex]. To simplify a fraction, we divide the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 48 and 36 is 12. Therefore,
[tex]\[ \frac{48}{36} = \frac{48 \div 12}{36 \div 12} = \frac{4}{3} \][/tex]
So, [tex]\(\frac{3}{4} \times \frac{16}{9} = \frac{4}{3}\)[/tex].
The best answer is:
B. [tex]\(\frac{4}{3}\)[/tex]
