Sure, let's solve this problem step-by-step:
Step 1: Multiply the numerators
Given fractions are [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{16}{9}\)[/tex].
To multiply fractions, we multiply the numerators together:
[tex]\[ 3 \times 16 = 48 \][/tex]
Step 2: Multiply the denominators
Next, we multiply the denominators together:
[tex]\[ 4 \times 9 = 36 \][/tex]
So, the product of the two fractions is:
[tex]\[ \frac{48}{36} \][/tex]
Step 3: Simplify the fraction
To simplify [tex]\(\frac{48}{36}\)[/tex], we need to find the greatest common divisor (GCD) of 48 and 36.
The GCD of 48 and 36 is 12.
We divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{48 \div 12}{36 \div 12} = \frac{4}{3} \][/tex]
Step 4: Match the simplified fraction to the given options
The simplified fraction is [tex]\(\frac{4}{3}\)[/tex].
Looking at the options provided:
- A) [tex]\( \frac{3}{4} \)[/tex]
- B) [tex]\( \frac{64}{27} \)[/tex]
- C) [tex]\( \frac{4}{3} \)[/tex]
- D) [tex]\( \frac{27}{64} \)[/tex]
The correct answer is:
C) [tex]\( \frac{4}{3} \)[/tex]
So, the result of multiplying [tex]\(\frac{3}{4}\)[/tex] by [tex]\(\frac{16}{9}\)[/tex] is [tex]\(\frac{4}{3}\)[/tex], which corresponds to option C.
