To determine which fraction is equal to [tex]\(\frac{3}{4}\)[/tex], let's compare each given fraction to [tex]\(\frac{3}{4}\)[/tex].
We start with option A:
[tex]\[ \text{Option A:} \quad \frac{9}{16} \][/tex]
To compare [tex]\(\frac{9}{16}\)[/tex] with [tex]\(\frac{3}{4}\)[/tex], we can convert [tex]\(\frac{3}{4}\)[/tex] to have a common denominator of 16:
[tex]\[ \frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16} \][/tex]
Clearly, [tex]\(\frac{9}{16} \neq \frac{12}{16}\)[/tex].
Next, we consider option B:
[tex]\[ \text{Option B:} \quad \frac{12}{12} \][/tex]
This simplifies to:
[tex]\[ \frac{12}{12} = 1 \][/tex]
Since [tex]\(\frac{3}{4} \neq 1\)[/tex], option B is also incorrect.
Now, let's check option C:
[tex]\[ \text{Option C:} \quad \frac{12}{16} \][/tex]
We can simplify [tex]\(\frac{12}{16}\)[/tex]:
[tex]\[ \frac{12}{16} = \frac{12 \div 4}{16 \div 4} = \frac{3}{4} \][/tex]
This matches [tex]\(\frac{3}{4}\)[/tex], so option C is correct.
Lastly, consider option D:
[tex]\[ \text{Option D:} \quad \frac{4}{3} \][/tex]
Which simplifies to:
[tex]\[ \frac{4}{3} = 1.\overline{3} \][/tex]
Clearly, [tex]\(\frac{3}{4} \neq \frac{4}{3}\)[/tex].
Therefore, the fraction that has a value equal to [tex]\(\frac{3}{4}\)[/tex] is:
[tex]\[ \boxed{\text{C}} \][/tex]
