To convert the fraction [tex]\(\frac{1}{3}\)[/tex] to an equivalent fraction with a denominator of 9, follow these steps:
1. Identify the current numerator and denominator of the fraction. For [tex]\(\frac{1}{3}\)[/tex], the numerator is 1 and the denominator is 3.
2. Determine what number you need to multiply the original denominator (3) by to get the new denominator (9). This is done by dividing the new denominator (9) by the original denominator (3):
[tex]\[
9 \div 3 = 3
\][/tex]
3. Multiply both the numerator and the denominator of the original fraction by this number (3):
[tex]\[
\frac{1}{3} \times \frac{3}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
\][/tex]
The equivalent fraction with a denominator of 9 is [tex]\(\frac{3}{9}\)[/tex].
Therefore, the correct answer is:
[tex]\[
\frac{3}{9}
\][/tex]
