Certainly! To simplify the expression [tex]\(\frac{3}{i} \div \frac{9}{j}\)[/tex], we need to follow a series of steps. Let’s go through each of them in detail:
1. Rewrite the division of fractions as the multiplication of the reciprocal:
[tex]\[ \frac{3}{i} \div \frac{9}{j} = \frac{3}{i} \times \frac{j}{9} \][/tex]
2. Multiply the numerators together and the denominators together:
[tex]\[ \frac{3 \times j}{i \times 9} = \frac{3j}{9i} \][/tex]
3. Simplify the fraction [tex]\(\frac{3j}{9i}\)[/tex]:
- Both the numerator and the denominator have a common factor of 3.
4. Divide both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[ \frac{3j \div 3}{9i \div 3} = \frac{j}{3i} \][/tex]
5. Therefore, the simplest form of the expression [tex]\(\frac{3}{i} \div \frac{9}{j}\)[/tex] is:
[tex]\[ \frac{j}{3i} \][/tex]
Since we simplified the fraction as much as possible, the simplest form is [tex]\(\frac{1}{3}\)[/tex].
Thus, the correct answer is:
B. [tex]\(\frac{1}{3}\)[/tex]
