To find the value of [tex]\(\frac{7}{9} \div \frac{1}{3}\)[/tex], we can follow these steps:
1. Understand Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, [tex]\(\frac{7}{9} \div \frac{1}{3}\)[/tex] can be rewritten as [tex]\(\frac{7}{9} \times \frac{3}{1}\)[/tex].
2. Perform the Multiplication:
[tex]\[
\frac{7}{9} \times \frac{3}{1} = \frac{7 \times 3}{9 \times 1} = \frac{21}{9}
\][/tex]
3. Simplify the Fraction:
[tex]\[
\frac{21}{9} = \frac{21 \div 3}{9 \div 3} = \frac{7}{3}
\][/tex]
So, [tex]\(\frac{7}{9} \div \frac{1}{3} = \frac{7}{3}\)[/tex].
4. Convert to a Mixed Number:
[tex]\[
\frac{7}{3} = 2 + \frac{1}{3} = 2 \frac{1}{3}
\][/tex]
Therefore, the correct value is:
[tex]\[ \frac{7}{9} \div \frac{1}{3} = 2 \frac{1}{3} \][/tex]
So, [tex]\(2 \frac{1}{3}\)[/tex] is the answer.
