Analyze the mathematical expressions in the image and provide a structured breakdown of each, including any associated numbering or symbols.

Mathematical Expressions Analysis

The image contains several mathematical expressions and notations, seemingly from a math assignment or notes.

Expression 1:

• The expression is labeled with the number ①.


• It begins with a fraction: \( \frac{1}{3} \).


• This is followed by an addition symbol: +.


• The next term is a fraction: \( \frac{2}{9} \).


• The entire expression is enclosed in parentheses: ( \( \frac{1}{3} \) + \( \frac{2}{9} \) ).


• This parenthesized expression is followed by a division symbol: \(\cdot\) (appears to be a multiplication dot, but context suggests division).

Expression 2:

• This expression is labeled with the number ③.


• It starts with a fraction: \( \frac{4}{9} \).


• This fraction is enclosed in parentheses: ( \( \frac{4}{9} \) ).


• This is followed by a division symbol: \(\cdot\) (appears to be a multiplication dot, but context suggests division).


• The next part is a fraction: \( \frac{4}{26} \) which simplifies to \( \frac{2}{13} \).


• This is followed by a subtraction symbol: -.


• Finally, there is a fraction: \( \frac{1}{6} \).


• The entire expression is enclosed in parentheses: ( \( \frac{4}{9} \) \(\cdot\) \( \frac{4}{26} \) - \( \frac{1}{6} \) ).

Expression 3:

• This expression is labeled with the number ②.


• It starts with a fraction: \( \frac{5}{21} \).


• This fraction is enclosed in parentheses: ( \( \frac{5}{21} \) ).

Other Notations:

• A number 6 is circled in red.


• The Roman numeral XI is written to the right, with a curved line underneath.


• There are other handwritten numbers and symbols that are less clear or potentially part of other problems (e.g., 2, 4, 1).