Convert the given mixed numbers into improper fractions and complete the table.

To complete the table, we need to convert each mixed number into an improper fraction. A mixed number $A \frac{B}{C}$ can be converted to an improper fraction using the formula $\frac{(A \times C) + B}{C}$.

Here are the calculations for each row:

Row 1:
The mixed number is $3 \frac{1}{2}$.
The improper fraction is $\frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}$. This is already filled in the table.

Row 2:
The mixed number is $1 \frac{4}{12}$.
The improper fraction is $\frac{(1 \times 12) + 4}{12} = \frac{12 + 4}{12} = \frac{16}{12}$.

Row 3:
The mixed number is $2 \frac{4}{6}$.
The improper fraction is $\frac{(2 \times 6) + 4}{6} = \frac{12 + 4}{6} = \frac{16}{6}$.

Row 4:
The mixed number is $2 \frac{2}{5}$.
The improper fraction is $\frac{(2 \times 5) + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}$.

Row 5:
The mixed number is $3 \frac{2}{8}$.
The improper fraction is $\frac{(3 \times 8) + 2}{8} = \frac{24 + 2}{8} = \frac{26}{8}$.

Row 6:
The mixed number is $2 \frac{3}{9}$.
The improper fraction is $\frac{(2 \times 9) + 3}{9} = \frac{18 + 3}{9} = \frac{21}{9}$.

Row 7:
The mixed number is $3 \frac{1}{4}$.
The improper fraction is $\frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}$.

Here is the completed "Improper fraction" column:

Shapes	Mixed number Whole number	Proper fraction number	Improper fraction
(Image)	3	$\frac{1}{2}$	$\frac{7}{2}$
(Image)	1	$\frac{4}{12}$	$\boxed{\frac{16}{12}}$
(Image)	2	$\frac{4}{6}$	$\boxed{\frac{16}{6}}$
(Image)	2	$\frac{2}{5}$	$\boxed{\frac{12}{5}}$
(Image)	3	$\frac{2}{8}$	$\boxed{\frac{26}{8}}$
(Image)	2	$\frac{3}{9}$	$\boxed{\frac{21}{9}}$
(Image)	3	$\frac{1}{4}$	$\boxed{\frac{13}{4}}$