Compare the fractions: `3(1)/(9) and 22/(9)`.

Answer

To compare the fractions \(3 \frac{1}{9}\) and \(\frac{22}{9}\), we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction \(3 \frac{1}{9}\) can be converted to an improper fraction. To do this, we multiply the whole number (3) by the denominator (9) and then add the numerator (1).

\[ 3 \frac{1}{9} = \frac{(3 \times 9) + 1}{9} = \frac{27 + 1}{9} = \frac{28}{9} \]

### Step 2: Write down the two fractions
Now we have the two fractions:
- \(3 \frac{1}{9} = \frac{28}{9}\)
- \(\frac{22}{9}\)

### Step 3: Compare the fractions
Since both fractions have the same denominator (9), we can compare their numerators directly.

- The numerator of the first fraction is 28.
- The numerator of the second fraction is 22.

### Step 4: Determine which fraction is greater
Now we compare the numerators:
- \(28 > 22\)

Since 28 is greater than 22, we can conclude that:

\[ \frac{28}{9} > \frac{22}{9} \]

### Final Conclusion
Thus, we can say:

\[ 3 \frac{1}{9} > \frac{22}{9} \]