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`2(5)/(45)square2(2)/(25)`

Answer

To solve the problem of comparing the two mixed numbers \(2 \frac{5}{45}\) and \(2 \frac{2}{25}\), we will follow these steps:

### Step 1: Convert the mixed numbers to improper fractions.

1. For \(2 \frac{5}{45}\):
- Multiply the whole number (2) by the denominator (45):
\[ 2 \times 45 = 90 \]
- Add the numerator (5):
\[ 90 + 5 = 95 \]
- So, \(2 \frac{5}{45} = \frac{95}{45}\).

2. For \(2 \frac{2}{25}\):
- Multiply the whole number (2) by the denominator (25):
\[ 2 \times 25 = 50 \]
- Add the numerator (2):
\[ 50 + 2 = 52 \]
- So, \(2 \frac{2}{25} = \frac{52}{25}\).

### Step 2: Simplify the fractions if possible.

1. The fraction \(\frac{95}{45}\) can be simplified:
- Both 95 and 45 can be divided by 5:
\[ \frac{95 \div 5}{45 \div 5} = \frac{19}{9} \]

2. The fraction \(\frac{52}{25}\) is already in simplest form.

### Step 3: Compare the two fractions \(\frac{19}{9}\) and \(\frac{52}{25}\).

To compare these fractions, we can use cross-multiplication:

1. Cross-multiply:
- Multiply the numerator of the first fraction by the denominator of the second:
\[ 19 \times 25 = 475 \]
- Multiply the numerator of the second fraction by the denominator of the first:
\[ 52 \times 9 = 468 \]

### Step 4: Determine which fraction is greater.

Now we compare the results of the cross-multiplication:
- Since \(475 > 468\), we conclude that:
\[ \frac{19}{9} > \frac{52}{25} \]

### Final Conclusion:

Thus, we can say:
\[ 2 \frac{5}{45} > 2 \frac{2}{25} \]

### Summary:

The answer to the question is:
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