Compare the ratio:
`5:7 and 2:5`

Answer

To compare the ratios \(5:7\) and \(2:5\), we can follow these steps:

### Step 1: Convert the ratios to fractions
The ratios \(5:7\) and \(2:5\) can be expressed as fractions:
- \(5:7\) can be written as \(\frac{5}{7}\)
- \(2:5\) can be written as \(\frac{2}{5}\)

### Step 2: Find a common denominator
To compare the two fractions, we need to find a common denominator. The least common multiple (LCM) of the denominators \(7\) and \(5\) is \(35\).

### Step 3: Convert both fractions to have the common denominator
Now we will convert both fractions to have the denominator of \(35\).

For \(\frac{5}{7}\):
- Multiply both the numerator and the denominator by \(5\):
\[ \frac{5 \times 5}{7 \times 5} = \frac{25}{35} \]

For \(\frac{2}{5}\):
- Multiply both the numerator and the denominator by \(7\):
\[ \frac{2 \times 7}{5 \times 7} = \frac{14}{35} \]

### Step 4: Compare the numerators
Now we have:
- \(\frac{25}{35}\) for \(5:7\)
- \(\frac{14}{35}\) for \(2:5\)

Since the denominators are the same, we can compare the numerators:
- \(25\) (from \(\frac{25}{35}\)) is greater than \(14\) (from \(\frac{14}{35}\)).

### Step 5: Conclusion
Since \(25 > 14\), we conclude that:
\[ 5:7 > 2:5 \]

### Summary
Thus, the ratio \(5:7\) is greater than the ratio \(2:5\).

---