Compare the following ratios:
`2:9 and 5:12`

Answer

To compare the ratios \(2:9\) and \(5:12\), we can follow these steps:

### Step 1: Write the Ratios as Fractions
We can express the ratios as fractions:
- \(2:9\) can be written as \(\frac{2}{9}\)
- \(5:12\) can be written as \(\frac{5}{12}\)

### Step 2: Check if the Fractions can be Simplified
Next, we check if these fractions can be simplified.
- The fraction \(\frac{2}{9}\) cannot be simplified further since 2 and 9 have no common factors.
- The fraction \(\frac{5}{12}\) also cannot be simplified further since 5 and 12 have no common factors.

### Step 3: Cross-Multiply to Compare
To compare the two fractions, we can use the cross-multiplication method:
- Multiply the numerator of the first fraction by the denominator of the second fraction: \(2 \times 12 = 24\)
- Multiply the numerator of the second fraction by the denominator of the first fraction: \(5 \times 9 = 45\)

### Step 4: Compare the Results
Now we compare the results of the cross-multiplication:
- We have \(24\) from \(2 \times 12\) and \(45\) from \(5 \times 9\).
- Since \(45 > 24\), we conclude that \(\frac{5}{12} > \frac{2}{9}\).

### Conclusion
Thus, we can say that \(5:12\) is greater than \(2:9\).

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