Compare the ratio:
`3:4 and 5:12`

Answer

To compare the ratios \(3:4\) and \(5:12\), we can follow these steps:

### Step 1: Write the Ratios as Fractions
Convert the ratios into fractions:
- \(3:4\) can be written as \(\frac{3}{4}\)
- \(5:12\) can be written as \(\frac{5}{12}\)

### Step 2: Find a Common Denominator
To compare the two fractions, we need a common denominator. The denominators here are \(4\) and \(12\). The least common multiple (LCM) of \(4\) and \(12\) is \(12\).

### Step 3: Convert \(\frac{3}{4}\) to Have the Common Denominator
To convert \(\frac{3}{4}\) to a fraction with a denominator of \(12\), we multiply both the numerator and the denominator by \(3\):
\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]

### Step 4: Compare the Two Fractions
Now we have:
- \(\frac{9}{12}\) (which is equivalent to \(3:4\))
- \(\frac{5}{12}\) (which is equivalent to \(5:12\))

Since both fractions now have the same denominator, we can compare the numerators:
- \(9\) (from \(\frac{9}{12}\)) is greater than \(5\) (from \(\frac{5}{12}\)).

### Step 5: Conclusion
Since \(9 > 5\), we conclude that:
\[ \frac{3}{4} > \frac{5}{12} \]
Thus, the ratio \(3:4\) is greater than the ratio \(5:12\).

### Final Answer
The ratio \(3:4\) is greater than the ratio \(5:12\).

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