Compare the ratios: 5:6 and 3:4

Answer

To compare the ratios 5:6 and 3:4, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Ratios to Fractions**:
- The ratio 5:6 can be expressed as the fraction \( \frac{5}{6} \).
- The ratio 3:4 can be expressed as the fraction \( \frac{3}{4} \).

2. **Find a Common Denominator**:
- The denominators of the fractions are 6 and 4. The least common multiple (LCM) of 6 and 4 is 12.

3. **Convert Fractions to Like Fractions**:
- To convert \( \frac{5}{6} \) to a fraction with a denominator of 12, we multiply both the numerator and the denominator by 2:
\[ \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \]
- To convert \( \frac{3}{4} \) to a fraction with a denominator of 12, we multiply both the numerator and the denominator by 3:
\[ \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]

4. **Compare the Numerators**:
- Now we have two fractions: \( \frac{10}{12} \) and \( \frac{9}{12} \).
- Since the denominators are the same, we can compare the numerators directly. Here, 10 is greater than 9.

5. **Conclusion**:
- Therefore, \( \frac{5}{6} > \frac{3}{4} \).
- This means that the ratio 5:6 is greater than the ratio 3:4.

### Final Answer:
The ratio 5:6 is greater than the ratio 3:4.