Compare the ratios `3:4 and 2:5.`

Answer

To compare the ratios \(3:4\) and \(2:5\), we can follow these steps:

### Step 1: Convert the Ratios to Fractions
We can express the ratios as fractions:
- The first ratio \(3:4\) can be written as \(\frac{3}{4}\).
- The second ratio \(2:5\) 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 denominators here are \(4\) and \(5\). The least common multiple (LCM) of \(4\) and \(5\) is \(20\).

### Step 3: Convert the Fractions to Have the Common Denominator
Now, we will convert both fractions to have the denominator of \(20\):
- For \(\frac{3}{4}\):
\[ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \]
- For \(\frac{2}{5}\):
\[ \frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \]

### Step 4: Compare the Numerators
Now that both fractions have the same denominator, we can compare the numerators:
- The numerator of \(\frac{3}{4}\) is \(15\).
- The numerator of \(\frac{2}{5}\) is \(8\).

Since \(15 > 8\), we can conclude that:
\[ \frac{3}{4} > \frac{2}{5} \]

### Conclusion
Thus, the ratio \(3:4\) is greater than the ratio \(2:5\).

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