Choose the correct statement:

Options

A. ` (5:8) gt (3:4)`
B. `(5:8) lt (3:4)`
C. two ratios cannot be compared
D. none of these

Answer

To solve the problem of comparing the two ratios \(5:8\) and \(3:4\), we will follow these steps:

### Step 1: Write the Ratios as Fractions
Convert the ratios into fractions:
- \(5:8\) can be written as \(\frac{5}{8}\)
- \(3:4\) can be written as \(\frac{3}{4}\)

### Step 2: Find a Common Denominator
To compare the two fractions, we can find a common denominator. The least common multiple (LCM) of the denominators \(8\) and \(4\) is \(8\).

### Step 3: Convert the Fractions
Convert \(\frac{3}{4}\) to have the same denominator as \(\frac{5}{8}\):
\[ \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \]

### Step 4: Compare the Numerators
Now we can compare the two fractions:
- \(\frac{5}{8}\) and \(\frac{6}{8}\)

Since \(5 < 6\), we can conclude:
\[ \frac{5}{8} < \frac{6}{8} \]

### Step 5: State the Conclusion
Thus, we can say that:
\[ 5:8 < 3:4 \]

### Final Answer
The correct statement is that \(5:8\) is less than \(3:4\).

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