Among the ratios 3 : 4, 5 : 8, 1 : 2, 6 : 9 which is the greatest?

The correct answer is 3 : 4.

To find which ratio is the greatest among the given options, we can convert each ratio into its equivalent decimal form.

1. Convert each ratio to a fraction and then to a decimal:

• For the ratio 3 : 4:
$\frac{3}{4}$ = 0.75

• For the ratio 5 : 8:
$\frac{5}{8}$ = 0.625

• For the ratio 1 : 2:
$\frac{1}{2}$ = 0.5

• For the ratio 6 : 9:
$\frac{6}{9}$ = $\frac{2}{3}$ ≈ 0.6667

2. Compare the decimal values:

Comparing the decimal values obtained:
0.75 > 0.6667 > 0.625 > 0.5

Since 0.75 is the largest decimal value, the ratio 3 : 4 is the greatest among all the given options.