Question : Which of the following is the greatest?
2 : 5, 1 : 2, 8 : 15, 3 : 5
Option 1: 8 : 15
Option 2: 3 : 5
Option 3: 1 : 2
Option 4: 2 : 5
Correct Answer: 3 : 5
Solution :
Given, 2 : 5, 1 : 2, 8 : 15, 3 : 5
Make the denominators of each fraction the same.
LCM of 5, 2, 15 and 5 = 30
Now,
$\frac{2}{5}\times \frac{6}{6}=\frac{12}{30}$
$\frac{1}{2}\times \frac{15}{15}=\frac{15}{30}$
$\frac{8}{15}\times \frac{2}{2}=\frac{16}{30}$
$\frac{3}{5}\times \frac{6}{6}=\frac{18}{30}$
The greatest fraction = $\frac{18}{30} = 3 : 5$
Hence, the correct answer is 3 : 5.
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