Question : What is the difference between the largest and smallest of the given fractions?
$\frac{5}{11}, \frac{5}{7}, \frac{3}{8}, \frac{6}{13}$
Option 1: $\frac{17}{56}$
Option 2: $\frac{19}{56}$
Option 3: $\frac{1}{ 7}$
Option 4: $\frac{23}{56}$
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Correct Answer: $\frac{19}{56}$
Solution :
L.C.M. of 11, 7, 8, 13 = 8008
Now, $(\frac{5}{11},\frac{5}{7},\frac{3}{8},\frac{6}{13})\times$ 8008
⇒ 5 × 728, 5 × 1144, 3 × 1001, 6 × 616
⇒ 3640, 5720, 3003, 3696
Least fraction = $\frac{3}{8}$
Greatest fraction = $\frac{5}{7}$
Difference = $\frac{5}{7} - \frac{3}{8} = \frac{(40 - 21)}{56} = \frac{19}{56}$
Hence, the correct answer is $\frac{19}{56}$.
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