Using the distributive property of rational numbers, determine the value of $\frac{1}{11} \times (\frac{5}{7} - \frac{1}{19})$

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$\frac{102}{133}$

$\frac{8}{133}$

$\frac{29}{131}$

$\frac{7}{8}$

answer is D.

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Detailed Solution

Given,

$\frac{1}{11} \times (\frac{5}{7} - \frac{1}{19})$ $= (\frac{1}{11} \times \frac{5}{7}) - (\frac{1}{11} \times \frac{1}{19})$

(Using the distributive property)

$= \frac{5}{77} - \frac{1}{209}$ (LCM of 77, 209 is 1463).

$= \frac{19 \times 5 - 7}{1463} = \frac{95 - 7}{1463}$

$= \frac{88}{1463}$ = $\frac{8}{133}$

Therefore, $\frac{1}{11} \times (\frac{5}{7} - \frac{1}{19})$ $= \frac{8}{133}$ .

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