Question

find
$\frac{3}{7} + ( \frac{ - 6}{11} + ( \frac{ - 8}{21} ) + ( \frac{5}{22} )$
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Answer 1

Heya!

Here is ur answer....

= 3/7+(-6/11)+(-8/21)+5/22

= 3/7-6/11-8/21+5/22

= 198-252-176+105/462

= -125/462

Answer 2

Answer

$\frac{3}{7} + ( \frac{ - 6}{11} ) + ( \frac{ - 8}{21} ) + ( \frac{5}{22})$

$= \frac{198}{462} + ( \frac{ - 252}{462} ) + ( \frac{ - 176}{462} ) + ( \frac{105}{462} )$

Note that 462 is the LCM of 7,11,21,22

$= \frac{198 - 252 - 176 + 105}{462} = \frac{ - 125}{462}$

Another method

$\frac{3}{7} ( \frac{ - 6}{11} ) + ( \frac{ - 8}{21} ) + \frac{5}{22}$

$= ( \frac{3}{7} + ( \frac{ - 8}{21}) + ( \frac{ - 8}{21} ) + ( \frac{ - 6}{11} + \frac{5}{22}$

By using communicative and associative

$= ( \frac{9 + ( - 8)}{21} ) + ( \frac{ - 21 + 5}{22} )$

LCM of 7 and 21 is 21 and LCM of 11 and 22 is 22

$= \frac{1}{21} + ( \frac{ - 7}{22} = \frac{22 - 147}{462} = \frac{ - 125}{462}$