Question:
Tick (✓) the correct answer
$\left(\frac{2}{3}+\frac{-4}{5}+\frac{7}{15}+\frac{-11}{20}\right)=?$
(a) $\frac{-1}{5}$
(b) $\frac{-4}{15}$
(c) $\frac{-13}{60}$
(d) $\frac{-7}{30}$
Solution:
(c) $\frac{-13}{60}$
Using the commutative and associative laws, we can arrange the terms in any suitable manner. Using this rearrangement property, we have:
$\frac{2}{3}+\frac{-4}{5}+\frac{7}{15}+\frac{-11}{20}=\left(\frac{2}{3}+\frac{7}{15}\right)+\left(\frac{-4}{5}+\frac{-11}{20}\right)$
$=\frac{(10+7)}{15}+\frac{[(-16)+(-11)]}{20}$
$=\left(\frac{17}{15}+\frac{-27}{20}\right)$
$=\frac{[68+(-81)]}{60}$
$=\frac{-13}{60}$