Find the sum:

$\dfrac{4}{7} + \dfrac{2}{-3} + \dfrac{5}{21} + \dfrac{-8}{9}$

First express each rational number with a positive denominator.

$\dfrac{2}{-3} = \dfrac{2 \times (-1)}{-3 \times (-1)} = \dfrac{-2}{3}$

The denominators are different, so express the rational numbers with the LCM of their denominators as the common denominator and then add.

LCM of 7, 3, 21 and 9 = 63

$\dfrac{4}{7} + \dfrac{-2}{3} + \dfrac{5}{21} + \dfrac{-8}{9} = \dfrac{4 \times 9 + (-2) \times 21 + 5 \times 3 + (-8) \times 7}{63} \\[1em] = \dfrac{36 - 42 + 15 - 56}{63} \\[1em] = \dfrac{51 - 98}{63} \\[1em] = \dfrac{-47}{63}$

Hence, $\mathbf{\dfrac{4}{7} + \dfrac{2}{-3} + \dfrac{5}{21} + \dfrac{-8}{9} = \dfrac{-47}{63}}$.