Aside from solving this out like below, is there a pattern to notice (or trick) that gets you there quicker?
(1/5 - 1/6) + (1/7 - 1/8) + 1/9
= (1/30) + (1/56) + (1/9)
= (56/1680) + (30/1680) + (188/1680)
= 274/1680
Determine whether
-\frac{1}{6} + \frac{1}{7} - \frac{1}{8} + \frac{1}{9}
is greater than or less than 0
A further hint: take pairs. Can you deduce whether each pair is positive or negative? Can you further use that to reason on the solution to the overall problem?
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