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

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?

1 Like