Question + Thanks!

[BeachGeek]

Hello! First off, I want to sincerely thank everyone on this forum. I have been lurking around in obscurity on here for some time, and the information I've gleaned from yall has helped me tremendously in my first and final year of competitive Number Sense. As a 1A competitor, I do not have access to (m)any resources. In fact, I am my own coach. My scores, though meager by most standards, would be GREATLY diminished if not for the folks here. Again, thank you!!!

I'd also like to ask a question... On this year's tests, I keep running into questions like these...

1/10 + 1/40 + /1/88 = ?
1/18 + 1/54 + 1/108 = ?

Is there a better way to do these than just getting the LCD?

Thanks!

[Fredfredburger]

The second one can be rewritten as
[unparseable or potentially dangerous latex formula]

The sequence 2, 6, 12 is of the form [unparseable or potentially dangerous latex formula]

The sum of that is given by
[unparseable or potentially dangerous latex formula]

Here you can just factor out the 9 on the bottom
[unparseable or potentially dangerous latex formula]

I don't see anything for the first one, but I kind of # at number sense, so yeah. I would just find the lcm really fast. The 88 only needs to be multiplied by 5 to get to lcm, 440, and you can convert the rest really fast.

[rcoker7]

There's a nice trick that works for both of these problems.

For the first one, we can write it as 1/(2*5)+1/(5*8)+1/(8*11). Notice that 2,5,8,11 is an arithmetic sequence. Whenever there's an arithmetic sequence like this, you do (number of terms in sum)/(first term of sequence*last term) which in this case would be 3/(2*11)=3/22.

For the second one, it's 1/(3*6)+1/(6*9)+1/(9*12) so we have 3/(3*12)=1/12.