ShmoopTube

00:03

And here's your shmoop du jour.

00:06

1/3 plus 2/9 minus 5/12 equals... what?

00:10

And here are the potential answers...

00:16

Riddle us this: what is the least common denominator of 3, 9, and 12?

00:21

The easiest way to solve these LCD problems is to first frame them.

00:30

That is, 'at worst', we can multiply the two terms...

00:33

...like... 9 times 12 which is 108, but there's probably a lower and easier way

00:38

to manage term that will keep things... sane.

00:41

Take the larger of the two numbers and mumble to yourself like a withered old politician

00:45

in the 17th hour of a filibuster.

00:48

He mumbles 12... does 9 go into 24 evenly? No -- keep going... 36?

00:58

Ahh... ding ding ding! We have a winner. So 36 should be the LCD for this fraction.

01:04

Oh and by the way, note that we didn't even bother to worry about the 3 there -- it goes

01:08

into 9 AND 12 evenly, so by default it's going to work.

01:12

Now we just rewrite the problem with 36 as the denominator across the board:

01:17

One third becomes 12/36... plus 8/36... minus 15/36.

01:31

And the answer is 5/36, or C.

01:34

Phew. Now no one needs to be carted off to the loony bin.

Full Transcript