MathChat

But what’s really annoying is that your teacher says it like it’s so easy:

“Blah, blah blah … and then, find the LCM (aka, the LCD) for the two fractions.”

Meanwhile, you’re sitting there, thinking, “Right, and uh, how do I do that, again?”

Math Cafe, Open 24/7 = 3.42857 …

Well, it turns out that there’s a pretty easy way to find the LCD when you’re adding or subtracting fractions. In fact, there’s a secret, shortcut way that you probably won’t find anywhere else on the internet. But you will find it here.

All you need to do is follow few surefire steps. I’ll show you the steps right now through this example problem:

5/12 + 3/20

1st) State the challenge.
We need the LCD for our two denominators: 12 and 20.

2nd)  Make a proper fraction out of the two denominators. A proper fraction is just a “normal fraction” — smaller number on top, larger number on the bottom.
Fraction we make:  12/20

3rd) Simplify that fraction to lowest terms and then flip it (get its ‘reciprocal.’)
12/20 simplifies to 3/5. Reciprocal (“flip”) of 3/5 is 5/3.

4th) Multiply the original fraction by the reciprocal (the flipped fraction).
12/20 x 5/3 = 60/60

5th) You just found the LCD. The number that’s repeated in your answer is the LCD.
Fraction we got was 60/60. This means that 60 is the LCD of 12 & 20.

Now of course, once you have the LCD, you’ll multiply top and bottom of the original problem’s fractions to make their denominators equal to the LCD, equal to 60, in this example. So here you’d multiply the original fractions — 5/12 and 3/20 — so they have a denominator of 60.

One nice thing about this process. It shows you what you need to multiply the fractions by.

The 4th step shows that you multiply 12 by 5 to get 60. So that means  you will multiply 5/12 by 5/5:  5/12 x 5/5 =  25/60

The 4th step also shows that you multiply 20 by 3 to get 60. So that means  you will multiply 3/20 by 3/3:  3/20 x 3/3  = 9/60

To finish your fraction addition problem, you simply add those converted fractions:
25/60 + 9/60 = 34/60 = 17/30