GED Math: Subtracting Fractions

Hey, all. Here’s a good GED math question about subtracting fractions that came up from one of the passGED students, from a GED textbook…and I’ve put a little more information in my answer, to make it clearer to everyone:

At the complete GED prep guide by Steck-Vaughn ( P. 491 ) there are 10 exercises at the top of that page for Operations with Fractions . two of them ( 7 and 8 ) were not clear enough for me although , I did them the right way by referring to the answers page ( 830 ) . What I was unable to figure out is , for example , the question 7 : 20-1/3 – 8-2/3 = 11-2/3 . For that question , the order of operations was not given I think in detail or at least , why 20-1/3 = 19-3/3 + 1/3 ( from where we got that 1/3 ? ) I had the same with question 8 because it uses the same method or order of operation .

Okay, so maybe everyone isn’t using the same book, but we all got to look at math stuff…online, in a book…wherever. This is a good question, because it’s part of the basic idea of using fractions, somethin’ that’s important all over the GED test. Don’t matter what kind of math you’re using…geometry, algebra, or just basic addition, you’re gonna run into some fractions. Why? Cuz things don’t just always come in whole parts! The world’s complicated, and so math’s gotta keep up with the world. Okay, enough philosophizin’.

The question’s not really about order of operations. There’s only one operation… subtraction. (Operations are the kinds of math you are doin’ in the problem… addition, subtraction, multiplication, division, and the order of operations is the order you do different kinds of math…which you do first.) The book don’t really clearly explain what’s going on. Here’s the problem it’s talking about…

20-1/3 – 8-2/3 = 11-2/3

Point is, how did you get there? How do you get the answer to 20-1/3 – 8-2/3? The basic trouble with this problem is, if you try to subtract the fractions, you run into difficulties because 2/3 is bigger than 1/3. What they’re trying to get at is how to deal with the fractions. They show you this:

20-1/3 = 19-3/3 + 1/3

See, 19-3/3 is the same as 20, since 3/3 equals 1. They change 20-1/3 to 19-3/3 + 1/3 to get enough “thirds” to subtract 2/3. Dat make any sense? It’s more about explainin’ how the fractions ’sposed to work than anything else. So that, if you’re tryin’ to subtract 8-2/3 from 20-1/3, you’ve got to change a digit in 20-1/3 to thirds. You can’t subtract 2/3 from 1/3, so you take one off the 20 (makin’ it 19) and change the 1/3 to 4/3 (20-1/3 = 19-4/3, or 19-3/3 + 1/3, as they put it.) Then, you can subtract 8-2/3 from 19-4/3 (19 – 8 = 11, and 4/3 – 2/3 = 2/3, so the answer is 11-2/3).

The idea is the same as “borrowing” in regular subtraction. When you first learned to subtract, you used “borrowing.” So if you got:

You “borrow” 1 from the tens column, like this, to make the 5 into 15:

So that you can just subtract 7 from 15 to get 8….

And bring down the 1 to get 18…. simple, basic math, right? You remember doing that. Now, you’re probably so used to subtracting that you don’t go through those steps anymore…

But, now you gotta deal with fractions. So, you’ve got a problem like this…

And it’s just like the other, simple math. You can’t take 2/3 from 1/3, so you “borrow” 1 from the 20 and change 20 to 19. Since the 1 you borrowed equals 3/3 (three-thirds is one whole), you’ve now got 4/3.

Subtract 2/3 from 4/3 and you get 2/3…

Subtract 8 from 19, and you get 11…

And that’s it. Just the same basic math, just done a little different cuz of the fractions! Yeah, fractions mess up people all the time, but just take ‘em one step at a time, and you’ll get through!

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passGED.com.