Fractions for the GED: Lower Terms, Improper Fractions

Hey, all. Bet you all studyin’ hard, right? Get that GED. It’s totally worth it. I got another question here, from Claudia. She say:

I’m not understanding fractions but i get everything else okay… i just don’t get the lower terms, improper, need some help.. claudia

OK. Fractions. That throws lots of people. Part of it is jus’ that all those names for stuff is confusin’. Lower terms? Improper? Numerator? Denominator? All that stuff can throw you off. The big idea is really understandin’ what a fraction means.

So, what’s a fraction?

A fraction is a part of something. So, it’s not a whole thing, it’s jus’ a piece. Right? Like my man D-man like to say, think of it like a pizza. The whole round pizza pie is 1 pizza. Any piece of pizza you gonna get is a fraction. A part of the pizza.

So, how’s that translate into all those numbers you see? Well, the bottom number is an amount of even-sized pieces you could divide the whole thing into (pizza in this example, but it don’t matter… it’s whatever your fraction be talkin’ bout.) The bottom number is called the “denominator.” It tells you what kind of pieces you talking about. If you talkin’ about thirds, the bottom number’s a three, and you’re talkin’ about dividing the whole into three pieces.

The top number is called “numerator.” That’s the NUMBER of pieces you got. (see, “numerator” sounds kinda like “number.”) So, the top tells you how many pieces you got, and the bottom tells you how big the pieces are. So, if you got 1/3, you’ve got 1 of 3 equal pieces. If you got 15/38, then you’ve got 15 of 38 equal pieces. It don’t matter what the numbers are. If you understand what it means, it’s easier, right?

So, that’s what a fraction is. Now, onto the harder stuff…

What’s “lowest terms” for a fraction?

Lowest terms is the smallest numbers you can use for a fraction, to make them easier to read. Best way to show you is an example. So you know what 1/3 is… it’s one of three equal sized parts. Pretty easy to understand.

But what if you got 4/12? You’ve got 4 out of 12 equal sized parts. That’s a little harder to follow, right? But if you look at an example, 1/3 is the same as 4/12.

So, when you’re sayin’ 4/12, you’re sayin’ the same thing as 1/3. It’s the same amount of the whole. When you put a fraction in the “lowest terms,” you want the easiest way to say the same fraction… the smallest numbers.

How do you get there? Well, that’s when it helps to really know just your basic multiplication and division. If you look at 4/12, to find the lowest terms, you gotta figure out… is there any number can divide into both 4 and 12? First thing I see is they’re both even numbers, so I know I can divide 2 into them… then I do it… divide 2 into 4, goes 2 times. Divide 2 into 12, goes 6 times. Now I got 2/6. And they’re both even numbers again, so I can do the same thing again, and I get 1/3. That’s the lowest terms.

It can get harder with bigger numbers, like 140/260 … but it’s the same idea. They both end in “0,” so I can divide both by 10, and I get 14/26. Now, they’re both even and I can divide by 2 and get 7/13. That’s where I stop. Nuthin’ goes into 7 and 13 even, except 1, so I’m done.

Here’s a website where you can type in any fraction, and it’ll show you how it reduces: http://www.webmath.com/redfract.html

Here’s another site, that’s got two methods for reducing fractions: http://www.mathleague.com/help/fractions/fractions.htm#lowestterms

And here’s my favorite….a good one for practice, that shows you what the fraction looks like, as part of a circle: http://www.visualfractions.com/LowestCircle.html

Now, what’s an “improper” fraction? Like, what’s wrong with it anyway?

An “improper” fraction is when the top number is bigger than the bottom number. If the top number shows how many parts you divide up a whole thing into, and the top says how many pieces you’ve got, what does it mean when you’ve got more pieces than are in a whole? Think about it….

It means you’ve got more than a whole… that is, more than 1.

Let’s take pizza. Say I’ve got 5/3 of a whole pizza (that’s an improper fraction.) How much pizza do I have? How many is in 1 pizza? 3/3 right? Then, I’ve got 2/3 left over. So, I’ve got 1-2/3 pizzas.

Just like the lowest denominator, “improper” fractions is just another way of looking at the same number. 5/3 is just a different way of saying 1-2/3. But 1-2/3 is easier to understand, so people usually change improper fractions to “mixed” numbers…that is, a whole number plus a fraction, like 1-2/3.

To do the math for this, you need basic math again… this time division. So, you gotta divide the bottom number (how many pieces make up a whole) into the top number (how many pieces you got) to find out how many wholes you’ve got. That gives you your whole number. Then, whatever’s left becomes the top number in the fraction. So, if I’ve got 5/3, I divide 3 into 5… it goes 1 times, so I got 1. Then, there’s 2 left over, so I got 1-2/3.

Same with a bigger number. If I got 341/5, then I divide 5 into 341… and I get 68 with 1 left over… 68-1/5.

Here’s some websites to check out about improper fractions for more explanations and games:

http://mathforum.org/library/drmath/view/58074.html

http://www.quia.com/cb/186132.html

http://www.webmath.com/convfract.html

Hope this helps with your GED! If you got any more fraction questions, send a comment.

For more information about the GED test and GED test preparation, visit The GED Academy at passged.com.