http://www.teachertube.com/view_video.php?viewkey=ebd7c1e1b7118af88edc&page=1&viewtype=&category=

So, here’s somethin’ that happened. And I figure it makes a pretty good word problem, especially since it’s got to do with fractions. So, lemme explain somethin’ first. I don’t cook, generally. But my friend Liz, she cooks all the time. She says it’s better for you to eat at home, and cheaper, too, and I guess I can’t argue too much widdat. So, she says she gonna teach me how to cook, right? So, she’s showin’ me how to make pancakes.

Well, the recipe for pancakes says 1-1/2 cups flour, but I don’t got a lot of measuring cups and stuff in my kitchen, and after looking around, all I could come up with is a 1/3-cup measuring cup, which I don’t know how it got there, but there it was. So, here’s the question: how many 1/3 cups of flour do I need to put in to get 1-1/2 cups?

How’s that for a word problem?

Any ideas? How’d you set about it, d’y think?

Well, here’s how I did it. I know that 3 of the 1/3 measures will give me 1 cup. Then, I need 1/2 cup. Well, if three 1/3 cups give me a whole cup, then half of that will give me a half cup. Follow? That’s 1-1/2 of the 1/3 measures. So all together, three plus 1-1/2 is 4-1/2 of the 1/3 cup measures. So, I measure out 4 and eyeball a half of the 1/3 measure. That gives me 1-1/2 cups, but I got to get some measuring cups!! Did you figure it out?

Well, how about lookin’ at the math? What we’re really doin’ here is dividing…. how many times do 1/3 go into 1-1/2… how many 1/3rds are in 1-1/2 cups? So you could write it out:

1-1/2 ÷ 1/3 =

Now, first off, I’m going to change 1-1/2 to an improper fraction, so it’s all one fraction. 1-1/2 is the same as 3/2 (that’s 2/2 plus 1/2)… so we got:

3/2 ÷ 1/3 =

Now, to DIVIDE fractions, you gotta do a switcheroo. You turn over the second fraction, so 1/3 becomes 3/1, and you change division to multiplication…

3/2 × 3/1 =

Both those steps just make the problem easier. Now, to multiply two fractions, you multiply across the top (3 × 3 = 9) to get the top, and multiply across the bottom (2 × 1 = 2) to get the bottom:

3/2 × 3/1 = 9/2

How much is 9/2? 2 goes into 9 four times, with 1 left over:

3/2 × 3/1 = 9/2 = 4-1/2

Four and a half! Same as I got just by thinkin’ it through. How’s that for some math?

How’d you do? Be sure to send me any GED problems you havin’ trouble with!

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

am having problem with Lesson-7 page 491 on A. on Add or subtract as Directed reduce to the lowest terms.Am trying to figure out the form to work the fractions. am stuck on this one. Michael

Okay, here’s the rule with adding and subtracting fractions. Let’s start with a problem:

5/12 + 2/5

For starters, make sure you got the same number on the bottom of both fractions (the same denominator). If the denominators are different (like 12 and 5), how do you get them the same?

Well, you can change the number on the bottom of a fraction by multiplying or dividing BOTH the number at the top (numerator) and the number at the bottom (denominator) by the same number. So, what’s a number you can multiply 12 and 5 into evenly? Gotta go all the way up to 60 to do it. I figure it out by seeing what the multiples of 12 are, until I find one that 5 goes into (cuz I know 5 will go into it if it ends in 5 or 0). Hey, practice those times tables!

So, since 12 x 5 is 60, you change the denominator of the first fraction to 60 by multiplying the top and bottom by 5:

5/12 = (5 x 5) / (12 x 5) = 25/60

For the second fraction, you gotta multiply by 12:

2/5 = (2 x 12) / (5 x 12) = 24/60

So, the problem gets to be:

25/60 + 24/60 =

Now, it’s easy. Just add the top numbers, and the bottom number stays the same:

25/60 + 24/60 = 49/60

Now, you want to REDUCE. That means, is there anything you can divide evenly into the top and bottom? No, there isn’t. So the answer is 49/60. Let’s try a subtraction problem… they’re similar. Make the bottom numbers the same, and then subtract the top numbers. But let’s mix it up with mixed numbers.

5-1/4 – 3-2/3 =

Okay, there are a couple of ways to do this, but I find the easiest is to make them into improper fractions first. How many 4ths is 5? It’s 20/4 (4 x 5 = 20). So, 5-1/4 = 21/4… you can do the same thing with 3-2/3. Three is the same as 9/3 (or 3 x 3 thirds), so 3-2/3 = 11/3 (9 thirds plus 2 thirds is 11 thirds). Now, it’s just fractions:

21/4 – 11/3 =

So, how do we make 4 and 3 the same? What do they both go into? 12.

21/4 = (21 x 3) / (4 x 3) = 63/12

11/3 = (11 x 4) / (3 x 4) = 44/12

To figure out the problem, just subtract the top numbers, and leave the bottom one the same:

63/12 – 44/12 = (63 – 44)/12 = 19/12

Now, what’s 19/12? Take 12/12 out to make 1, and you’ve got 7/12 left: 1-7/12.

Okay, we didn’t really reduce on any of these, so let’s do one that needs to reduce.

11/36 + 7/36 =

The bottom numbers are already the same, so just add the top numbers and leave the bottom number the same:

11/36 + 7/36 = (11 + 7)/36 = 18/36

Okay, now we got 18/36. It needs to be reduced. How do I know? Well, first they’re both even numbers, so I know for sure that 2 goes into both. (If they both ended in either 0 or 5, I’d know 5 went into both… seriously, check your times tables.)

Since 2 goes into both, I can divide both by 2:

18/36 = (18 ÷ 2) / (36 ÷ 2) = 9/18

Now, I can see pretty clear that 9 goes into 18:

9/18 = (9 ÷ 9) / (18 ÷ 9) = 1/2

So, 18/36 is 1/2. If I saw right away that 36 was twice 18, I wouldn’t'a had to divide twice… that’s why it helps your GED to get really good at the basic math, dividing, multiplyin’, just workin’ with numbers.

Let me know if this helps studyin’ for your GED! And let me know if you got any more questions abou adding and subtracting fractions.

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

hi all need adding mixed fractions please.

and:

Hi curtis its valerie in florida again new question wow took the tape test and im ready to do the GED in Reading wow ok in math the total score was 5.0 G.E that she said had to get to 10.0 right ok she said to start in Estimation what is this rounding off ? please tell me what to do where to go in the ged study video ty.

Hey there, Valerie! First off, congrats on bein’ down with the reading. That’s one more done! Now, the math…

Estimating

Estimation is rounding off, like you said. But it’s also part of what I call mental math. In the passGED study program, you can go to the first math course (Learning about Numbers), and go to Unit 1, Lesson 6, to learn all about it. I call it mental math. You can estimate to make your job on the GED a lot easier, so you don’t have to do so much math. That means, goin’ through a problem an’ figuring out about what the numbers are, in round numbers that’re easy to work with. With multiple choice answers, if you figure out about what the right answer is, you save a lot of time. You don’t have to get it exact.

Say, I got a problem:

5,890 + 8,799 + 2,014 + 9,882 + 4,649

Okay, that’s gonna take a little time to work out on paper, but I also got some multiple choice answers:

A) 35,892

B) 31,234

C) 29,449

Can I figure it out without goin’ through all the math? Prolly. Here I go…

5,890 is about 6,000, and 8,799 is about 9,000, and 2,014 is about 2,000, and 9,882 is about 10,000, and 4,649 is about 4,500… so the question is ABOUT

6,000 + 9,000 + 2,000 + 10,000 + 4,500 which is ABOUT

6 + 9 + 2 + 10 + 4-1/2 thousand.

That’s like 6 + 9, is 15, plus 2 is 17, plus 10 is 27, plus 4-1/2 is 31-1/2…

So, it’s about 31,500. That’s pretty close to answer B. So that’s my choice. If you figure it out on a calculator, that’s it. See how good that can be savin’ you time on a test?

Adding Mixed Fractions

Fraction Basics…

Befo’ starting about fractions, here’s the link  to all my articles on fractions… http://www.passged.com/student_blogs/curtis/category/fractions/

You gotta start by really lookin’ at what a fraction is… I mean, you got two numbers in a fraction, right? One on top an’ one on the bottom. Like, 1/2… that’s an easy one to think about. The top number (1) is called the numerator, and the bottom number (2) is called the denominator. But that’s not the point. Remembering what they’z called is jus’ to help you understand what math books is talking about. What’s really important is what they mean. Think about a pizza. It’s divided in half. Each half is 1/2, right? That’s basic. The top number (1) is really the number of parts you have, and the bottom number (2) is the number of equal parts the whole thing is divided into. That make sense? So you got 1 part out of 2 parts… then, you got half.

Same thing if you got 3/4… say you got 3/4 of a box of candy. That means, if you divide the box into 4 equal parts, you got three of them. What happened to the other 1/4? Who knows? Maybe someone ate it.

So, if the whole box of candy originally had 16 chocolates in it, and you got 3/4 of the box, how many chocolates you got?

Now, there’s a GED math question for you… this is also called a ‘ratio,’ but really if you understand what fractions are, it’s pretty easy.

Say you got 16 chocolates, and you wanna divide it into 4 parts (see, 3/4 means its divided into 4 parts, right?) Then, you divide 16 by 4, and you get 4. See, 4 piles of 4 chocolates each is 16 all together… and each pile of 4 is 1/4 of all the chocolates. Hey, get 16 chocolates (or paperclips or anything) and give it a try. No way to learn like actually seeing it, right?

So if you got 3/4 of the chocolates, then you got 3 of the 4 piles. So, you multiply the number of chocolates in 1 pile (4) by the number of piles you got (3) to get the total number of chocolates you got… 12. D’you follow? Here it is in math terms:

How much is 3/4 of 16? (Of usually means multiply, so…)

3/4 x 16 = 3 x (16 ÷ 4) = 3 x 4 = 12

So, if 2/6 of the 24 people in your office vote to have hamburgers for lunch, how many people voted to have hamburgers for lunch?

2/6 x 24 = 2 x (24 ÷ 6) = 2 x 4 = 8

See how it works? If you divide 24 people into 6 equal groups, there are 4 people in each group. An’ if 2 groups vote for hamburgers, that’s 8 people.

Now on to the real question…

Adding Mixed Fractions

Mixed fractions is when you got a whole number like 3 plus a fraction like 3/4. So, if you’re addin’ mixed fractions you got something like this:

1-4/5 + 6-2/3

Problem is, it’s hard to add two fractions that have different bottom numbers. It’s like I was sayin’, if you have one set divided into 5 equal groups, and another set of things divided into 3 different groups, the groups will be different sizes. So, it’s like apples and oranges. You can’t add ‘em together.

So, you gotta figure out the smallest number that can go at the bottom of the fraction to make both fractions have the same bottom number. Well, a lot of the time, that number is the two denominators (bottom numbers) multiplied together. And that’s the case here. You can change both fraction to something-15ths.

4/5 = ?/15

This is jus’ like I was talking about before. Say you got a box of 30 chocolates, divided into 5 groups. Then, you got 6 chocolates in each group, right? And 4/5 of the chocolates would be 24 chocolates. (4 groups of 6 chocolates).

Now, what if you divide the chocolates into 15 groups? How many groups make up 24 chocolates? Well, if you divide 30 chocolates into 15 groups, you got 2 chocolates in each group. And 12 groups makes up 24 chocolates… 12 groups of 15 is the same as 4 groups of 5.

4/5 = 12/15

There’s a shortcut way to figure it out… because 5 x 3 is 15, you multiply the top number by the same thing (3) to get 12 on top. This always works! So…

2/3 = ?/15
since 3 x 5 = 15…
2/3 = (2 x 5)/15 = 10/15

Okay, now you got your numbers the same at the bottom….

1-4/5 + 6-2/3 = 1-12/15 + 6-10/15

Next step is to add the whole numbers and add the fractions. When you add fractions, just add the top numbers (12 groups plus 10 groups is 22 groups, no matter how big the groups are, right?)

1-4/5 + 6-2/3 = 1-12/15 + 6-10/15 = 7-22/15

Now, 22/15? If the top number’s bigger, then you got more than one. 15/15 is a complete set of groups… so it’s 1. That means, 22/15 = 1-7/15. So…

1-4/5 + 6-2/3 = 1-12/15 + 6-10/15 = 7-22/15 = 8-7/15

Hope this helps!

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.

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.

I used to work in a machine shop. Sometimes I would have to convert fractions to inches like 1/3. I know how to do that, all you have to do is divide 1 by 3. The question is, I always had to use a calculator, and I would like to do that without using a calcualtor. Every time I tried I would’nt get the proper answer. How do you do that without using a calculator.
Mark

Yeah, that’s the key, Mark. Doin’ stuff in your head makes it easier and faster, an’ helps a lot on the GED. Part of it is jus’ knowin’ or rememberin’ some of the fractions you see all the time.

Think of it in terms of dollars and cents to remember the real easy ones:

1/4 (a quarter) = 25 cents or .2

1/2 (half dollar) = 50 cents or .5

3/4 (three quarters) = 75 cents or .75

1/10 (a dime) = 10 cents or .1

Tenths are easy. It’s always gonna be point-whatever-is-on-top:

2/10 = .2

3/10 = .3

4/10 = .4

5/10 = .5

6/10 = .6

7/10 = .7

8/10 = .8

9/10 = .9

Fifths is always point-the-top-number-times-2.

1/5 = .2

2/5 = .4

3/5= .6

4/5 = .8

Then, there’s the thirds. These are pretty easy to remember, but they don’t give even numbers:

1/3 = .3333 (remember the 3 from 1/3)

2/3 = .6667 (remember that 2 x 3 = 6)

Then, there’s eighths.

1/8 = half of a quarter = .125 (you can remember it cuz 12 is kinda like 1/2 and 25 is a quarter)

2/8 = 1/4 = .25

3/8 = 1/8 + 2/8 = .125 + .25 = .375

4/8 = 1/2 = .5

5/8 = 1/2 + 1/8 = .5 + .125 = .625

6/8 = 3/4 = .75

7/8 = 3/4 + 1/8 = .75 + .125 = .875

Then, what about more complicated ones? You can still do ‘em in your head. You gotta divide the bottom number into the top, so like 2 into 1 = .5 … on harder ones, it’s harder to do in your head.

Say you have 11/25 … you gotta divide 25 into 11… Start by adding a zero to the 11. So you got 25 into 110… 25 goes into 100 four times, so you got a 4… and ten left over. Add another zero… and that’s 25 into 100 again… that’s 44. Now, where’s the decimal go? Well, it’s before the first number, .44 … you can check it by thinking, 11/25 is almost a half, and .44 in almost .5. So you’re good.

Another way is to try to make the bottom number 100. So, 11/25 = 44/100. Then you take the top number and move the decimal place 2 points, so 11/25 = .44

Here’s some places to go for some more explanation and practice:

http://www.mathsisfun.com/converting-fractions-decimals.html

http://www.curiousmath.com/index.php?name=News&file=article&sid=77

http://www.learningwave.com/chapters/decimal13/basics/convert.html

http://www.coolmath.com/decimals/04-decimals-converting-fraction-to-decimal.html

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