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I need some serious maths help

I just CAN'T get my head around adding more than two mixed numbers, could some please explain to me, like you're explaining to a young child, how to do it, this is the way my teacher said but it doesn't make any sense

for instance

4 1/2 + 3 5/6 + 2 1/3

Find common lower number (denominator) =6

Change to top heavy fractions

9/2 + 23/6 + 7/3

Make denominator 6

9*3/6 + 23/6 + 7*2/6

Ok this is where I am confused as hell, WHY do I have to say 9 times 3 and 7 times 2!? I don't get it at all, because how does that equal the denominator 6? how is that in any relation to 6, oh someone help me please I am going to go insane

Anyway he moves on to this

27/6 + 23/6 + 14/6= 64/6 = 10 2/3

that bit is simple enough but its the other bit, the 9 times 3 and 7 times 2, where the hell did he get that from, this is really depressing me, I feel so stupid, I just don't understand why 9*3 would equal the denominator 6 and 7 times 2 equal donominator 6, oh kill me, oh gosh this is terrible

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Reply 1
well if you multiply the bottom of a fraction you have to multiply the top by it as well if you want it to stay the same.
Think about 51\frac{5}{1} this is obviously equal to 5
If you want to get something else that is equal to 5 but say with a 10 on the bottom then you have to multiply the top by 10 as well or it's not still going to be equal to 5
so 51=5×1010\frac{5}{1}=\frac{5 \times 10}{10}which is 5010\frac{50}{10} or 50 divided by 10 which is still 5 :smile:
Reply 2
Think of it this way-you want to put all of them over the same thing, in this case it turns out to be 6(you want the lowest common multiple of the denominators), so you try to work out what they each are.
First:
9/2=x/6
How do you work out x? Since you multiply the bottom by 3 to get from 2 to 6, you must do the same to 9, so x is 9*3. Make sense?
Reply 3
Original post by Slumpy
Think of it this way-you want to put all of them over the same thing, in this case it turns out to be 6(you want the lowest common multiple of the denominators), so you try to work out what they each are.
First:
9/2=x/6
How do you work out x? Since you multiply the bottom by 3 to get from 2 to 6, you must do the same to 9, so x is 9*3. Make sense?



No not at all! I'm seriously screwed
Reply 4
I am sure that you know that

1218=23\frac{12}{18} = \frac{2}{3} because you can divide numerator and denominator by 6

so, if you had 23\frac{2}{3} and you wanted to turn it into a fraction with 18 as the denominator you would be able to multiply the numerator and denominator by ... ...

In the question you have you want to change 92\frac{9}{2} into a fraction with 6 as the denominator so what would you have to multiply numerator and denominator by
Reply 5
Original post by mickno
I just CAN'T get my head around adding more than two mixed numbers, could some please explain to me, like you're explaining to a young child, how to do it, this is the way my teacher said but it doesn't make any sense

for instance

4 1/2 + 3 5/6 + 2 1/3

Find common lower number (denominator) =6

Change to top heavy fractions

9/2 + 23/6 + 7/3

Make denominator 6

9*3/6 + 23/6 + 7*2/6

Ok this is where I am confused as hell, WHY do I have to say 9 times 3 and 7 times 2!? I don't get it at all, because how does that equal the denominator 6? how is that in any relation to 6, oh someone help me please I am going to go insane

Anyway he moves on to this

27/6 + 23/6 + 14/6= 64/6 = 10 2/3

that bit is simple enough but its the other bit, the 9 times 3 and 7 times 2, where the hell did he get that from, this is really depressing me, I feel so stupid, I just don't understand why 9*3 would equal the denominator 6 and 7 times 2 equal donominator 6, oh kill me, oh gosh this is terrible



Lets just deal with the first one, the topheavy fraction being 9/2. If you wanted the denominator to be 4, then you have doubled the bottom. And whatever you do to the bottom, you have to do to the top. So you double the top, 9*2 = 18. So 9/2=18/4

So the same goes when you want the denominator to be 6. You have multiplied it by 3, so you need to do the same to the top :smile: Does that makes more sense now?
Reply 6
I have no idea why I have to times 9 by 3 or 7 by 2, it just makes no sense I know I have to change the top but how the HELL does 9 times 3 or 7 times 2 have ANY relation to the denominator 6, OMG
Original post by mickno
.


Okay, not the best explanation by any means but:

So you wan't to add the fractions together yh; and you know that the denonminators have to be the same. You also have to remember that the number has to be the same value as before otherwise you wont be adding the same three numbers together. So what you do is times the number by 1, BUT look how it works:

9/2 * 3/3 (which is one) = 27/6
23/6 * 1/1 (which is one) = 23/6
7/3 * 2/2 (which is one) = 14/6

See how you get what your teacher got now.
(edited 12 years ago)
Reply 8
Original post by twelve
Lets just deal with the first one, the topheavy fraction being 9/2. If you wanted the denominator to be 4, then you have doubled the bottom. And whatever you do to the bottom, you have to do to the top. So you double the top, 9*2 = 18. So 9/2=18/4

So the same goes when you want the denominator to be 6. You have multiplied it by 3, so you need to do the same to the top :smile: Does that makes more sense now?



No because 9 times 3 doesn't equal 6 nor does 7 times 2, they don't even devide evenly into six ffs!
Reply 9
Original post by 4mar_ar5en4l
Okay, not the best explanation by any means but:

So you wan't to add the fractions together yh; and you know that the denonminators have to be the same. You also have to remember that the number has to be the same value as before otherwise you wont be adding the same three numbers together. So what you do is times the number by 1, BUT look how it works:

9/2 * 3/3 (which is one) = 27/6
23/6 * 1/1 (which is one) = 23/6
7/3 * 2/2 (which is one) = 14/6

See how you get what your teacher got now.



Right now I'm even more confused what do you mean 1!? Where you getting one from, and it's still not explaining why 9 has to be times'd by 3 or why 7 has to be times'd by two because they have no relation to 6, I might aswell times they them by any number I like, why 6? why not 4? or 8? seriouisly wtf
Do you understand that these are all the same

86=8060=43=1612=\frac{8}{6} = \frac{80}{60} = \frac{4}{3} = \frac{16}{12}=

etc
Reply 11
Original post by TenOfThem
Do you understand that these are all the same

86=8060=43=1612=\frac{8}{6} = \frac{80}{60} = \frac{4}{3} = \frac{16}{12}=

etc




Yeah but that has got nothing to do with my question, I want to stick to my question
Original post by mickno
Right now I'm even more confused what do you mean 1!? Where you getting one from, and it's still not explaining why 9 has to be times'd by 3 or why 7 has to be times'd by two because they have no relation to 6, I might aswell times they them by any number I like, why 6? why not 4? or 8? seriouisly wtf


Okay. You don't wanna be changing the numbers that your adding together so that they're different to the question, so you have to do the same to the top and bottom so that the number stays the same.

You want to get all the denominators the same so that you can add the three fractions together right? thats the point of the question. So you need to find the lowest common factor of all the denominators, which happens to be six. With that knowledge you now must make all the fractions go so that they're over 6. And you have to remember than you times the top and bottom by the same.
Original post by mickno
Yeah but that has got nothing to do with my question, I want to stick to my question


Yes it has

So you have 92\frac{9}{2}

do you know that you can find as many fractions that are the same as that as you wish (as per my example)
Reply 14
Original post by 4mar_ar5en4l
okay. You don't wanna be changing the numbers that your adding together so that they're different to the question, so you have to do the same to the top and bottom so that the number stays the same.

You want to get all the denominators the same so that you can add the three fractions together right? Thats the point of the question. So you need to find the lowest common factor of all the denominators, which happens to be six. With that knowledge you now must make all the fractions go so that they're over 6. And you have to remember than you times the top and bottom by the same.


but how the hell does 9 times 3 or 7 times 2 equal 6!!!!!!???? It doesn't even divide into it!!!!! I am going to blow my head off this is terrible, i want to know why he said 9 times 3 and 7 times 2, no one is explaining the relationship it has between 6!!!!!!!!!!!!
Reply 15
Original post by tenofthem
yes it has

so you have 92\frac{9}{2}

do you know that you can find as many fractions that are the same as that as you wish (as per my example)




but how the hell does it!!!!!!!!!!!!!!?
Original post by mickno
but how the hell does 9 times 3 or 7 times 2 equal 6!!!!!!???? It doesn't even divide into it!!!!! I am going to blow my head off this is terrible, i want to know why he said 9 times 3 and 7 times 2, no one is explaining the relationship it has between 6!!!!!!!!!!!!


Actually a number of us have explained the relationship

you need to change the denominator from 2 to 6 ... what is the relationship there
Original post by mickno
but how the hell does it!!!!!!!!!!!!!!?


in Post 12 You said that you understood this
Reply 18
Original post by mickno
No because 9 times 3 doesn't equal 6 nor does 7 times 2, they don't even devide evenly into six ffs!


Numerator is on the top; denominator is on the bottom.
If you have 9/2, and multiply the denominator by 3, then you will get 6 (2 * 3 = 6). But you must also multiply the numerator by 3.

*** NOTE: Anything you do to the bottom, you must to do the top.

So, 9 * 3 = 27. The fraction you will get is 27/6. Which is equivalent to 9/2.

Just think about it like this. You have a pizza with 4 slices in total. Half of that pizza is 2 slices, correct? (Or 2/4)

Now you have a pizza with 6 slices. Half of that pizza is 3 slices, correct? (Or 3/6).

So, 2/4 and 3/6 are equivalent, and both equal 1/2.

Hopefully with that cleared, we can focus on addition.

Let's say you have 1/2 + 2/3 + 1/6. All of these have different denominators. In order for them to be added together, you must make the denominators the same, through multiplication.

Obviously, you can see that 6 is the least common denominator, since, 2 * 3 = 6 and 3 * 2 = 6.

Therefore, you must do this:

(1/2) * (3/3) + (2/3) * (2/2) + 1/6. You are multiplying it by (3/3) and (2/2) since what you do to the bottom, you must do to the top. And because (3/3) and (2/2) are equivalent to 1.

So, now you have 3/6 + 4/6 + 1/6.

Add the numerators together (keeping the denominator the same), and you end up with 8/6. Using equivalent fractions, we can reduce this to 4/3.

As for your question, you're basically dealing with fraction multiplication. 9 * (3/4) is basically (9/1) * (3/4). When multiplying fractions, you multiply the numerators and the denominators. So, 9 * 3 = 27, and 1 * 4 = 4. So, your fraction is 27/4. Understand?

Also, I understand that you're frustrated, but these people are here helping voluntarily, so you could attempt to be a bit less abrasive.
(edited 12 years ago)
Reply 19
Original post by TenOfThem
Actually a number of us have explained the relationship

you need to change the denominator from 2 to 6 ... what is the relationship there



But how does 9 times 3 got anything to do with changing the denominator from 2 to 6

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