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hmmm, well, first you have to convert into some common denominator
so first, let's convert the mixed numbers into straight fractions
3 1/3 = 9/3 + 1/3 = 10/3
2 2/5 = 10/5 + 2/5 = 12/5
so now we need a common denominator for 3 and 5
15 is one
so 10/3 - 12/5 = 10*5/3*5 - 12*3/5*3 = 50/15 - 36/15 = 14/15
wait im still at 12/5 that still needs to be simplefied correct?
well, 12/5 can't be simplified, since they have no common divisor (a number that divides evenly into them besides one)
the point is, you can multiply anything by 1 and get an equivalent number
so if you have 10/3 and 12/5 , then to easily subtract one from the other you need to same number on the bottom for both fractions
the easiest way to do that is to find a common denominator - but that only works because you can multiply any number by 1 and you know you have the same number - but maybe in a different form (fraction)
sorry im slow.. so im going to back up a little.. so now we have 9/3 - 12/5 and we are finding common denomiator for 3 & 5 correct?
so 10/3 - I can multiply this by 1/1, 2/2, 3/3, 4/4, 5/5 etc... and it will be the same number
wich you said was 15
yes you're right, but 10/3
so 10/3, and 12/5
your thought process at this point should be - "what do both 3 and 5 divide evenly into - since then i can just multiply to get that number at the bottom"
so really you're looking at 3 and 5
what number do they commonly divide into?
the answer is 15 - and that's always a sure method to get a common denominator - just multiply them by each other
ok and the next part is what gets me so we find their common denomitator what do we do witht the top numbers?
so now your thought process should be - ok - so I they both divide evenly into 15 - what version of "1" can I multiply both fractions by to get 15? since again - I know if I multiple *any* number by "1", it's equivalent - so it's really just another way to write the same number
so for 3 - I know I multiply it by 5 to get 15
so I multiple 10/4 x 5/5 (again, multiplying by 1 means I get the same thing, different way of writing it)
so 10/3 x 5/5 = 10x5/3x5 = 50/15
I get what your saying but im confused... wich doesnt take much :(
now the second fraction, how do I turn 12/5 into (some number)/15
well, I can multiply the bottom by 3 to get 15 (the common denominator) - but to keep the make the top number equal I need to multiply the top by the same number
so 12/5 = 12/5 * 3/3 (1) = 12*3/5*3 = 36/15
and once you have everything with the same common denominator, you can subtract across
so 50/15 - 36/15 = 50-36/15 = 14/15
but let's practice common denominators
so let's say 2/3 and 3/6 are your fractions
what number do both 3 and 6 divide evenly into?
common denominator would be 6? sorry 3
nope you were right the first time
since 6/3 = 3, and 6/6 = 1
so that's good =)
ok so now you want to think - how can I make the bottom number a six for both of them?
so 2/3 = ?/6
and the main thing to learn, is that you can multipel *anything* by 1 and get the same number
i.e. 1x1 = 1, 2x1=2, 3x1 = 3
but that works with fractions too
so for 2/3, if I want to make the bottom number a six, I know I multiply it by 2 -
so to CONVERT 2/3, to ?/6, I just multiply by 2/2 - since it's another way of writing 1 (x/x always equals 1)
so 2/3 = 2/3 * 2/2 = 4/6
great =) . so now convert 4/8 to ?/16
your first thought should be - what do I multiply 8 by to get 16
exactly =). so now you can multiply 4/8 x 2/2 (since again, you're just multplying by "1" when you multiply by 2/20 - and get the equivalent fraction with 16 on the bottom
so 4/8 *2/2 = 4*2/8*2 = 8/16
and check this out - you could get an infinite number of equivalent fractions by just multiplying by different forms of 1
so 2/3 = 2/3 * 1/1 = 2/3 (duh) 2/3 = 2/3*2/2 = 4/6 2/3 = 2/3*3/3 = 6/9 2/3 = 2/3*4/4 = 8/12 etc...
those are all equivalent fractions - i.e. 2/3 = 4/6 = 6/9 = 8/12
and that's all a common denominator wants you to to
so earlier we just choose 2/2 becuase that was the common denominator?
well, we chose 2/2 because we knew it would get us an equivalent fraction - the same exact value
when finding a common denominator, you choose the bottom number so that it makes the same thing the other fraction can make if it's multiplied by some number
so e.g. 3/5 and 2/3
well, I can multiply the bottom number of the first one by something to get 15, and I can multiply the bottom of the second number by something to also make it 15
15 is my common denominator
your so patient with me...
and to convert 3/5 to ?/15, I know I multiply the bottom by 3, so I know I have to muitiply the top by 3 too - since that guarantees me I get the same number, but just "over" 15 instead of "over" 5
so 3/5 = 3/5 *3/3 (3/3 is just "1") = (3*3)/(5*3) = 9/15
and it's ok =) fractions are HARD until you understand them
the whole point again is - you can freely convert fractions to different forms as long as you multiply by 1
thanks... A LOT!
no problem =)
but let's do a couple more
so let's say I want you to convert 1/4 into ?/16
what is 1/4 if you make it ?/16
so your first thought should be, what do I need to to multiply 4 by to get 16 - since those are the two bottom numbers?
1/4 X 4/4?
yep =) now put it into your calculator to check
nope, you were right, 4/16
well, they are both right lol
the thing with fractions, is you can also divide the top and the bottom by the same number and get the same thing
so 4/16 = (4/4)/ (16/4) = 1/4 !
didnt see that at all...i just simplefied
and you can go the other way too =)
e.g. you can get all of the equivalent fractions starting at 1/4, by multiplying by different forms of 1
so 1/4 = 1/4 x 1/1 = 1/4 (duh) 1/4 = 1/4 x 2/2 = 2/8 1/4 = 1/4 x 3/3 = 3/13 1/4 = 1/4 x 4/4 = 4/16 1/4 = 1/4 x 5/5 = 5/20 etc...
and yep, 4/16 is on that list
ok so, let's do 5/6 = ?/18
5/6 x 3/3 ?
and don't be afraid to use your calc to check , especially while you're learning
if you type in 15/18 and 5/6, I guarantee it's the same decimal
yep sure is
ok so now is the biggest leap - make 3/5 and 2/3 so that they have the same number on the bottom
so im finding commond denominator for 5 and 3 correct?
your first thought should be, what number can I make both of the bottom numbers (5 and 3 ) into by multiplying
so 3/5 is ?/15
3/5 x 3/3
and the next number, 2/3 = ?/15
then 2/3 x5/5
mhmmmm, which is?
yep =) . so what's 2/3 - 3/5 ?
nope - so you just converted both of those numbers to ?/15
so if 2/3 = 10/15
and 3/5 = 9/15
2/3 - 3/5 = 10/15 - 9/15
wait so you can change the order around?
well - I was giving you the order by telling you 2/3 - 3/5
first you want to find the common denominator - which you found
and then once you've converted each fraction to the same common denominator, you want to subtract across
so if 2/3 = 10/15 and 3/5 = 9/15 then 2/3 - 3/5 = 10/15 - 9/15
so would it be 1/15?
mhmmm exactly =)
so what's 2/3 + 3/5?
ok so what's 3/5 - 2/3?
yep you were right
negatives are possible in fractions?
mhmmm, are negatives possible in decimals?
a fraction is just a different way of representing the same number
got it.. :)
duh! i forget they convert to decimals
ok now letting you go yet =) 1. 2/4 + 4/8
same time tomorrow for fractions with whole numbers?
oh ok i can do one more..
yay you can do it =)
so again - you want the same bottom number for both fractions
wait ... is that a whole number that you already aded is that problem #1 lol...
well, I'm asking you plainly, and you were on the right track - what's 2/4 + 4/8?
whatever form you want
4/8 + 4/8 =1
wooo hooo!!! :)
you got his =)
i love it that you are patient!!
it's no problem, I had many patient teachers
with me.. :)
thanks so much.. gotta go to bed now.. same time tomorrow?? :)
sure I'll be around! good work =) I'm happy you fought through it. you'll get it. the first understanding is always the toughest