anonymous
  • anonymous
How do you solve? 3 1/3 - 2 2/5=
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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sandra
  • sandra
hmmm, well, first you have to convert into some common denominator
sandra
  • sandra
so first, let's convert the mixed numbers into straight fractions
sandra
  • sandra
3 1/3 = 9/3 + 1/3 = 10/3

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sandra
  • sandra
2 2/5 = 10/5 + 2/5 = 12/5
sandra
  • sandra
so now we need a common denominator for 3 and 5
sandra
  • sandra
15 is one
sandra
  • sandra
so 10/3 - 12/5 = 10*5/3*5 - 12*3/5*3 = 50/15 - 36/15 = 14/15
anonymous
  • anonymous
wait im still at 12/5 that still needs to be simplefied correct?
sandra
  • sandra
well, 12/5 can't be simplified, since they have no common divisor (a number that divides evenly into them besides one)
sandra
  • sandra
the point is, you can multiply anything by 1 and get an equivalent number
sandra
  • sandra
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
sandra
  • sandra
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)
anonymous
  • anonymous
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?
sandra
  • sandra
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
anonymous
  • anonymous
wich you said was 15
sandra
  • sandra
yes you're right, but 10/3
sandra
  • sandra
so 10/3, and 12/5
sandra
  • sandra
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"
sandra
  • sandra
so really you're looking at 3 and 5
sandra
  • sandra
what number do they commonly divide into?
sandra
  • sandra
the answer is 15 - and that's always a sure method to get a common denominator - just multiply them by each other
anonymous
  • anonymous
ok and the next part is what gets me so we find their common denomitator what do we do witht the top numbers?
sandra
  • sandra
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
sandra
  • sandra
so for 3 - I know I multiply it by 5 to get 15
sandra
  • sandra
so I multiple 10/4 x 5/5 (again, multiplying by 1 means I get the same thing, different way of writing it)
sandra
  • sandra
sorry 10/3
sandra
  • sandra
so 10/3 x 5/5 = 10x5/3x5 = 50/15
anonymous
  • anonymous
I get what your saying but im confused... wich doesnt take much :(
sandra
  • sandra
now the second fraction, how do I turn 12/5 into (some number)/15
sandra
  • sandra
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
sandra
  • sandra
so 12/5 = 12/5 * 3/3 (1) = 12*3/5*3 = 36/15
sandra
  • sandra
and once you have everything with the same common denominator, you can subtract across
sandra
  • sandra
so 50/15 - 36/15 = 50-36/15 = 14/15
sandra
  • sandra
but let's practice common denominators
sandra
  • sandra
so let's say 2/3 and 3/6 are your fractions
sandra
  • sandra
what number do both 3 and 6 divide evenly into?
anonymous
  • anonymous
common denominator would be 6? sorry 3
sandra
  • sandra
nope you were right the first time
sandra
  • sandra
6
sandra
  • sandra
since 6/3 = 3, and 6/6 = 1
sandra
  • sandra
so that's good =)
sandra
  • sandra
ok so now you want to think - how can I make the bottom number a six for both of them?
sandra
  • sandra
so 2/3 = ?/6
sandra
  • sandra
and the main thing to learn, is that you can multipel *anything* by 1 and get the same number
sandra
  • sandra
i.e. 1x1 = 1, 2x1=2, 3x1 = 3
sandra
  • sandra
but that works with fractions too
sandra
  • sandra
so for 2/3, if I want to make the bottom number a six, I know I multiply it by 2 -
sandra
  • sandra
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)
sandra
  • sandra
so 2/3 = 2/3 * 2/2 = 4/6
anonymous
  • anonymous
ok..ok
sandra
  • sandra
great =) . so now convert 4/8 to ?/16
sandra
  • sandra
your first thought should be - what do I multiply 8 by to get 16
anonymous
  • anonymous
2
sandra
  • sandra
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
sandra
  • sandra
so 4/8 *2/2 = 4*2/8*2 = 8/16
sandra
  • sandra
and check this out - you could get an infinite number of equivalent fractions by just multiplying by different forms of 1
sandra
  • sandra
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...
sandra
  • sandra
those are all equivalent fractions - i.e. 2/3 = 4/6 = 6/9 = 8/12
sandra
  • sandra
and that's all a common denominator wants you to to
anonymous
  • anonymous
so earlier we just choose 2/2 becuase that was the common denominator?
sandra
  • sandra
well, we chose 2/2 because we knew it would get us an equivalent fraction - the same exact value
sandra
  • sandra
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
sandra
  • sandra
so e.g. 3/5 and 2/3
sandra
  • sandra
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
sandra
  • sandra
15 is my common denominator
anonymous
  • anonymous
your so patient with me...
sandra
  • sandra
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
sandra
  • sandra
so 3/5 = 3/5 *3/3 (3/3 is just "1") = (3*3)/(5*3) = 9/15
sandra
  • sandra
and it's ok =) fractions are HARD until you understand them
sandra
  • sandra
the whole point again is - you can freely convert fractions to different forms as long as you multiply by 1
anonymous
  • anonymous
thanks... A LOT!
anonymous
  • anonymous
:)
sandra
  • sandra
no problem =)
sandra
  • sandra
but let's do a couple more
anonymous
  • anonymous
absolutely!
sandra
  • sandra
so let's say I want you to convert 1/4 into ?/16
sandra
  • sandra
what is 1/4 if you make it ?/16
sandra
  • sandra
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?
anonymous
  • anonymous
1/4 X 4/4?
sandra
  • sandra
exactly!
sandra
  • sandra
which is?
anonymous
  • anonymous
4/16
anonymous
  • anonymous
or 1/4?
sandra
  • sandra
yep =) now put it into your calculator to check
sandra
  • sandra
nope, you were right, 4/16
sandra
  • sandra
well, they are both right lol
sandra
  • sandra
the thing with fractions, is you can also divide the top and the bottom by the same number and get the same thing
sandra
  • sandra
so 4/16 = (4/4)/ (16/4) = 1/4 !
anonymous
  • anonymous
didnt see that at all...i just simplefied
sandra
  • sandra
and you can go the other way too =)
sandra
  • sandra
e.g. you can get all of the equivalent fractions starting at 1/4, by multiplying by different forms of 1
sandra
  • sandra
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...
sandra
  • sandra
and yep, 4/16 is on that list
sandra
  • sandra
ok so, let's do 5/6 = ?/18
anonymous
  • anonymous
5/6 x 3/3 ?
sandra
  • sandra
exactly =)
anonymous
  • anonymous
15/18
anonymous
  • anonymous
horray!!!
sandra
  • sandra
yep!
sandra
  • sandra
and don't be afraid to use your calc to check , especially while you're learning
sandra
  • sandra
if you type in 15/18 and 5/6, I guarantee it's the same decimal
anonymous
  • anonymous
yep sure is
sandra
  • sandra
ok so now is the biggest leap - make 3/5 and 2/3 so that they have the same number on the bottom
anonymous
  • anonymous
so im finding commond denominator for 5 and 3 correct?
sandra
  • sandra
your first thought should be, what number can I make both of the bottom numbers (5 and 3 ) into by multiplying
sandra
  • sandra
yep
anonymous
  • anonymous
15
sandra
  • sandra
exactly
sandra
  • sandra
so 3/5 is ?/15
anonymous
  • anonymous
3/5 x 3/3
sandra
  • sandra
=)
sandra
  • sandra
which is?
anonymous
  • anonymous
9/15
sandra
  • sandra
yep =)
sandra
  • sandra
and the next number, 2/3 = ?/15
anonymous
  • anonymous
then 2/3 x5/5
sandra
  • sandra
mhmmmm, which is?
anonymous
  • anonymous
10/15
sandra
  • sandra
yep =) . so what's 2/3 - 3/5 ?
anonymous
  • anonymous
7/12???
sandra
  • sandra
nope - so you just converted both of those numbers to ?/15
sandra
  • sandra
so if 2/3 = 10/15
anonymous
  • anonymous
9/15- 10/15
sandra
  • sandra
and 3/5 = 9/15
sandra
  • sandra
2/3 - 3/5 = 10/15 - 9/15
sandra
  • sandra
which is?
anonymous
  • anonymous
wait so you can change the order around?
sandra
  • sandra
well - I was giving you the order by telling you 2/3 - 3/5
sandra
  • sandra
first you want to find the common denominator - which you found
sandra
  • sandra
and then once you've converted each fraction to the same common denominator, you want to subtract across
anonymous
  • anonymous
ok
sandra
  • sandra
so if 2/3 = 10/15 and 3/5 = 9/15 then 2/3 - 3/5 = 10/15 - 9/15
anonymous
  • anonymous
so would it be 1/15?
sandra
  • sandra
mhmmm exactly =)
sandra
  • sandra
so what's 2/3 + 3/5?
anonymous
  • anonymous
19/15
sandra
  • sandra
yep =)
sandra
  • sandra
ok so what's 3/5 - 2/3?
anonymous
  • anonymous
-1/15
sandra
  • sandra
yay! =)
anonymous
  • anonymous
really?
sandra
  • sandra
yep you were right
anonymous
  • anonymous
negatives are possible in fractions?
sandra
  • sandra
mhmmm, are negatives possible in decimals?
sandra
  • sandra
a fraction is just a different way of representing the same number
anonymous
  • anonymous
got it.. :)
anonymous
  • anonymous
duh! i forget they convert to decimals
sandra
  • sandra
ok now letting you go yet =) 1. 2/4 + 4/8
anonymous
  • anonymous
same time tomorrow for fractions with whole numbers?
anonymous
  • anonymous
oh ok i can do one more..
sandra
  • sandra
yay you can do it =)
sandra
  • sandra
so again - you want the same bottom number for both fractions
anonymous
  • anonymous
2/4 x2/2
sandra
  • sandra
=)
sandra
  • sandra
mhmmm and...
anonymous
  • anonymous
wait ... is that a whole number that you already aded is that problem #1 lol...
sandra
  • sandra
well, I'm asking you plainly, and you were on the right track - what's 2/4 + 4/8?
sandra
  • sandra
whatever form you want
anonymous
  • anonymous
4/8
anonymous
  • anonymous
1
sandra
  • sandra
=)
sandra
  • sandra
correct
anonymous
  • anonymous
4/8 + 4/8 =1
sandra
  • sandra
exactly =)
anonymous
  • anonymous
wooo hooo!!! :)
sandra
  • sandra
good job!
sandra
  • sandra
you got his =)
sandra
  • sandra
*this
anonymous
  • anonymous
i love it that you are patient!!
sandra
  • sandra
it's no problem, I had many patient teachers
anonymous
  • anonymous
with me.. :)
anonymous
  • anonymous
thanks so much.. gotta go to bed now.. same time tomorrow?? :)
sandra
  • sandra
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
sandra
  • sandra
'night
anonymous
  • anonymous
nite... :)

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