How do you solve? 3 1/3 - 2 2/5=

- anonymous

How do you solve? 3 1/3 - 2 2/5=

- chestercat

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- sandra

hmmm, well, first you have to convert into some common denominator

- sandra

so first, let's convert the mixed numbers into straight fractions

- sandra

3 1/3 = 9/3 + 1/3 = 10/3

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## More answers

- sandra

2 2/5 = 10/5 + 2/5 = 12/5

- sandra

so now we need a common denominator for 3 and 5

- sandra

15 is one

- sandra

so 10/3 - 12/5 = 10*5/3*5 - 12*3/5*3 = 50/15 - 36/15 = 14/15

- anonymous

wait im still at 12/5 that still needs to be simplefied correct?

- sandra

well, 12/5 can't be simplified, since they have no common divisor (a number that divides evenly into them besides one)

- sandra

the point is, you can multiply anything by 1 and get an equivalent number

- 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

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

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

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

wich you said was 15

- sandra

yes you're right, but 10/3

- sandra

so 10/3, and 12/5

- 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

so really you're looking at 3 and 5

- sandra

what number do they commonly divide into?

- sandra

the answer is 15 - and that's always a sure method to get a common denominator - just multiply them by each other

- 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

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

so for 3 - I know I multiply it by 5 to get 15

- 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

sorry 10/3

- sandra

so 10/3 x 5/5 = 10x5/3x5 = 50/15

- anonymous

I get what your saying but im confused... wich doesnt take much :(

- sandra

now the second fraction, how do I turn 12/5 into (some number)/15

- 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

so 12/5 = 12/5 * 3/3 (1) = 12*3/5*3 = 36/15

- sandra

and once you have everything with the same common denominator, you can subtract across

- sandra

so 50/15 - 36/15 = 50-36/15 = 14/15

- sandra

but let's practice common denominators

- sandra

so let's say 2/3 and 3/6 are your fractions

- sandra

what number do both 3 and 6 divide evenly into?

- anonymous

common denominator would be 6?
sorry 3

- sandra

nope you were right the first time

- sandra

6

- sandra

since 6/3 = 3, and 6/6 = 1

- sandra

so that's good =)

- sandra

ok so now you want to think - how can I make the bottom number a six for both of them?

- sandra

so 2/3 = ?/6

- sandra

and the main thing to learn, is that you can multipel *anything* by 1 and get the same number

- sandra

i.e. 1x1 = 1, 2x1=2, 3x1 = 3

- sandra

but that works with fractions too

- sandra

so for 2/3, if I want to make the bottom number a six, I know I multiply it by 2 -

- 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

so 2/3 = 2/3 * 2/2 = 4/6

- anonymous

ok..ok

- sandra

great =) . so now convert 4/8 to ?/16

- sandra

your first thought should be - what do I multiply 8 by to get 16

- anonymous

2

- 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

so 4/8 *2/2 = 4*2/8*2 = 8/16

- sandra

and check this out - you could get an infinite number of equivalent fractions by just multiplying by different forms of 1

- 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

those are all equivalent fractions - i.e. 2/3 = 4/6 = 6/9 = 8/12

- sandra

and that's all a common denominator wants you to to

- anonymous

so earlier we just choose 2/2 becuase that was the common denominator?

- sandra

well, we chose 2/2 because we knew it would get us an equivalent fraction - the same exact value

- 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

so e.g. 3/5 and 2/3

- 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

15 is my common denominator

- anonymous

your so patient with me...

- 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

so 3/5 = 3/5 *3/3 (3/3 is just "1") = (3*3)/(5*3) = 9/15

- sandra

and it's ok =) fractions are HARD until you understand them

- sandra

the whole point again is - you can freely convert fractions to different forms as long as you multiply by 1

- anonymous

thanks... A LOT!

- anonymous

:)

- sandra

no problem =)

- sandra

but let's do a couple more

- anonymous

absolutely!

- sandra

so let's say I want you to convert 1/4 into ?/16

- sandra

what is 1/4 if you make it ?/16

- 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

1/4 X 4/4?

- sandra

exactly!

- sandra

which is?

- anonymous

4/16

- anonymous

or 1/4?

- sandra

yep =) now put it into your calculator to check

- sandra

nope, you were right, 4/16

- sandra

well, they are both right lol

- 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

so 4/16 = (4/4)/ (16/4) = 1/4 !

- anonymous

didnt see that at all...i just simplefied

- sandra

and you can go the other way too =)

- sandra

e.g. you can get all of the equivalent fractions starting at 1/4, by multiplying by different forms of 1

- 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

and yep, 4/16 is on that list

- sandra

ok so, let's do 5/6 = ?/18

- anonymous

5/6 x 3/3 ?

- sandra

exactly =)

- anonymous

15/18

- anonymous

horray!!!

- sandra

yep!

- sandra

and don't be afraid to use your calc to check , especially while you're learning

- sandra

if you type in 15/18 and 5/6, I guarantee it's the same decimal

- anonymous

yep sure is

- 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

so im finding commond denominator for 5 and 3 correct?

- sandra

your first thought should be, what number can I make both of the bottom numbers (5 and 3 ) into by multiplying

- sandra

yep

- anonymous

15

- sandra

exactly

- sandra

so 3/5 is ?/15

- anonymous

3/5 x 3/3

- sandra

=)

- sandra

which is?

- anonymous

9/15

- sandra

yep =)

- sandra

and the next number, 2/3 = ?/15

- anonymous

then 2/3 x5/5

- sandra

mhmmmm, which is?

- anonymous

10/15

- sandra

yep =) . so what's 2/3 - 3/5 ?

- anonymous

7/12???

- sandra

nope - so you just converted both of those numbers to ?/15

- sandra

so if 2/3 = 10/15

- anonymous

9/15- 10/15

- sandra

and 3/5 = 9/15

- sandra

2/3 - 3/5 = 10/15 - 9/15

- sandra

which is?

- anonymous

wait so you can change the order around?

- sandra

well - I was giving you the order by telling you 2/3 - 3/5

- sandra

first you want to find the common denominator - which you found

- sandra

and then once you've converted each fraction to the same common denominator, you want to subtract across

- anonymous

ok

- sandra

so if 2/3 = 10/15
and 3/5 = 9/15
then 2/3 - 3/5 = 10/15 - 9/15

- anonymous

so would it be 1/15?

- sandra

mhmmm exactly =)

- sandra

so what's 2/3 + 3/5?

- anonymous

19/15

- sandra

yep =)

- sandra

ok so what's 3/5 - 2/3?

- anonymous

-1/15

- sandra

yay! =)

- anonymous

really?

- sandra

yep you were right

- anonymous

negatives are possible in fractions?

- sandra

mhmmm, are negatives possible in decimals?

- sandra

a fraction is just a different way of representing the same number

- anonymous

got it..
:)

- anonymous

duh! i forget they convert to decimals

- sandra

ok now letting you go yet =)
1. 2/4 + 4/8

- anonymous

same time tomorrow for fractions with whole numbers?

- anonymous

oh ok i can do one more..

- sandra

yay you can do it =)

- sandra

so again - you want the same bottom number for both fractions

- anonymous

2/4 x2/2

- sandra

=)

- sandra

mhmmm and...

- anonymous

wait ...
is that a whole number that you already aded is that problem #1 lol...

- sandra

well, I'm asking you plainly, and you were on the right track - what's 2/4 + 4/8?

- sandra

whatever form you want

- anonymous

4/8

- anonymous

1

- sandra

=)

- sandra

correct

- anonymous

4/8 + 4/8 =1

- sandra

exactly =)

- anonymous

wooo hooo!!! :)

- sandra

good job!

- sandra

you got his =)

- sandra

*this

- anonymous

i love it that you are patient!!

- sandra

it's no problem, I had many patient teachers

- anonymous

with me.. :)

- anonymous

thanks so much.. gotta go to bed now.. same time tomorrow?? :)

- 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

'night

- anonymous

nite... :)

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