Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

so now we need a common denominator for 3 and 5

Answer 6

15 is one

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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)

Answer 13

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?

Answer 14

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

Answer 15

wich you said was 15

Answer 16

yes you're right, but 10/3

Answer 17

so 10/3, and 12/5

Answer 18

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"

Answer 19

so really you're looking at 3 and 5

Answer 20

what number do they commonly divide into?

Answer 21

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

Answer 22

ok and the next part is what gets me so we find their common denomitator what do we do witht the top numbers?

Answer 23

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

Answer 24

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

Answer 25

so I multiple 10/4 x 5/5 (again, multiplying by 1 means I get the same thing, different way of writing it)

Answer 26

sorry 10/3

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

but let's practice common denominators

Answer 35

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

Answer 36

what number do both 3 and 6 divide evenly into?

Answer 37

common denominator would be 6?
sorry 3

Answer 38

nope you were right the first time

Answer 39

6

Answer 40

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

Answer 41

so that's good =)

Answer 42

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

Answer 43

so 2/3 = ?/6

Answer 44

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

Answer 45

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

Answer 46

but that works with fractions too

Answer 47

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

Answer 48

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)

Answer 49

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

Answer 50

ok..ok

Answer 51

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

Answer 52

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

Answer 53

2

Answer 54

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

Answer 55

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

Answer 56

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

Answer 57

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...

Answer 58

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

Answer 59

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

Answer 60

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

Answer 61

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

Answer 62

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

Answer 63

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

Answer 64

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

Answer 65

15 is my common denominator

Answer 66

your so patient with me...

Answer 67

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

Answer 68

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

Answer 69

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

Answer 70

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

Answer 71

thanks... A LOT!

Answer 72

:)

Answer 73

no problem =)

Answer 74

but let's do a couple more

Answer 75

absolutely!

Answer 76

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

Answer 77

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

Answer 78

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?

Answer 79

1/4 X 4/4?

Answer 80

exactly!

Answer 81

which is?

Answer 82

4/16

Answer 83

or 1/4?

Answer 84

yep =) now put it into your calculator to check

Answer 85

nope, you were right, 4/16

Answer 86

well, they are both right lol

Answer 87

the thing with fractions, is you can also divide the top and the bottom by the same number and get the same thing

Answer 88

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

Answer 89

didnt see that at all...i just simplefied

Answer 90

and you can go the other way too =)

Answer 91

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

Answer 92

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...

Answer 93

and yep, 4/16 is on that list

Answer 94

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

Answer 95

5/6 x 3/3 ?

Answer 96

exactly =)

Answer 97

15/18

Answer 98

horray!!!