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anonymous

  • 5 years ago

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

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  1. sandra
    • 5 years ago
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    hmmm, well, first you have to convert into some common denominator

  2. sandra
    • 5 years ago
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    so first, let's convert the mixed numbers into straight fractions

  3. sandra
    • 5 years ago
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    3 1/3 = 9/3 + 1/3 = 10/3

  4. sandra
    • 5 years ago
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    2 2/5 = 10/5 + 2/5 = 12/5

  5. sandra
    • 5 years ago
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    so now we need a common denominator for 3 and 5

  6. sandra
    • 5 years ago
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    15 is one

  7. sandra
    • 5 years ago
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    so 10/3 - 12/5 = 10*5/3*5 - 12*3/5*3 = 50/15 - 36/15 = 14/15

  8. anonymous
    • 5 years ago
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    wait im still at 12/5 that still needs to be simplefied correct?

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

  10. sandra
    • 5 years ago
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    the point is, you can multiply anything by 1 and get an equivalent number

  11. sandra
    • 5 years ago
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    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

  12. sandra
    • 5 years ago
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    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)

  13. anonymous
    • 5 years ago
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    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?

  14. sandra
    • 5 years ago
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    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

  15. anonymous
    • 5 years ago
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    wich you said was 15

  16. sandra
    • 5 years ago
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    yes you're right, but 10/3

  17. sandra
    • 5 years ago
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    so 10/3, and 12/5

  18. sandra
    • 5 years ago
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    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"

  19. sandra
    • 5 years ago
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    so really you're looking at 3 and 5

  20. sandra
    • 5 years ago
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    what number do they commonly divide into?

  21. sandra
    • 5 years ago
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    the answer is 15 - and that's always a sure method to get a common denominator - just multiply them by each other

  22. anonymous
    • 5 years ago
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    ok and the next part is what gets me so we find their common denomitator what do we do witht the top numbers?

  23. sandra
    • 5 years ago
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    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

  24. sandra
    • 5 years ago
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    so for 3 - I know I multiply it by 5 to get 15

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

  26. sandra
    • 5 years ago
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    sorry 10/3

  27. sandra
    • 5 years ago
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    so 10/3 x 5/5 = 10x5/3x5 = 50/15

  28. anonymous
    • 5 years ago
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    I get what your saying but im confused... wich doesnt take much :(

  29. sandra
    • 5 years ago
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    now the second fraction, how do I turn 12/5 into (some number)/15

  30. sandra
    • 5 years ago
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    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

  31. sandra
    • 5 years ago
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    so 12/5 = 12/5 * 3/3 (1) = 12*3/5*3 = 36/15

  32. sandra
    • 5 years ago
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    and once you have everything with the same common denominator, you can subtract across

  33. sandra
    • 5 years ago
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    so 50/15 - 36/15 = 50-36/15 = 14/15

  34. sandra
    • 5 years ago
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    but let's practice common denominators

  35. sandra
    • 5 years ago
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    so let's say 2/3 and 3/6 are your fractions

  36. sandra
    • 5 years ago
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    what number do both 3 and 6 divide evenly into?

  37. anonymous
    • 5 years ago
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    common denominator would be 6? sorry 3

  38. sandra
    • 5 years ago
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    nope you were right the first time

  39. sandra
    • 5 years ago
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    6

  40. sandra
    • 5 years ago
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    since 6/3 = 3, and 6/6 = 1

  41. sandra
    • 5 years ago
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    so that's good =)

  42. sandra
    • 5 years ago
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    ok so now you want to think - how can I make the bottom number a six for both of them?

  43. sandra
    • 5 years ago
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    so 2/3 = ?/6

  44. sandra
    • 5 years ago
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    and the main thing to learn, is that you can multipel *anything* by 1 and get the same number

  45. sandra
    • 5 years ago
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    i.e. 1x1 = 1, 2x1=2, 3x1 = 3

  46. sandra
    • 5 years ago
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    but that works with fractions too

  47. sandra
    • 5 years ago
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    so for 2/3, if I want to make the bottom number a six, I know I multiply it by 2 -

  48. sandra
    • 5 years ago
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    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)

  49. sandra
    • 5 years ago
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    so 2/3 = 2/3 * 2/2 = 4/6

  50. anonymous
    • 5 years ago
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    ok..ok

  51. sandra
    • 5 years ago
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    great =) . so now convert 4/8 to ?/16

  52. sandra
    • 5 years ago
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    your first thought should be - what do I multiply 8 by to get 16

  53. anonymous
    • 5 years ago
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    2

  54. sandra
    • 5 years ago
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    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

  55. sandra
    • 5 years ago
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    so 4/8 *2/2 = 4*2/8*2 = 8/16

  56. sandra
    • 5 years ago
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    and check this out - you could get an infinite number of equivalent fractions by just multiplying by different forms of 1

  57. sandra
    • 5 years ago
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    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...

  58. sandra
    • 5 years ago
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    those are all equivalent fractions - i.e. 2/3 = 4/6 = 6/9 = 8/12

  59. sandra
    • 5 years ago
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    and that's all a common denominator wants you to to

  60. anonymous
    • 5 years ago
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    so earlier we just choose 2/2 becuase that was the common denominator?

  61. sandra
    • 5 years ago
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    well, we chose 2/2 because we knew it would get us an equivalent fraction - the same exact value

  62. sandra
    • 5 years ago
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    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

  63. sandra
    • 5 years ago
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    so e.g. 3/5 and 2/3

  64. sandra
    • 5 years ago
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    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

  65. sandra
    • 5 years ago
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    15 is my common denominator

  66. anonymous
    • 5 years ago
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    your so patient with me...

  67. sandra
    • 5 years ago
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    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

  68. sandra
    • 5 years ago
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    so 3/5 = 3/5 *3/3 (3/3 is just "1") = (3*3)/(5*3) = 9/15

  69. sandra
    • 5 years ago
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    and it's ok =) fractions are HARD until you understand them

  70. sandra
    • 5 years ago
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    the whole point again is - you can freely convert fractions to different forms as long as you multiply by 1

  71. anonymous
    • 5 years ago
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    thanks... A LOT!

  72. anonymous
    • 5 years ago
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    :)

  73. sandra
    • 5 years ago
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    no problem =)

  74. sandra
    • 5 years ago
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    but let's do a couple more

  75. anonymous
    • 5 years ago
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    absolutely!

  76. sandra
    • 5 years ago
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    so let's say I want you to convert 1/4 into ?/16

  77. sandra
    • 5 years ago
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    what is 1/4 if you make it ?/16

  78. sandra
    • 5 years ago
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    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?

  79. anonymous
    • 5 years ago
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    1/4 X 4/4?

  80. sandra
    • 5 years ago
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    exactly!

  81. sandra
    • 5 years ago
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    which is?

  82. anonymous
    • 5 years ago
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    4/16

  83. anonymous
    • 5 years ago
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    or 1/4?

  84. sandra
    • 5 years ago
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    yep =) now put it into your calculator to check

  85. sandra
    • 5 years ago
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    nope, you were right, 4/16

  86. sandra
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    well, they are both right lol

  87. sandra
    • 5 years ago
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    the thing with fractions, is you can also divide the top and the bottom by the same number and get the same thing

  88. sandra
    • 5 years ago
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    so 4/16 = (4/4)/ (16/4) = 1/4 !

  89. anonymous
    • 5 years ago
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    didnt see that at all...i just simplefied

  90. sandra
    • 5 years ago
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    and you can go the other way too =)

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

  92. sandra
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    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...

  93. sandra
    • 5 years ago
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    and yep, 4/16 is on that list

  94. sandra
    • 5 years ago
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    ok so, let's do 5/6 = ?/18

  95. anonymous
    • 5 years ago
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    5/6 x 3/3 ?

  96. sandra
    • 5 years ago
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    exactly =)

  97. anonymous
    • 5 years ago
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    15/18

  98. anonymous
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    horray!!!

  99. sandra
    • 5 years ago
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    yep!

  100. sandra
    • 5 years ago
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    and don't be afraid to use your calc to check , especially while you're learning

  101. sandra
    • 5 years ago
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    if you type in 15/18 and 5/6, I guarantee it's the same decimal

  102. anonymous
    • 5 years ago
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    yep sure is

  103. sandra
    • 5 years ago
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    ok so now is the biggest leap - make 3/5 and 2/3 so that they have the same number on the bottom

  104. anonymous
    • 5 years ago
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    so im finding commond denominator for 5 and 3 correct?

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

  106. sandra
    • 5 years ago
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    yep

  107. anonymous
    • 5 years ago
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    15

  108. sandra
    • 5 years ago
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    exactly

  109. sandra
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    so 3/5 is ?/15

  110. anonymous
    • 5 years ago
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    3/5 x 3/3

  111. sandra
    • 5 years ago
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    =)

  112. sandra
    • 5 years ago
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    which is?

  113. anonymous
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    9/15

  114. sandra
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    yep =)

  115. sandra
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    and the next number, 2/3 = ?/15

  116. anonymous
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    then 2/3 x5/5

  117. sandra
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    mhmmmm, which is?

  118. anonymous
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    10/15

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

  120. anonymous
    • 5 years ago
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    7/12???

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

  122. sandra
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    so if 2/3 = 10/15

  123. anonymous
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    9/15- 10/15

  124. sandra
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    and 3/5 = 9/15

  125. sandra
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    2/3 - 3/5 = 10/15 - 9/15

  126. sandra
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    which is?

  127. anonymous
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    wait so you can change the order around?

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

  129. sandra
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    first you want to find the common denominator - which you found

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

  131. anonymous
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    ok

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

  133. anonymous
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    so would it be 1/15?

  134. sandra
    • 5 years ago
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    mhmmm exactly =)

  135. sandra
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    so what's 2/3 + 3/5?

  136. anonymous
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    19/15

  137. sandra
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    yep =)

  138. sandra
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    ok so what's 3/5 - 2/3?

  139. anonymous
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    -1/15

  140. sandra
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    yay! =)

  141. anonymous
    • 5 years ago
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    really?

  142. sandra
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    yep you were right

  143. anonymous
    • 5 years ago
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    negatives are possible in fractions?

  144. sandra
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    mhmmm, are negatives possible in decimals?

  145. sandra
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    a fraction is just a different way of representing the same number

  146. anonymous
    • 5 years ago
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    got it.. :)

  147. anonymous
    • 5 years ago
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    duh! i forget they convert to decimals

  148. sandra
    • 5 years ago
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    ok now letting you go yet =) 1. 2/4 + 4/8

  149. anonymous
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    same time tomorrow for fractions with whole numbers?

  150. anonymous
    • 5 years ago
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    oh ok i can do one more..

  151. sandra
    • 5 years ago
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    yay you can do it =)

  152. sandra
    • 5 years ago
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    so again - you want the same bottom number for both fractions

  153. anonymous
    • 5 years ago
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    2/4 x2/2

  154. sandra
    • 5 years ago
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    =)

  155. sandra
    • 5 years ago
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    mhmmm and...

  156. anonymous
    • 5 years ago
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    wait ... is that a whole number that you already aded is that problem #1 lol...

  157. sandra
    • 5 years ago
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    well, I'm asking you plainly, and you were on the right track - what's 2/4 + 4/8?

  158. sandra
    • 5 years ago
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    whatever form you want

  159. anonymous
    • 5 years ago
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    4/8

  160. anonymous
    • 5 years ago
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    1

  161. sandra
    • 5 years ago
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    =)

  162. sandra
    • 5 years ago
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    correct

  163. anonymous
    • 5 years ago
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    4/8 + 4/8 =1

  164. sandra
    • 5 years ago
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    exactly =)

  165. anonymous
    • 5 years ago
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    wooo hooo!!! :)

  166. sandra
    • 5 years ago
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    good job!

  167. sandra
    • 5 years ago
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    you got his =)

  168. sandra
    • 5 years ago
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    *this

  169. anonymous
    • 5 years ago
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    i love it that you are patient!!

  170. sandra
    • 5 years ago
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    it's no problem, I had many patient teachers

  171. anonymous
    • 5 years ago
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    with me.. :)

  172. anonymous
    • 5 years ago
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    thanks so much.. gotta go to bed now.. same time tomorrow?? :)

  173. sandra
    • 5 years ago
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    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

  174. sandra
    • 5 years ago
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    'night

  175. anonymous
    • 5 years ago
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    nite... :)

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spraguer (Moderator)
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