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Faman39

  • one year ago

I have a question, how do you reduce large fraction fast? If you don't remember more multiplication.

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  1. welshfella
    • one year ago
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    find their prime factors

  2. Faman39
    • one year ago
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    for example 456/678

  3. welshfella
    • one year ago
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    456 = 2 * 2 * 2* 3 * 19 678 = 2 * 3 * 113 cancel out the duplicates in this case they are 2 and 3 so we have 2* 2* 19 / 113 = 76/113

  4. welshfella
    • one year ago
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    that took me a while - then I'm an old guy! lol

  5. Faman39
    • one year ago
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    Do we usually need to reduce all large fraction with 2 or 3 ? yeah, I was thinking that how we can reduce large fraction like that faster if we don't remember longest or bigger multiplications

  6. welshfella
    • one year ago
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    I don't think there's a faster way of doing this for large numbers All the division you do are pretty simple. You can use a calculator of course.

  7. mathmate
    • one year ago
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    @Faman39 It depends on whether you can divide mentally by one-digit numbers.

  8. Faman39
    • one year ago
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    Actually, I need to take tabe test within few month. They dont allow us to use calculator and they give really short time to solve those type of problem.

  9. welshfella
    • one year ago
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    |dw:1443102044415:dw|

  10. welshfella
    • one year ago
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    - thats how i do it by hand

  11. mathmate
    • one year ago
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    Then practise dividing by single digit numbers. For the example, try 2 456/678=228/339 then try 3 228/339=76/113 and that's the end of it. Also, learn dvisibilities so you can spot easy factors, like 2,3,5,11. Example of a difficult one: 529/253 If you know divisibilities, you know 253=23*11 (note 2+3=5, therefore divisible by 23 and 11) Then try divide 529 by 23, or 529=23^2 so 529/253=23/11 Also, memorizing the squares of numbers from 1-20 (or even 30) helps you factorize the difficult ones (like 529).

  12. Faman39
    • one year ago
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    Thank you so much for helping :)

  13. welshfella
    • one year ago
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    Practicing as much as possible is I believe, the key here.

  14. Faman39
    • one year ago
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    okay. Thanks so much @welshfella @mathmate

  15. welshfella
    • one year ago
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    one tip If you have a large odd number , to find if its divisible by 3, add up all the digits until you get a single number - if you get 3,6 or 9 then its divisible by 3.

  16. welshfella
    • one year ago
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    yw

  17. mathmate
    • one year ago
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    you're welcome! ;)

  18. Faman39
    • one year ago
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    @DanJS @ganeshie8, Do you guys have any ideas for my this post?

  19. DanJS
    • one year ago
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    reducing fractions, i just use a calculator, but nah just keep taking common factors from top and bottom

  20. DanJS
    • one year ago
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    i use a calculator to do addition, :-)

  21. DanJS
    • one year ago
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    even numbers, keep taking out 2's till you cant anymore

  22. ganeshie8
    • one year ago
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    try reducing \(\dfrac{1963}{2567}\)

  23. ganeshie8
    • one year ago
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    actually i have just figured out a nice method do you know how to find the gcd of two numbers using euclid gcd algorithm ?

  24. phi
    • one year ago
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    Here is info you should learn 1) divisibility rules https://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_rules_for_numbers_1.E2.80.9320 (at least the easy ones up to 10) 2) prime numbers https://en.wikipedia.org/wiki/List_of_prime_numbers#The_first_500_prime_numbers It is good to learn the primes up to 100. The more you remember of these, the easier to simplify big fractions

  25. phi
    • one year ago
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    In general, people are not fast at reducing fractions, and with calculators and computer so common, there probably isn't any need to be.

  26. ganeshie8
    • one year ago
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    Let \(d=\gcd(a,b)\). Then it is easy to find the integers satisfying \(a=a'd\) and \(b=b'd\). \[\dfrac{a}{b} = \dfrac{a'd}{b'd} = \dfrac{a'}{b'}\] It cannot reduce further since \(\gcd\) is the max factor that is common.

  27. Faman39
    • one year ago
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    Thank you so much @phi @ganeshie8 @DanJS for coming here and helping me. I missed you all, wonderful openstudy moderators and friends.

  28. ganeshie8
    • one year ago
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    np look up euclid gcd algorithm incase if you haven't before, pretty sure you will find it interesting :)

  29. Faman39
    • one year ago
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    gcd, okay. Thing is, I can't use calculator on tabe test for solving large fraction like this. So I was confused and don't know what to do. And they give really short time to solve those problem

  30. ganeshie8
    • one year ago
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    as the name says, it is an algorithm from "euclid" days: 300BC he had been able to invent that simple yet powerful algorithm probably because there were no calculators at that time

  31. Faman39
    • one year ago
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    okay, I will try it. Thanks so much for amazing tricks! :)

  32. Faman39
    • one year ago
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    Can you show me one more how do you solve large fraction with euclid? Cuz I am dumb enough :D

  33. ganeshie8
    • one year ago
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    you'r not dumb do you have teamviewer ?

  34. Faman39
    • one year ago
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    No

  35. ganeshie8
    • one year ago
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    so do you see how gcd is related to our problem ?

  36. Faman39
    • one year ago
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    yes.

  37. ganeshie8
    • one year ago
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    explain quick so that i know that you know :)

  38. DanJS
    • one year ago
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    is there a way to show a ridiculous ratio is in reduced form. one that would take time longer than the universe to calculate by hand or machine?

  39. Faman39
    • one year ago
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    You set it up large fraction as cross multiply breaking in order reduce them easily

  40. DanJS
    • one year ago
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    are there infinite primes?

  41. ganeshie8
    • one year ago
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    lol yes and yes @DanJS

  42. Faman39
    • one year ago
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    I know, Im wrong @ganeshie8

  43. ganeshie8
    • one year ago
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    You're not wrong, I did not phrase the question properly. If you understand the question, you will answer it easily. Let me rephrase the question..

  44. DanJS
    • one year ago
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    I think there is a numberphile video on that actually on the youtube

  45. ganeshie8
    • one year ago
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    maybe lets see an example

  46. ganeshie8
    • one year ago
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    \(\dfrac{15}{6}\) is that in reduced form ?

  47. Faman39
    • one year ago
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    5/2

  48. ganeshie8
    • one year ago
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    how did u get 5/2 ?

  49. ganeshie8
    • one year ago
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    you have cancelled 3 whats special about 3 ?

  50. ganeshie8
    • one year ago
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    gcd(15, 6) = ?

  51. Faman39
    • one year ago
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    okay common factor is 3 for 15 and 6

  52. ganeshie8
    • one year ago
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    3 is not just a common factor it is the GREATEST common factor i want you see that first

  53. mathmate
    • one year ago
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    Try 437/851 to see the power of Euclid!

  54. Faman39
    • one year ago
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    well, this is large one and I can't figure out what would be common factor of large number like this cuz I often forgot large multiplication

  55. ganeshie8
    • one year ago
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    Exactly! that is the kind of problem which makes you love euclid dude.

  56. ganeshie8
    • one year ago
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    so you do see that if you figure out the "greatest common factor" of 437 and 851 "somehow", then you can reduce the fraction easily

  57. Faman39
    • one year ago
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    5?

  58. ganeshie8
    • one year ago
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    what 5

  59. Faman39
    • one year ago
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    common factor. I am guessing but not sure

  60. ganeshie8
    • one year ago
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    Look at the numbers : 437 and 851 Is any one of them "appear" like divisible by 5 ?

  61. ganeshie8
    • one year ago
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    both the numbers must be divisible by "common factor" that is the definition of "common factor"

  62. Faman39
    • one year ago
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    I think, two?

  63. Faman39
    • one year ago
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    that's also wrong

  64. ganeshie8
    • one year ago
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    Are you saying 437 and 851 are divisible by 2 ?

  65. ganeshie8
    • one year ago
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    doesn't matter if it is right/wrong... i appreciate that you're asking nice questions :)

  66. Faman39
    • one year ago
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    okay. But I still don't get, how do I reduce large fraction quick if I can't figure out common factor or use euclid

  67. Faman39
    • one year ago
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    okay. But I still don't get, how do I reduce large fraction quick if I can't figure out common factor or use euclid?

  68. ganeshie8
    • one year ago
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    first you need to practice few simple things

  69. Faman39
    • one year ago
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    okay

  70. ganeshie8
    • one year ago
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    what do you know about even and odd ?

  71. Faman39
    • one year ago
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    okay.

  72. ganeshie8
    • one year ago
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    how do you say an integer is even or odd ?

  73. ganeshie8
    • one year ago
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    Is 6 even/odd ?

  74. Faman39
    • one year ago
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    even

  75. ganeshie8
    • one year ago
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    why

  76. Faman39
    • one year ago
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    I don't know why, but I know it's even

  77. ganeshie8
    • one year ago
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    good, is 31 even ?

  78. Faman39
    • one year ago
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    odd

  79. ganeshie8
    • one year ago
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    how about 437 ?

  80. Faman39
    • one year ago
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    odd?

  81. ganeshie8
    • one year ago
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    Yes! here is the trick : An integer is even if it is divisible by 2.

  82. ganeshie8
    • one year ago
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    6 is even because it is divisible by 2 : 6/2 = 3 leaves no remainder.

  83. ganeshie8
    • one year ago
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    31 is not even because it is not divisible by 2 : 31/2 = 15, R=1 remainder is not 0, so not divisible by 2.

  84. ganeshie8
    • one year ago
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    so when somebody asks you the definition of an "even" number, you can say this : A number is even if it is divisible by 2.

  85. Faman39
    • one year ago
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    okay. Thanks so much for explaining me thoroughly :)

  86. ganeshie8
    • one year ago
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    437 and 851 so do you see why "2" cannot be a common factor of above numbers ?

  87. Faman39
    • one year ago
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    cuz they are odd number?

  88. ganeshie8
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    Yes, neither of them is divisible by 2; they are odd. So 2 is not a factor of any of them.

  89. ganeshie8
    • one year ago
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    do you know how to tell if a number is divisible by 5 just by looking at the number ?

  90. Faman39
    • one year ago
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    no

  91. ganeshie8
    • one year ago
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    Is 10 divisible by 5 ?

  92. Faman39
    • one year ago
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    yes

  93. ganeshie8
    • one year ago
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    why

  94. Faman39
    • one year ago
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    cuz 5x2 is 10, so yes

  95. ganeshie8
    • one year ago
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    good, Is 13 divisible by 5 ?

  96. Faman39
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    no

  97. ganeshie8
    • one year ago
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    why

  98. Faman39
    • one year ago
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    13 is not divisible with any number

  99. ganeshie8
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    right, but why is it not divisible by 5

  100. ganeshie8
    • one year ago
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    just divide and see

  101. ganeshie8
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    13/5 = 5*2, R=3 remainder is not 0, so we say that 13 is not divisible by 5

  102. ganeshie8
    • one year ago
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    to say that a 13 is divisible by 5, the remainder when 13 is divided by 5 must be 0. but here the remainder is 3, which is not 0. so 13 is not divisible by 5.

  103. Faman39
    • one year ago
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    got it now

  104. ganeshie8
    • one year ago
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    lets do couple more quick examples

  105. ganeshie8
    • one year ago
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    Is 18 divisible by 5 ?

  106. Faman39
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    no, cuz it will also leave remainder of 3

  107. ganeshie8
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    Good! Is 22 divisible by 5 ?

  108. Faman39
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    No, it will also give us remainder of 2 not 0.

  109. ganeshie8
    • one year ago
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    Exactly! Now, can you write down first few positive integers that are divisible by 5 ?

  110. Faman39
    • one year ago
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    11, 2

  111. ganeshie8
    • one year ago
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    how

  112. Faman39
    • one year ago
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    11x2 = 22 and 2x11 = 22 as well

  113. ganeshie8
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    Ahh ok. My question was different question. I was asking for the first few integers that are divisible by 5.

  114. Faman39
    • one year ago
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    20, 10, 25, 30, 35, 40, 45

  115. ganeshie8
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    good, see anything special in them ?

  116. Faman39
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    they are increasing my 5

  117. Faman39
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    they are increasing by 5

  118. ganeshie8
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    thats true, more importantly, notice that the units digit in each of those numbers is either 0 or 5

  119. ganeshie8
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    so can we say this : if the units digit is 0 or 5, then the number is divisible by 5. ?

  120. Faman39
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    hmm, got it :) thanks

  121. ganeshie8
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    so, Is 3434345 divisible by 5 ?

  122. Faman39
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    well, I think so but not sure about it, cuz it has two 34 and one 45

  123. ganeshie8
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    It doesn't matter. The units digit is 5, so it is divisible by 5.

  124. Faman39
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    okay. so how do I divide with 5 this such long number?

  125. ganeshie8
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    we don't need to. if the units digit is 5 or 0, then the number is divisible by 5.

  126. Faman39
    • one year ago
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    okay, I understood what you're saying. But if I need to reduce the largest like that digit, in that I often get blank, because I can't find common factor and how to reduce to them. Because I often forget bigger multiplication

  127. ganeshie8
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    one thing at a time

  128. Faman39
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    okay.

  129. ganeshie8
    • one year ago
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    by now, you know how to tell if a number is divisible by 5, yes ?

  130. Faman39
    • one year ago
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    yes

  131. ganeshie8
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    Is 898985 divisible by 5 ?

  132. Faman39
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    yes, it is divisible by 5

  133. ganeshie8
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    Yes, notice that, we don't need to divide the number and look at remainder to tell if a number is divisible by 5. That is really powerful.

  134. Faman39
    • one year ago
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    ok

  135. ganeshie8
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    Is 894852 divisible by 5 ?

  136. Faman39
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    It is not divisible by 5

  137. ganeshie8
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    good, I see you got it!

  138. ganeshie8
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    Now throw them away, we don't really need all those divisibility rules because we're going to use euclid algorithm to find the gcd directly.

  139. Faman39
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    okay

  140. ganeshie8
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    Here it is https://www.youtube.com/watch?v=AJn843kplDw it is just 2 minutes long, but it explains very nicely... let me know if something doens't make sense..

  141. Faman39
    • one year ago
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    okay, it makes sense in video but how do I apply it in fraction?

  142. ganeshie8
    • one year ago
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    suppose we want to reduce \(\dfrac{12}{30}\) step1) find \(\gcd(12, 30)\)

  143. Faman39
    • one year ago
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    so, we just need to divide denominator with numerator

  144. Faman39
    • one year ago
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    is that correct?

  145. ganeshie8
    • one year ago
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    yes, that video explains it better

  146. Faman39
    • one year ago
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    I am sorry, I must be made you really tired. Extremely apologize you had to stuck here quite long for me. Thanks soooooo much for taking time for explaining everything thoroughly. You really helped me to understand everything very clearly.

  147. Faman39
    • one year ago
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    You made everything so easy to understand

  148. ganeshie8
    • one year ago
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    hey, no im not tired, i want you master euclid algorithm and use it to reduce fractions but just so you know... when i was first learning, it took me more than a week to understand euclid algorithm

  149. Faman39
    • one year ago
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    But, really you did a lot to explain, which really helped. It mean a lot to me that you stayed with me quite long until I don't understand everything well. Thanks so much! I really appreciate what you did for me today. I was quite struggling with this kind of problem

  150. Faman39
    • one year ago
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    So thank you sooooooooooooooooooooooooo much for help!

  151. Faman39
    • one year ago
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    I can't believe you made everything so clear and easy for me, now I feel quite confident about doing the large fractions

  152. ganeshie8
    • one year ago
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    np good to see that that you took time to find efficient methods in reducign fractions, that's exactly the kind of attitude is necessary to get good at math. keep it up :)

  153. ganeshie8
    • one year ago
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    there is always more than one way to do a particular thing in math but often there is exactly one best way to do a thing.. if you spend time, you will find it...

  154. Faman39
    • one year ago
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    Thanks for encouragement :) You're really genius math magician and amazing instructor :) I had really great time learning from you. Truly really enjoyed.

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