6AM Quiz (2011, July 9): It's not that complicated...

There is more than one way to evaluate this fraction. What are they?

Describe 2 methods that you could approach this question.

15 comments:

  1. 1. let 6 be a and 5 be b.
    So, a*b + 2a*2b + 3a*3b = ab(1+2+3)
    = ab(6)
    = 6ab
    Also the denominator of the fraction would be the same result.
    Thus, after substituting the algebraic into numbers...
    180/36= 5

    2. The fraction can also be 6x5+2(6x5)+3(6x5)
    2x3+2(2x3)+3(2x3)
    The result would still be 6x5/2x3 as the adding would add to the (2x3) multiplied. So 30/6 = 5.

    Owen here ._.

    ReplyDelete
  2. 1. 6x5+12x10+18x15
    =6x5+2x6x5x2+3x6x5x3
    =(6x5)(1+2x2+3x3)

    2x3+4x6+6x9
    =2x3+2x2x3x2+3x2x3x3
    =(2x3)(1+2x2+3x3)

    the fraction = (6x5)/(2x3)
    = 5

    2. 6x5+12x10+18x15
    =2x3x5+2x2x3x2x5+2x3x3x3x5

    2x3+4x6+6x9
    =2x3+2x2x3x2+2x3x3x3

    the fiction = (2x3+2x2x3x2+2x3x3x3)x5/(2x3+2x2x3x2+2x3x3x3)
    = 5

    Nina Ding

    ReplyDelete
  3. 1.
    6x5+12x10+18x15=30+120+270=420
    2x3+4x6+6x9=6+24+54=84
    420/84=5

    2.
    6x5+12x10+18x15=6x5+2(6x5)+3(6x5)=420
    2x3+4x6+6x9=2x3+2(2x3)+3(2x3)=84
    420/84=5

    Ryan

    ReplyDelete
  4. 1. We can factorise them first, so
    6*5+12*10+18*15/2*3+4*6+6*9 becomes
    2*3*5+2*2*2*3*5+2*3*3*3*5/2*3+2*2*2*3+2*3*3*3
    =420/84
    =5

    2. We can just multiply them straight away and add the sums together.
    6*5+12*10+18*15/2*3+4*6+6*9
    =420/84
    =5

    ReplyDelete
  5. (1)
    6*5+12*10+18*15=30+120+270
    =420
    2*3+4*6+6*9=6+24+54
    =84
    420/84=5

    (2)
    6*5+2(6*5)+3(6*5)=6(6*5)
    =180
    2*3+2(2*3)+3(2*3)=6(2*3)
    =36
    180/36=5

    ReplyDelete
  6. 1) 6*5+12*10+18*15 ÷ 2*3+4*6+6*9 =
    30+120+270 ÷ 6+24+54 = 420 ÷ 84
    = 5

    2) 6(5+2*10+3*15) ÷ 3(2+4*2+6*3) = 420 ÷ 84
    = 5

    ReplyDelete
  7. 1)
    6x5+12x10+18x15 / 2x3+4x6+6x9
    = 30+120+270 / 6+24+54
    = 420 / 84
    = 5

    2)
    6x5+12x10+18x15 / 2x3+4x6+6x9
    = (6x5)(1+4+9) / (2x3)(1+4+9)
    =420 / 84
    =5

    ReplyDelete
  8. the first method is of course to just punch everything into the calculator and you'll get ur answer.

    But the second method is more interesting ;D
    Let the equation '6*5' as a whole be called x.
    You will realise that 6*5+12*10+18*15 can also be represented as 6*5+6*2*5*2+6*3*5*3 which can then be factorized into 6*5+4(6*5)+9(6*5) which after substitution is x+4x+9x.
    x+4x+9x=14x
    14*6*5=420

    Now we know the numerator, we can find the denominator using the same method.
    2*3+4*6+6*9
    = 2*3+4(2*3)+9(2*3)
    =14(2*3)
    =84

    420/84=5

    Anyway isn't this similar to the first question in the Maths TDP Selection Test? LOL.

    -Lovy

    ReplyDelete
  9. The first method is to use a calculator ;P, punch in the numbers and you get your answer.

    The second method is to add all of the numerator and denominator and then simplify.

    ReplyDelete
  10. the first method: get a calculator/paper and pen and work it out.
    the second method: factorise the fraction.

    ReplyDelete
  11. METHOD ONE:

    6x5 + 12x10 + 18x15
    _________________
    2x3 + 4x6 + 6x9

    equals:
    30 + 120 + 270
    _____________
    6 + 24 + 54

    equals:
    420
    ____
    84

    equals:
    5

    METHOD TWO:
    6x5 + 12x10 + 18x15
    ________________
    2x3 + 4x6 + 6x9

    equals:
    2x3x5 + 2x3x2x2x5 + 3x3x2x5x5x5
    ____________________________
    2x3 + 2x2x3x2 + 3x2x3x3

    equals:
    5

    ReplyDelete
  12. Method One:
    6 x 5 + 12 x 10 + 18 x 15
    __________________________
    2 x 3 + 4x 6 + 6 x 9

    = 30 + 120 + 270
    _________________
    6 + 24 + 54

    = 420
    __________
    84

    = 5

    Method 2
    6x5 + 12x10 + 18x15
    ________________
    2x3 + 4x6 + 6x9

    =
    2x3x5 + 2x3x2x2x5 + 3x3x2x5x5x5
    ____________________________
    2x3 + 2x2x3x2 + 3x2x3x3
    =
    5

    ReplyDelete
  13. 1. Method

    We can work out the multiplication first .
    6*5+12*10+18*15
    _________________
    2*3+4*6+6*9

    = 30 + 120+270
    _______________
    6+24+54

    = 420
    ____ Add the sum of the numerator and the denominator .

    84

    = 5 The answer will be 5 .

    2. Method --- Prime Factorisation

    Factorise the numbers after multiplying

    30+120+270
    ______________ Prime factorise the numbers
    6+24+54

    = 2*3*5 + 2*2*2*3*5 + 2*3*3*5*5*5
    __________________________________
    2*3+2*2*2*3 + 2*3*3*3*3

    = 5

    ReplyDelete
  14. 1.
    6=2*3
    5=2½*2
    12=2*6
    10=2½*4
    18=2*9
    15=2½*6
    2*2½ = 5

    2.
    6*5 + 12*10 + 18*15
    -------------------
    2*3 + 4*6 + 6*9

    =

    30 + 120 + 270
    --------------
    6 + 24 + 54

    =

    420
    ----
    84

    = 5

    ReplyDelete
  15. We have discussed the 'solution' in class, that involves the application of factorisation to solve the problem :)

    Some of you are able to see the patterns and able to pull out the 'common factors' to be further manipulated. Well done.

    The rest... more opportunities await for you to sharpen and hone your skills :)

    ReplyDelete