### 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.

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 ._.

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

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

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

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

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

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

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

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.

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

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

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

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

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

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 :)