Monday, April 5, 2010

Fraction P6 2009 SA1 P2 RGS Q11

11. Jane was thinking of a fraction. The sum of its numerator and denominator was 34. After I added 98 to its denominator, the fraction became 1/11. What was the fraction that Jane was thinking of? [3]

 
N []          )
D [    ]      ) 34

N []         
D [][][][][][][][][][][]
   [    ][      98        ]
11 u - 98

12 u -- > 34 + 98 = 132
1 u -- > 132 ÷ 12 = 11

11 u -- > 11 x 11 = 121

121 – 98 = 23

11/23


The fraction that Jane was thinking of is 11/23.


Alternative method

N + D -- > 34

N/(D + 98) -- > 1/11
11 N -- > D + 98
11 N – D -- > 98

12 N -- > 34 + 98 = 132
1 N -- > 132 ÷ 12 = 11

D -- > 34 – 11 = 23

N/D -- > 11/23

The fraction that Jane was thinking of is 11/23.

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