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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