When we add 1 to the numerator of a fraction and simplify it we get 2/3.when add 1 to the denominator and simplify it we get 1/2.which is the fraction?
Answers
Step-by-step explanation:
let the the fraction be x/y.
Adding 1 to numerator gives 2/3
(x+1) /y = 2/3
3(x+1) = 2y
3x + 3 = 2y
Adding 1 to denominator gives 1/2
x/(y+1) = 1/2
2x = y + 1
2x - 1 = y
substituting y = 2x - 1 in above expression
3x + 3 = 2y
3x + 3 = 2(2x - 1)
3x + 3 = 4x -2
3x + 5 = 4x
5 = 4x - 3x
5 = x
therefore y = 2x - 1 = 10 - 1 = 9 (as x = 5 from above)
Fraction is x/y = 5/9
Answer :-
Let us assume that, the fraction is N/D .
so,
case 1) :-
→ N+1/D = 2/3
cross - multiply,
→ 3N + 3 = 2D
→ 3N - 2D = (-3) --------- Eqn.(1)
case 2) :-
→ N / D + 1 = 1/2
→ 2N = D + 1
→ 2N - D = 1 ------------ Eqn.(2)
multiply Eqn.(2) by 2 and subtracting from Eqn.(1)
→ (3N - 2D) - 2(2N - D) = (-3) - 2*1
→ 3N - 4N - 2D + 2D = -3 - 2
→ - N = - 5
→ N = 5
then, putting value of N in Eqn.(2)
→ 2 * 5 - D = 1
→ 10 - 1 = D
→ D = 9
therefore,
→ Required fraction = N/D = (5/9) (Ans.)
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