If 1 is added to the numerator the fraction become 1/2 and 1 is added to the denominator the fraction becomes 1/3 find the number
Answers
Let the numerator be 'x' and the denominator be 'y'
Fraction = x/y
(x+1)/y = 1/5 [According to question]
5x+5 = y [Cross Multiplication]
5x-y = -5 ......................... (1)
x/(y-1) = 1/7 [According to question]
y-1 = 7x [Cross Multiplication]
7x-y = -1 ........................ (2)
[Elimination Method]
5x - y = -5
(-)7x(+)y = (+)1 [Symbols of equation change]
---------------------
-2x = -4
x = -4/-2 = 2
Since,
5x-y = -5
y = 5x+5 = 15
Therefore,
Fraction = 2/15
Answer: 3/8
Step-by-step explanation:
Let the fraction be x/y
Given,
(x + 1) / y = 1/2
=> 2x + 2 = y ------(i)
Also,
x / (y + 1) = 1/3
=> 3x = y + 1
=> 3x - 1 = y ------(ii)
Subtracting,
(i)-(ii)
=> 2x + 2 = y
-(3x - 1) = -y
=> -x + 3 = 0
=> -x = -3
=> x = 3
Substituting the value of x in (i),
2 × 3 + 2 = y
y = 8
Therefore, the fraction
= x/y
= 3/8
Hope it helped :)