Answer:
the numerator of the fraction x and the denominator y.
when the denominator is increased by 1, the fraction becomes 1/2 = (x / (y + 1)) = 1/2
when the numerator and denominator are increased by 4, the fraction becomes 2/3:
This means that ((x + 4) / (y + 4)) = 2/3.
we have 2 equations: (x / (y + 1)) = 1/2 and ((x + 4) / (y + 4)) = 2/3
1st equation: we multiply the two sides by (y + 1) to eliminate the denominator:
x = (1/2) * (y + 1)
x = (y + 1)/2
2nd equation: we multiply the two sides by (y + 4) to eliminate the denominator:
x + 4 = (2/3) * (y + 4)
x + 4 = (2y + 8)/3
we solve to find the values of x and y.
we substitute x in the first equation:
x = (y + 1)/2
we replace x by (y + 1)/2 in the second equation:
(y + 1)/2 + 4 = (2y + 8)/3
we put in the common denominator 6:(
(3y+3+24)/6=
(4y+16)/6
we simplify
3y+27=4y+16
we solve this equation
3y-4y=16-27
-y = -11
y=11
denominator = 11
we calculate x:
x = (y + 1)/2
x=(11+1)/2 = 12/2=6
the numerator =6
the fraction we are looking for: 6/11
we check:
Find the fraction which becomes 1/2 when the denominator is increased by 1 : 6/(11+1)= 6/12 =1/2
Find the fraction which becomes 2/3 lorsque le numérateur et le dénominateur sont augmentés de 4. : (6+4)/(11+4)= 10/15 = 2/3
Explanation: