the n of a fraction is 4 less than the d. if 1 is added to both its n and d , it becomes 1/2.find the fraction
Answers
Complete question :-
The numerator of a fraction is 4 less than the denominator. If 1 is added to both its numerator and denominator , it becomes 1/2. Find the fraction.
Solution :-
Let the denominator of the fraction be x
Numerator of the fraction = 4 less than the denominator = ( x - 4 )
Given :-
If 1 is added to both its numerator and denominator it becomes 1/2
⇒ { (x - 4) + 1 } / (x + 1) = 1/2
⇒ ( x - 4 + 1 ) / (x + 1) = 1/2
⇒ ( x - 3 ) / (x + 1) = 1/2
By cross multiplication
⇒ 2(x - 3) = 1(x + 1)
⇒ 2x - 6 = x + 1
⇒ 2x - x = 1 + 6
⇒ x = 7
Denominator = x = 7
Numerator = x - 4 = 7 - 4 = 3
Fraction = Numerator / Denominator = (x - 4)/x = 3/7
Hence, 3/7 is the required fraction.
Answer:
3/7
Step-by-step explanation:
Let the numerator be n
And the denominator be d.
So,
it is given that the numerator is 4 less than the denominator. And as we know we have to balance the equation to get the perfect answer.
Than n + 4 = d ( since numerator is 4 less than the denominator)
it is also given that if 1 is added to both numerator and denominator, the fraction becomes 1/2.
According to question :
n + 1 / d + 1 = ½
[ substituting the value of d here ]
n + 1 / (n + 4)+ 1 = ½
n + 1 / n + 5 = ½
2n + 5 = n + 5
n = 3
We got that numerator is 3 by above solution. So the denominator is 3 + 4 = 7. Fraction is 3/7.