the denominator of a fraction is 1 less than 4 times a numerator.if 1 is added to both the numerator and the denominator the fraction becomes 3/8.find the fraction
If the fraction is n/d, we are told that
d = 4n-1
Now we are told that
(n+1)/(d+1) = 3/8
(n+1)/(4n-1+1) = 3/8
(n+1)/(4n) = 3/8
8(n+1) = 3(4n)
8n+8 = 12n
8 = 4n
n = 2
The original fraction was 2/7
adding 1 top and bottom gives 3/8
I think its 1/4 + 3/8 Im Not Sure
To solve this problem, let's start by defining the unknowns. Let's assume the numerator of the fraction is represented by 'N', and the denominator is represented by 'D'.
According to the given information, the denominator is 1 less than 4 times the numerator, which can be expressed as:
D = 4N - 1
The problem also states that if 1 is added to both the numerator and the denominator, the resulting fraction is 3/8. We can express this as:
(N + 1) / (D + 1) = 3/8
Now, let's substitute the value of D from the first equation into the second equation:
(N + 1) / ((4N - 1) + 1) = 3/8
(N + 1) / (4N) = 3/8
To eliminate the fractions, we can cross-multiply:
8(N + 1) = 3(4N)
8N + 8 = 12N
Next, let's gather the variable terms on one side and the constant terms on the other:
8 - 12N = 0
-4N = -8
N = 2
Now that we have found the value of N, we can substitute it into either of the original equations to find the value of D. Let's use the first equation:
D = 4N - 1
D = 4(2) - 1
D = 8 - 1
D = 7
Therefore, the fraction is N/D = 2/7.