SOLUTION: The numerator of a fraction is 7 less than the denominator. If one and one third is added to it, the fraction obtained is 14/9. Find the original fraction.

Click here to see ALL problems on Equations

Question 1043253: The numerator of a fraction is 7 less than the denominator. If one and one third is added to it, the fraction obtained is 14/9. Find the original fraction.
Found 3 solutions by Cromlix, LinnW, MathTherapy:
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website!
Hi there,
The numerator of a fraction is 7 less than the denominator.
Make denominator = x
(x - 7)/x
If one and one third is added to it, the fraction obtained is 14/9.
(x - 7)/x + 4/3 = 14/9
Take lowest common denominator = 27x
[27(x - 7) + 9x(4) = 3x(14)]
[27x - 189 + 36x = 42x]
Collect like terms
27x + 36x - 42x = 189
21x = 189
x = 9
Original fraction =
(x - 7)/x
(9 -7)/9
2/9.
Proof:
2/9 + 4/3 = 14/9
Hope this helps :-)

Answer by LinnW(1048)   (Show Source):
You can put this solution on YOUR website!
Let n = numerator
Let d = denominator
d = n-7
fraction is

add -4/3 to each side

do cross products
9n = 2(n-7)
9n = 2n -14
add -2n to each side
7n = -14
divide each side by 7
n = -2
So the original fraction is

Answer by MathTherapy(10551)   (Show Source):
You can put this solution on YOUR website!

The numerator of a fraction is 7 less than the denominator. If one and one third is added to it, the fraction obtained is 14/9. Find the original fraction.

Let numerator be N
Then denominator is N + 7
We then get:

9N + 3(4)(N + 7) = 14(N + 7) ------ Multiplying by LCD, 9(N + 7)
Continue to solve for N, the numerator. You should get 2.
Add 7 to the numerator to get 9. This makes the original fraction: , or