The numerator of a fraction is 5 less than its denominator if one is added to the numerator and to the denominator new fraction is 2 upon 3 find the fraction
Let's assume the denominator of the fraction is x.
According to the given information, the numerator of the fraction is 5 less than its denominator.
So, the numerator = x - 5.
Now, if one is added to the numerator and the denominator, the new fraction is 2/3.
This can be represented as:
(x - 5 + 1)/(x + 1) = 2/3
Simplifying this equation:
(x - 4)/(x + 1) = 2/3
Cross multiplying:
3(x - 4) = 2(x + 1)
3x - 12 = 2x + 2
3x - 2x = 2 + 12
x = 14
Therefore, the denominator of the fraction is 14, and the numerator is 14 - 5 = 9.
So, the fraction is 9/14.
Let's assume the denominator of the fraction is "x".
According to the given information, the numerator is 5 less than the denominator, so the numerator can be expressed as (x - 5).
Now, if one is added to both the numerator and the denominator, we get (x - 5 + 1) / (x + 1).
The new fraction is given as 2/3, so we have the equation:
(x - 4) / (x + 1) = 2/3
To solve this equation, we can cross-multiply:
3(x - 4) = 2(x + 1)
Expanding both sides:
3x - 12 = 2x + 2
Simplifying:
3x - 2x = 2 + 12
x = 14
Therefore, the denominator is 14.
And the numerator, as given before, is (x - 5) which is (14 - 5 = 9).
Hence, the fraction is 9/14.