The denominator of a fraction is 4 more than the numerator. If both the denominator and the numerator are increased by 1, the resulting fraction equals 1/2. What is the original fraction?
**Need to show all work**
Thanks for the help.
Hint: The resulting fraction equals
1/2 = 2/4 = 3/6 = 4/8 = 5/10 ...
Try to find the original fraction.
3/6
To find the original fraction, we need to set up equations based on the given information. Let's denote the numerator as "x" and the denominator as "x + 4" since the denominator is 4 more than the numerator.
Now, let's write the first equation based on the given information: "If both the denominator and the numerator are increased by 1, the resulting fraction equals 1/2."
So, if we increase both the numerator and the denominator by 1, the new fraction can be represented as (x + 1)/(x + 4 + 1) = 1/2.
Next, we can simplify the equation:
(x + 1)/(x + 5) = 1/2
To solve this equation, we can cross-multiply:
2(x + 1) = 1(x + 5)
Simplifying further:
2x + 2 = x + 5
Now, let's isolate the variable:
2x - x = 5 - 2
x = 3
So, the numerator of the original fraction is 3.
Now, to find the denominator, we substitute the value of x back into the equation:
x + 4 = 3 + 4
x + 4 = 7
Therefore, the denominator of the original fraction is 7.
In conclusion, the original fraction is 3/7.