My denominator is 6 more than my numerator. My simplest form is 2/5 What fraction am I?_______
4/10
Let's denote the numerator of the fraction as "n" and the denominator as "d". According to the given information, we can set up the following equations:
d = n + 6 (The denominator is 6 more than the numerator)
n/d = 2/5 (The fraction is in simplest form)
To solve for the numerator and denominator, we can substitute the value of "n" from the first equation into the second equation:
(n + 6) / n = 2/5
To eliminate the fractions, we can cross multiply:
5(n + 6) = 2n
Expanding the equation:
5n + 30 = 2n
Rearranging the equation:
5n - 2n = -30
3n = -30
Dividing both sides of the equation by 3:
n = -10
Now, substitute the value of "n" back into the first equation to find the value of "d":
d = -10 + 6
d = -4
The fraction is -10/-4, but it can be simplified to 5/2.
Therefore, the fraction you are is 5/2.
To find the fraction when the denominator is 6 more than the numerator, we can set up an equation.
Let's say the numerator is represented by the variable 'x', then the denominator would be 'x + 6'.
So, we have the fraction x/(x + 6).
Given that the simplest form of the fraction is 2/5, we can set up another equation:
x/(x + 6) = 2/5
To solve this equation, we can cross-multiply:
5x = 2(x + 6)
Expanding the right side:
5x = 2x + 12
Bringing like terms to one side:
5x - 2x = 12
3x = 12
Dividing both sides by 3:
x = 12/3
Simplifying:
x = 4
Now we know that the numerator is 4.
To find the corresponding denominator, we add 6 to the numerator:
x + 6 = 4 + 6 = 10
Therefore, the fraction in question is 4/10 or simply 2/5 in its simplest form.