The number of a fraction is three more than twice the denominator. The fraction simplified is equal to 9/4 Find the fraction
To find the fraction, let's represent the fraction as x/y, where x is the numerator and y is the denominator.
Given that the number of the fraction is three more than twice the denominator, we can write the equation:
x = 2y + 3
We are also told that the fraction, when simplified, is equal to 9/4. Simplifying the fraction means that the numerator and denominator have no common factors other than 1.
So, we can write another equation by equating the simplified fraction to 9/4:
x/y = 9/4
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the substitution method:
From the first equation, x = 2y + 3. We can substitute this expression for x in the second equation:
(2y + 3)/y = 9/4
Now, cross-multiply and solve for y:
4(2y + 3) = 9y
8y + 12 = 9y
Subtracting 8y from both sides gives:
12 = y
Now, substitute the value of y back into the first equation to find the value of x:
x = 2y + 3
x = 2(12) + 3
x = 27
So, the fraction is 27/12, which can be simplified to 9/4 by dividing both the numerator and denominator by their greatest common divisor, which is 3.
Therefore, the fraction is 9/4.