the numerator of a fraction is one-half the denominator! If the numerator is is increased by 2 and denominator is decreased by 2, the value of the fraction is 2/3. What is the numerator of the original fraction?

n+2/2n-2

=2/3
(n+2)*(3)=2*(2n−2)
3n+6=4n−4
3n+6−4n=4n−4−4n
−n+6=−4
−n+6−6=−4−6
−n=−10
n=10

Well, well, we have ourselves a fraction conundrum! Let's solve this with a touch of clown logic, shall we?

Let's assume that the numerator of the original fraction is "x". According to your first statement, the denominator would then be "2x". So, our fraction is x/(2x).

Now, if we increase the numerator by 2, it becomes "x + 2", and if we decrease the denominator by 2, it becomes "2x - 2". According to your second statement, the new fraction is (x + 2)/(2x - 2) and it equals 2/3.

So, we can set up an equation: (x + 2)/(2x - 2) = 2/3.

Now, let me juggle some numbers and solve this equation for you. Bear with me, the clown algebra is about to begin!

3(x + 2) = 2(2x - 2)

3x + 6 = 4x - 4

6 + 4 = 4x - 3x

10 = x

Brace yourself for the final punchline! The numerator of the original fraction is 10. Ta-da!

To solve this problem, let's break it down step by step.

Step 1: Assign variables to the unknowns:
Let's call the numerator of the original fraction "x" and the denominator "y".

Step 2: Formulate the first equation:
The problem tells us that "the numerator of a fraction is one-half the denominator". So, mathematically, we can say that:
x = (1/2) * y.

Step 3: Formulate the second equation:
The problem also tells us that "If the numerator is increased by 2 and the denominator is decreased by 2, the value of the fraction is 2/3." So we can set up another equation:
(x + 2) / (y - 2) = 2/3.

Step 4: Solve the equation system:
Now, we have two equations:
x = (1/2) * y, and
(x + 2) / (y - 2) = 2/3.

We can start by solving the first equation for x:
x = (1/2) * y.

Next, substitute this value of x into the second equation:
((1/2) * y + 2) / (y - 2) = 2/3.

Simplify the equation by cross-multiplying:
3(1/2 * y + 2) = 2(y - 2).

Simplify further:
3/2 * y + 6 = 2y - 4.

Combine like terms:
(3/2)y - 2y = -4 - 6,
-(1/2)y = -10.

Now, multiply both sides of the equation by -2/1 to isolate y:
((-(1/2)y) * (-2/1)) = -10 * (-2/1),
y = 20.

Step 5: Find the numerator of the original fraction:
We know that x = (1/2) * y, so:
x = (1/2) * 20,
x = 10.

Therefore, the numerator of the original fraction is 10.

d = 2n

(n+2) / (2n-2) = 2/3

Now just solve for n. Be sure to check your answer.

1 is the numerator and 2 is the denominator. Basic maths.

In the fraction 1/2 what’s is the numerator and the denominator