The Denominator of a fraction exceeds the numerator by 4. When 3 is added to both the numerator and denominator, the fraction becomes 4/5. Find the fraction.

numerator --- x

denominator --x+4

(x+3)/(x+7) = 4/5
5x + 15 = 4x+28
x = 13

fraction was 13/17

check : add 3 to top and bottom ---> 16/20 = 4/5

13/17

if the denominator of a fraction be added to the numerator and the numerator be sub-tracted from the denominator, it becomes its numerator by 3. find the fraction. 4 1/3 the denominator of the fraction exceeds

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Why did the fraction go to therapy? It had a complex relationship with its denominator!

But fear not, I'm here to help you solve this mathematical riddle! Let's break it down step by step.

Let's say the numerator of the fraction is "x." Since the denominator exceeds the numerator by 4, we can express the denominator as "x + 4."

According to the problem, when 3 is added to both the numerator and denominator, the fraction becomes 4/5. So, our new numerator is "x + 3," and the new denominator is "x + 4 + 3," which simplifies to "x + 7."

Now we have the equation (x + 3) / (x + 7) = 4/5.

To solve this equation, we can cross-multiply:

5(x + 3) = 4(x + 7)

Now let's do some arithmetic:

5x + 15 = 4x + 28

Subtracting 4x from both sides and simplifying:

x + 15 = 28

Subtracting 15 from both sides:

x = 13

So, the numerator (x) is 13, and the denominator (x + 4) is 13 + 4, which equals 17.

Therefore, the fraction is 13/17. Voila!

Remember, math jokes may be irrational, but math solutions are always logical!

To find the fraction, let's start by setting up equations based on the given information.

Let's assume the numerator of the fraction is represented by "x". Since the denominator exceeds the numerator by 4, the denominator would be "x + 4".

The original fraction can be expressed as x/(x + 4).

When 3 is added to both the numerator and denominator, the new fraction becomes (x + 3)/((x + 4) + 3) = (x + 3)/(x + 7).

According to the information given, we know that this new fraction is equal to 4/5:

(x + 3)/(x + 7) = 4/5.

To solve this equation, we can cross multiply:

5(x + 3) = 4(x + 7).

Expanding both sides of the equation:

5x + 15 = 4x + 28.

Simplifying the equation:

5x - 4x = 28 - 15.

x = 13.

Now that we have the value of x as 13, we can substitute it back into the original fraction:

The fraction is 13/(13 + 4) = 13/17.