The numerator of a fractionis 5 less than twice the denominator. If the numerator is decreased by 1 and the denominator is increased by 3, the value of the new fraction is 5/4. Find the original fraction.

old denominator --- D

old numerator --- 2D-5

new denomintor D-1
new denom. 2D-5 + 3

so (D-1)/(2D-2) = 5/4

solve

I seem to be making some silly copying errors tonight

change to :

new denomintor D+3
new numerator 2D-5 - 1

so (2D-6)/(D+3) = 5/4

solve

This is my work:

D-1 5
-----= -- Cross multiply you get:
2D-2 4 10D-10=4D-4
-4D -4D
6D-10=-4
+10+10
6D=6
-----
6 6
D=1?

Oh now I get it. in the last step

3D=39
-----
3 3

so D=13
tysm!
your a genius.

THE DENOMINATOR IS 4 MORE THAN ITS NUMERATOR.IT IS DECREASED FROM NUMERATOR AND 2 IS ADDED TO THE DENOMINATOR,THE RESULTING FRACTION IS 3/4.FIND THE ORIGINAL FRACTION.

To solve this problem, let's assume that the denominator of the original fraction is denoted by "x."

According to the given information, the numerator of the fraction is 5 less than twice the denominator. Therefore, we can express the numerator as 2x - 5.

Now, we are given that if the numerator is decreased by 1 and the denominator is increased by 3, the value of the new fraction is 5/4.

We can represent the new fraction as (2x - 5 - 1) / (x + 3), which simplifies to (2x - 6) / (x + 3).

We are told that this new fraction is equal to 5/4. So, we can set up the equation:

(2x - 6) / (x + 3) = 5/4

To solve for x, we can cross-multiply:

4(2x - 6) = 5(x + 3)

Simplifying the equation further:

8x - 24 = 5x + 15

Combine like terms:

8x - 5x = 15 + 24

3x = 39

Divide both sides by 3:

x = 39/3

Simplifying:

x = 13

Therefore, the original fraction can be expressed as (2(13) - 5) / 13 = 21/13.