If i adds 2 to the numerator of a fraction,the fraction becomes 1/3.If he subtracts 3 from the denominator of the fraction,it becomes 1/4.What is the fraction?
let the fraction be x/y
(x+2)/y = 1/3 --> 3x + 6 = y
x/(y-3) = 1/4 ---> 4x = y-3 or y = 4x+3
then 4x+3 = 3x+6
x = 3,
y = 15
your fraction was 3/15
Well, it seems i has a magical touch with fractions! Let's figure this out.
Let's say the original fraction is x/y.
According to the question, when i adds 2 to the numerator, the new fraction becomes (x + 2)/y. This is equal to 1/3.
Similarly, when i subtracts 3 from the denominator, the new fraction becomes x/(y - 3). This is equal to 1/4.
Now we have two equations:
(x + 2)/y = 1/3
x/(y - 3) = 1/4
Solving these equations can make your brain feel like it's doing somersaults just like a clown!
But fear not! Let me do the calculations for you.
By simplifying the first equation, we get:
3(x + 2) = y
And by simplifying the second equation, we get:
4x = y - 3
Now, we can substitute the value of y from the first equation into the second equation, like this:
4x = 3(x + 2) - 3
Simplifying this equation, we get:
4x = 3x + 6 - 3
4x - 3x = 6 - 3
x = 3
Now, substituting this value of x back into the first equation, we get:
3(3 + 2) = y
3 * 5 = y
y = 15
So, the fraction is 3/15.
But wait! We can simplify this fraction further. Dividing both the numerator and denominator by 3, we get:
1/5
Voila! The fraction is 1/5.
So, i turned x/y into 1/5 by adding 2 to the numerator and subtracting 3 from the denominator. Quite the magical fraction-fiddler, isn't he?
Let's assume the fraction as x/y.
According to the given condition, if i adds 2 to the numerator, the fraction becomes 1/3. So, (x+2)/y = 1/3.
And if i subtracts 3 from the denominator, the fraction becomes 1/4. So, x/(y-3) = 1/4.
From the first equation, we can solve for x:
x + 2 = (y/3)
From the second equation, we can solve for x:
x = (y-3)/4
Setting the two equations equal to each other, we get:
(y/3) = (y-3)/4
To solve for y, we can cross multiply:
4y = 3(y-3)
Simplifying the equation:
4y = 3y - 9
4y - 3y = -9
y = -9
Using the value of y, we can solve for x in the first equation:
x + 2 = (-9/3)
x + 2 = -3
x = -3 - 2
x = -5
Hence, the fraction is -5/-9, which simplifies to 5/9.
To solve this problem, we need to set up two equations based on the given information and then solve for the fraction.
Let's assume that the fraction is represented as "x/y". According to the problem, if i adds 2 to the numerator, the fraction becomes 1/3. This can be written as:
(x+2)/y = 1/3 -- equation 1
Similarly, if i subtracts 3 from the denominator, the fraction becomes 1/4. This can be written as:
x/(y-3) = 1/4 -- equation 2
Now, we need to solve these two equations simultaneously to find the values of x and y.
First, let's rearrange equation 1:
x + 2 = y/3
Next, rearrange equation 2:
4x = y - 3
Now we have a system of equations:
x + 2 = y/3 -- equation 3
4x = y - 3 -- equation 4
To solve this system of equations, we can use the substitution method. Rearrange equation 3 to solve for x:
x = (y/3) - 2
Substitute this value of x into equation 4:
4((y/3) - 2) = y - 3
Simplify the equation:
4y/3 - 8 = y - 3
Multiply through by 3 to eliminate the fraction:
4y - 24 = 3y - 9
Now, isolate the variable y:
y = 15
Substitute this value of y back into equation 3 to find x:
x + 2 = 15/3
Simplify:
x + 2 = 5
Subtract 2 from both sides:
x = 3
Therefore, the fraction is 3/15, which can be simplified to 1/5.