after a fraction is increased by 1/4 of its value, the result is 3 1/3. What is the original fraction.
Let's assign a variable to represent the original fraction. Let's say the original fraction is x.
According to the problem, the fraction, when increased by 1/4 of its value, becomes 3 1/3.
So, we can write the equation as:
x + (1/4)x = 3 1/3
To calculate 3 1/3 as an improper fraction, we need to convert it.
3 1/3 = 3 + 1/3 = 10/3.
Rewriting the equation:
x + (1/4)x = 10/3
To solve for x, we'll combine the terms on the left side of the equation:
(1 + 1/4)x = 10/3
To simplify (1 + 1/4), we need to find a common denominator for 1 and 1/4, which is 4.
1/4 + 1 = 1/4 + 4/4 = 5/4.
So, the equation becomes:
(5/4)x = 10/3
To get rid of the fraction on the left side, we can multiply both sides of the equation by the reciprocal of (5/4), which is (4/5).
(4/5)(5/4)x = (4/5)(10/3)
Simplifying:
1x = 40/15
Therefore, the value of x, the original fraction, is:
x = 40/15
Simplifying the fraction:
x = 8/3
So, the original fraction is 8/3.
To find the original fraction, we will work step by step.
Let's assume the original fraction is x/y.
According to the question, when the fraction is increased by 1/4 of its value, the result is 3 1/3. We can write this as an equation:
(x/y) + (1/4)(x/y) = 3 1/3
To simplify further, we multiply both sides of the equation by the least common denominator (LCD), which is 12 (4 * 3):
12 * (x/y) + 12 * (1/4)(x/y) = 12 * (3 1/3)
Simplifying both sides:
12(x/y) + 3(x/y) = 40
Now, we can combine like terms on the left side:
(12x + 3x) / y = 40
Simplifying further:
15x / y = 40
To isolate the variable (x), we multiply both sides of the equation by y:
15x = 40y
Now, let's solve for x by dividing both sides of the equation by 15:
x = (40y) / 15
Since we are looking for the original fraction, we want to find x/y. Replacing x with (40y) / 15, we get:
x/y = [(40y) / 15] / y
Simplifying:
x/y = 40y / (15y)
x/y = 8/3
Therefore, the original fraction is 8/3.
(X * 1/4) + X = 3 1/3
X is the unknown number
1/4X + 4/4X = 10/3
5/4X = 10/3
X = 10/3 * 4/5
X = 40/15
X = 8/3 = 2 2/3
X + 1/4 = 3 1/3
X = 3 1/3 - 1/4