The sum of two fractions is 1 1/2.
Their difference is 5/12.
What are the fractions?
71/12
its imposible
Im stuck
x+y = 3/2
x-y = 5/12
2x = 11/12
...
To find the fractions, we can start by setting up two equations based on the given information.
Let's assume the first fraction is "a/b" and the second fraction is "c/d".
According to the problem, the sum of the two fractions is 1 1/2, which can be written as 3/2 in improper fraction form. Thus, our first equation is:
a/b + c/d = 3/2 -- Equation 1
The problem also states that the difference between the two fractions is 5/12. So, our second equation is:
a/b - c/d = 5/12 -- Equation 2
Now, we have a system of two equations with two unknowns (a, b, c, d). To solve this system, we'll use the method of substitution:
First, let's solve Equation 1 for a/b:
a/b = 3/2 - c/d
Next, substitute this expression for a/b in Equation 2:
3/2 - c/d - c/d = 5/12
Now, let's simplify the equation:
3/2 - 2c/d = 5/12
Next, let's simplify the fractions by multiplying each fraction by the least common denominator (12):
(12 * 3/2) - 2c = 5
36/2 - 2c = 5
18 - 2c = 5
Next, let's isolate -2c:
-2c = 5 - 18
-2c = -13
Now, divide both sides by -2 to solve for c:
c = (-13) / (-2)
c = 13/2 or 6 1/2
Now that we have the value of c, we can substitute it back into Equation 1 to solve for a/b:
a / b + (13/2) / d = 3/2
Next, let's multiply each fraction by the least common denominator (2d):
2ad / bd + 13/2d = 3/2
Now, let's multiply both sides of the equation by 2 to get rid of the fractions:
4ad / bd + 13/d = 3
Now, simplify the equation:
4ad + 13bd = 3bd
This equation doesn't give us a specific solution for a or b. However, we can find the fractions in terms of c by assigning a random value to d.
Let d = 2, for example:
So, 4a + 13b = 3(2)
4a + 13b = 6
Now, assign random values to a and solve for b:
Let a = 1, for example:
4(1) + 13b = 6
4 + 13b = 6
13b = 2
b = 2/13
Thus, when a = 1 and b = 2/13, the fraction a/b is 1/(2/13) or 13/2.
Therefore, the two fractions are 13/2 and 2/13.