When subtracted together, two fractions are equaled to 2/3. What are those fractions?
I have no idea. All we know is that one is 2/3 more than the other.
Not quite sure what "subtracted together" means. Usually you "add together"
To find the two fractions that, when subtracted, equal 2/3, we can set up an equation. Let's call the first fraction a/b and the second fraction c/d.
According to the problem, when these two fractions are subtracted, the result is 2/3. This can be written as:
(a/b) - (c/d) = 2/3
To solve for the fractions a/b and c/d, we need to find a common denominator for b and d. The common denominator will be the least common multiple (LCM) of b and d.
Once we have the common denominator, we can rewrite the equation:
(ad/bd) - (bc/bd) = 2/3
To make the subtraction easier, we can combine the fractions:
(ad - bc) / bd = 2/3
Now, we can see that the numerators of the fractions must be in the ratio 2:3. So, we can write:
ad - bc = 2x, where x is a positive integer
The next step is to assign specific values to x and solve for the variables a, b, c, and d. Let's use x = 1:
ad - bc = 2
We can choose values for a, b, c, and d that satisfy this equation. For example, we can let a = 1, b = 1, c = -1, and d = -1. Plugging these values into the equation gives:
(1)(-1) - (1)(-1) = 2
-1 + 1 = 2
0 = 2
Since the equation is not satisfied, we can conclude that there are no integer solutions to this problem.
However, if we allow for fractions as solutions, we can choose values such as a = 1/3, b = 1, c = -1/3, and d = 1. Plugging these values into the equation gives:
(1/3)(1) - (-1/3)(1) = 2/3
1/3 + 1/3 = 2/3
2/3 = 2/3
Thus, one solution to the problem is a/b = 1/3 and c/d = -1/3. Any other choices for a, b, c, and d that satisfy the equation would also be valid solutions.