To find the numbers that sum to a given value:
1. Start by defining the problem. Let's call the three different positive integers "a", "b", and "c", and let's call their sum "S".
2. Write an equation to represent the problem. The equation is: a + b + c = S.
3. Since no specific values are given for "a", "b", "c", or "S", we cannot determine the exact numbers. However, we can make some general observations:
- The three numbers must be positive, so they cannot be zero or negative.
- To find different numbers, we can set a lower limit for one of the numbers. For example, if we set "a" as the smallest number, it can be 1.
4. With these observations, we can generate possible sets of numbers that sum to "S":
- If "a" is set to 1, then "b" can be any positive integer greater than or equal to 1, and "c" will be the remaining value to make the sum equal to "S".
For example, if S = 10, one possible set of numbers could be: a = 1, b = 4, c = 5.
So, the solution to this problem is not a single set of numbers but rather an infinite number of sets that satisfy the given conditions.
For the second question:
To find the fraction that is halfway between 0.5 and another given fraction:
1. Let's call the given fraction "x" and the unknown fraction "y".
2. Write an equation to represent the problem. The equation is: (0.5 + x) / 2 = y.
3. Solve the equation for "y" by isolating it on one side of the equation.
4. Simplifying the equation, we get: 0.5 + x = 2y.
5. Rearrange the equation to solve for "y", dividing both sides by 2: y = (0.5 + x) / 2.
For example, if x = 8, substituting this value into the equation gives: y = (0.5 + 8) / 2 = 8.25 / 2 = 4.125.
Therefore, the fraction that is halfway between 0.5 and 8 is 4.125.