Hello, Sarah,
This requires a few painful conversions, but watch carefully:
We need to put all the numbers on the same basis so that we can add and subtract them.
We want 3/4 of the distance between 2 5/6 and 8 5/12. Let's start by finding the distance between the two points.
This means we subtract 2 5/6 from 8 5/12. Let's covert both to fractions with 12 in the denominator.
2 5/6: 2 becomes 24/12 and 5/6 becomes 10/12. Add them together to get 34/12.
8 5/12: 8 becomes 96/12 and 5/12 remains the same. Add to get 101/12.
Now we can subtract: 101/12 - 34/12 = 67/12
67/12 is the distance between the two points. We want 3/4 of that distance and add it to the starting point (2 5/6) to find "3/4 of the way" between the two."
Multiply 3/4 times 67/12 to get 201/48
201/48 is added to the 2 5/6 to find the point 3/4 of the way to 8 5/12.
Again, we need common denominators to add (201/48 + 2 5/6)
201/48 + 2 5/6
201/48 + 96/48 + 40/48 = 337/48
This can be reduced to 7 1/48. This is the point that is 3/4 of the way from 2 5/6 and 8 5/12.
That wasn't fun. It can be difficult to see the number patterns when picking the best number for a common denominator. Please check my steps to insure they are correct. You may find an easier route with a different approach to the denominators.
I hope it helps,
Bob
