Help with these fractions please!!!

[jtread]

I have 3 people owning 7/9 Interest in property. One owns 1/3, the other two own 2/9 each. They sell an undivided 1/2 interest leaving them with 5/18 Interest remaining (7/9 - 1/2). What is the remaining fraction interest of the three people?

 

[jtread]

I get 25/162 for the person with the original 1/3 and 5/81 for the people with the original 2/9 apiece. If you add those numbers plus the 1/2 plus the unaccounted for 2/9, you get 1. Am I wrong?

 

[stapel]

I have 3 people owning 7/9 Interest in property. One owns 1/3, the other two own 2/9 each. They sell an undivided 1/2 of their interest leaving them with 5/18 Interest remaining (7/9 - 1/2).

The three don't sell "1/2" of the "interest" (ownership rights); they sell one-half of their ownership rights. Since they didn't own the whole thing, then half of their interest in the property cannot be half of the whole thing. :wink:

 

[jtread]

The three don't sell "1/2" of the "interest" (ownership rights); they sell one-half of their ownership rights. Since they didn't own the whole thing, then half of their interest in the property cannot be half of the whole thing. :wink:

Changed. The calculation explained what I was trying to say. Can you help?

 

[stapel]

Changed. The calculation explained what I was trying to say. Can you help?

If I understand correctly, the three sell what equates to half of the interest in the entire property, with that half coming out of their 7/9. You state that they then are left with 5/18, but then you ask what fraction they are left with. Isn't that the 5/18?

Or are you perhaps asking what fraction each now owns of the entire property, assuming that they are dividing their 5/18 in the same proportions as they'd started (being 3:2:2)?

If the latter, then note that 3+2+2 = 7. Now find some way of expressing their total fraction in terms of some equivalent fraction which has a multiple of 7 for its numerator. Then split that expression into fractions whose numerators are in the same proportion of 3:2:2.

P.S. In future, please keep in mind that it's a lot easier to follow a conversation when people's statements aren't retroactively changed. Kindly please post corrections, changes, and other follow-ups as replies, rather than edits. Thank you! :wink:

 

[jtread]

Solved it. Inverted the 7/9 to 9/7. Multiplied 9/7 by each person's interest (1/3, 2/9, 2/9). Which comes out to 3/7, 2/7, 2/7. Multiply those numbers by the remaining 5/18 Interest. Gives you 5/42, 5/63, 5/63. Add back in the 1/2 and 2/9 =1.

 

[HallsofIvy]

No, that's completely wrong, partially because you are still assuming, when you say "add back in the 1/2 of 2/9", that they are selling 1/2 of the entire property. They can't do that- they cannot sell what they don't own! Each person can only sell half of what he/she owns. The first person owns 1/3 of 7/9 or 7/27 of the entire property. The second and third persons own 2/9 of 7/9 or 14/81 of the entire property. The sell 1/2 of what each owns that leaves each with 7/54, 7/81, 7/81 of the entire property. And, of course, together they still own 7/9 divided by 2= 7/18 of the entire property.