I understand what you’re asking, but you’re conflating acres and interest. Interest is a percentage representation. You can use a mix of fractions, decimals and percentages when calculating this. I’m going to use percentages. I’m not going to do net royalty acres because that is a different kind of calculation used to value royalty interest. Your interest needs to add up to 100% at all times, and your gross acres need to add up to the total gross acres in your section. I’ve included unknown owner to avoid confusion with the previous statement. If you add MI with MI it will equal 100%, RI with RI will equal 100% and you will include the MI of unknown owner in this calculation, and acres will equal 640, more or less, at all times. The decimals will fluctuate the numbers slightly:
520 mineral acres in a 640 acre section:
Party 1 owns 81.25% MI, or 520 net mineral acres (NMA)
[Unknown owner: 18.75% MI, 120 NMA]
2/3rds of his Royalty Interest gifted:
Party 1 now owns 81.25% MI, 27.083333% RI, he still owns 520 NMA.
7 kids get 1/7 of 2/3 NPRI each = 7.738095% RI each, 54.166667% RI TOTAL
[Unknown owner: 18.75% MI, 120 NMA]
NOTE: you confused me with your wording. You originally said he gifted 2/3 of his Royalty Interest, then later said the kids each received 1/7 of 2/3rds NPRI. Those are two different things. I am assuming you meant 2/3rds of Party 1’s RI, and not 2/3rds total.
Part 1 leaves all interest to Party 2. Party 2 sells 1/3 of her MI to Party B:
Party 2: 54.1666667% MI, 18.055556% RI, 346.666667 NMA
Party B: 27.083333% MI, 9.027778% RI, 173.333333 NMA
7 kids still have 1/7 of 2/3 NPRI each = 7.738095% RI each, 54.166667% RI TOTAL
[Unknown owner: 18.75% MI, 120 NMA]
Party 2 dies, leaves 91% equally to 7 kids, 9% to party C:
Party B: 27.083333% MI, 9.027778% RI, 173.333333 NMA
7 kids: 7.041667% MI, 10.085317% RI, 45.066667 NMA each, (OR 49.291667% MI, 70.597222% RI, 315.466667 NMA total)
Party C: 4.875% MI, 1.625% RI, 31.20 NMA
[Unknown owner: 18.75% MI, 120 NMA]
Hopefully that cleared something up for you. You were using acres as a representation of royalty interest. You can still do that with the royalty interest percentage multiplied by gross acres if it makes it easier for you to visualize. I didn’t do that here since the only term I could think to call it was net royalty acres, which is a term used for a different kind of calculation, and I didn’t want to confuse people. Basically just remember, at all times, all interest needs to add up to 100%, and if you’re using acres, they need to add to the gross acres in your tract. Let me know if you have any questions. I can send you the formulas if you need. This post is already too long.