Simple math isn’t always simple. As the Texas Supreme Court recently put it, “[o]nly in a legal text could the formula ‘one-half of one-eighth’ mean anything other than one-sixteenth.” No. 21-0146, 2023 WL 2053175 (Tex. 2023). Earlier this year, in Van Dyke v. Navigator Group, the Court grappled with a simple math problem that one might easily find in an elementary school classroom: 

In the context of an oil and gas mineral reservation, what is “one-half of one-eighth”?

Answer: ____________

If your answer is “one-sixteenth,” you should keep reading. 

The foregoing “math problem” is often referred to as the infamous “double fraction,” which was not uncommon in antique mineral conveyances entered into at the turn of the last century. The proper construction of instruments containing double-fraction language is a dilemma of increasing concern in the oil and gas industry as uncertainty grows, disputes proliferate, and courts apply varied approaches to this complicated issue. Hysaw v. Dawkins, 483 S.W.3d 1, 4 (Tex. 2016).

The dispute before the Court in Van Dyke v. Navigator Group arose out of an instrument executed in 1924, whereby George H. Mulkey and Frances E. Mulkey conveyed their ranch and the underlying minerals to G.R. White and G.W. Tom with the following reservation:

It is understood and agreed that one-half of one-eighth of all minerals and mineral rights in said land are reserved in grantors, Geo. H. Mulkey and Frances E. Mulkey, and are not conveyed herein.

For nearly ninety years, the parties and their predecessors treated the foregoing reservation as vesting both the grantors and the grantees each with one-half of the mineral interests. However, in 2013, a dispute arose putting at stake more than $44 million in accumulated royalties.

The ownership of these royalties turned on the answer to the question, what is “one-half of one-eighth”? The grantees’ successors asserted that the double fraction was merely an elementary arithmetic formula with no additional meaning, so that only a one-sixteenth interest was reserved. The grantors’ successors contended that the double fraction reflected a term of art common at the time the deed was drafted, and that the use of this term of art reserved one-half of the mineral interest to the grantor. The correct answer to this particular “math problem” didn’t just garner a passing grade, but was worth nearly $20 million.

The trial court sided with the grantees’ successors holding that one-half of one-eighth equals one-sixteenth. The court of appeals affirmed. The Texas Supreme Court agreed to consider the issue.

The Court’s analysis begins with its interpretation of the 1924 deed, which it deemed a “textual interpretation.” The Court acknowledged that “[t]he fact pattern may seem odd to those not steeped in Texas oil-and-gas law, but the legal framework for analyzing this text is the same as for any other.” Unless otherwise defined in the text, courts will adopt a term’s ordinary meaning.  One fundamental premise, however, is that the text retains the same meaning today that it had when it was drafted. Thus, the ordinary meaning at the time of drafting remains the exact same meaning to which courts must later adhere.

“Words must be given the meaning they had when the text was adopted.” The test is what the language would have reasonably meant to an ordinary speaker of the language who would have understood the original text in its context at the time it was used. The Court was clear that “whatever that meaning was then remains the meaning today.”

Thus, the Court stated that its analysis did not turn on what it might think “one-half of one-eighth” would mean if written today.  It simply does not matter whether that phrase would clearly mean one-sixteenth.  In fact, the challenge is not particularly legal in nature. One has to first overcome the cognitive dissonance that arises because, at least at first glance, “one-half of one-eighth” seems unusually clear. Setting aside this preconception and a natural instinct to resort to basic math, the only question is whether, in the context of a mineral conveyance instrument from 1924, the double fraction reasonably references arithmetic at all?

At the time the parties executed this deed, “1/8” was widely used as a term of art to refer to the total mineral estate. Notably, it is that fraction, not 1/3, 2/7, 6/241, or any other that is so commonly used. Thus, when a court is confronted with a double fraction involving “1/8” in an instrument, the analysis must begin with a presumption that the mere use of such a double fraction was not purposeful and that it reflects the entire mineral estate, not just one-eighth of it.  The Court reasoned that “it would be odd to say ‘one-half of one-eighth’ rather than simply ‘one-sixteenth’ if all that was intended by ‘one-half of one-eighth’ was 1/16.” While this presumption is rebuttable, the rebuttal must come from the document itself. The Court held that the “key point is that there must be some textually demonstrable basis to rebut the presumption.”

The Court held that “[t]he use of a double fraction in this deed, combined with the lack of anything that could rebut the presumption, is precisely why we can conclude as a matter of law that this deed did not use 1/8 in the arithmetical sense but instead reserved to the grantors a 1/2 interest in the mineral estate.” Thus, in the context of a reservation of a mineral interest under Texas law, the calculation of “one-half of one-eighth” sometimes equals one-half. And that’s why they don’t teach math in law school.

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