What Is PEMDAS? 6 ÷ 2(1 + 2) = 1 or 9?

Value of the Information & Strength of the Argument

The video delivers high-value information by demystifying a misleadingly simple arithmetic problem and revealing its deep roots in notation history and human convention. It argues convincingly that only part of PEMDAS is mathematically necessary (the stacking of repeated operations), while the rest is arbitrary and evolved through educational publishing. The argumentation is solid: it uses concrete examples (the apple and orange bag, algebraic expressions like 6/2X) to illustrate why multiplication must precede addition and why juxtaposition alters interpretation. It systematically addresses the calculator discrepancy as a design choice rather than a mathematical truth, and supports its claims with references to historical texts and modern standards. The reasoning is clear, logical, and well-structured, effectively dismantling the idea that the conflict reflects a flaw in mathematics itself rather than in notation.

Scientific Rigor, Source Quality, Title Accuracy

The video demonstrates strong scientific rigor by grounding its claims in documented sources: Cajori’s ‘A History of Mathematical Notations’ (1928), Smith’s ‘Algebra for Beginners’ (1905), the Physical Review Style and Notation Guide, and ISO 80000-2. It accurately names the origin of the obelus and credits Johann Rahn and John Pell. The presentation is balanced, acknowledging both sides of the debate and explaining why each answer can be defended. The title is well-matched to the content, directly referencing the viral problem and PEMDAS. The video does not overstate its conclusions; it explicitly states that the problem is ambiguous and recommends rewriting the expression, which is a practical and scientifically sound takeaway.

The title accurately reflects the content, addressing the viral expression and the concept of PEMDAS.

9/10

The video provides a thorough explanation of the origins of PEMDAS, cites historical sources (Cajori, Smith) and professional standards (Physical Review, ISO 80000-2), and clearly distinguishes between forced and conventional parts of the rule. It accurately describes calculator behavior and presents a well-reasoned conclusion.

• 00:00The viral problem that splits comment sections between 1 and 9
• 01:56What PEMDAS actually is and whether it is a law or a convention
• 03:30Why multiplication must come before addition, shown with real objects
• 06:33Where the division sign and the order of operations rules came from
• 09:00Implied multiplication and how algebra is really written
• 11:47Calculators that disagree, from TI-82 and TI-83 to Casio and ISO 80000-2
• 13:58Why the real fix is rewriting the expression, not memorizing harder

• A History of Mathematical Notations (Florian Cajori, 1928) — Mentioned as the standard reference for where math symbols come from, and noted that there was no agreement about which of multiplication and division should be carried out first.
• Algebra for Beginners (David Eugene Smith, 1905) — Cited as an early textbook that spells out order of operations rules.
• Physical Review Style and Notation Guide — Cited as setting the accepted order: powers first, then multiplication, then division, meaning 1/2N reads as 1 over 2N.
• ISO 80000-2 — Cited as recommending the cessation of using the obelus, suggesting fraction bars or brackets instead.
• TI-82 and TI-83 documentation — Mentioned to illustrate differing calculator implementations of implied multiplication priority.
• Casio FX-991 ES manual — Cited as placing multiplication in front of a bracket higher in priority than division.