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Answer each question based only on what was presented in the video lesson. No outside knowledge is needed — every answer can be found in the video.
Apply the order of operations (PEMDAS) to evaluate expressions correctly. Show all work step by step; problems increase in difficulty.
Why does the expression 4 × 2² + 3 + 5² equal 44 — and not 80, 96, or even 5,184? This lesson from Section 3.3 of OpenStax Contemporary Mathematics reveals how the order of operations acts as a universal mathematical syntax, ensuring that any expression has exactly one correct answer no matter who is solving it. From the EMDAS hierarchy to the role of parentheses as a "localized override," this video breaks down the logic behind rules you may have memorized but never fully understood. In this video: • Why the same expression (4 × 2² + 3 + 5²) can produce wildly different answers without agreed-upon rules — and how EMDAS fixes that • The analogy between scrambled English sentences and arithmetic without order-of-operations rules • How EMDAS (Exponents, Multiplication/Division, Addition/Subtraction) works as a universal calculation convention • The common misconception that multiplication always comes before division — and why both hold equal rank, resolved left to right • Why division is just multiplication by the reciprocal, and subtraction is just adding a negative number • How parentheses act as a 'localized override' to force operations out of standard order (e.g., (4 × 7)²) • How nested parentheses work — always resolving the innermost set first and working outward #OpenStax #OrderOfOperations #PEMDAS #ContemporaryMathematics #Math OpenStax Content adapted from "Contemporary Math", by OpenStax Licensed under CC BY 4.0. Content based on Web Version: Apr 23, 2026. Read the textbook online https://openstax.org/details/books/contemporary-mathematics Music first girl talking to me. by ikkun (ex. Barradeen) | https://soundcloud.com/ikkunwastaken Royalty Free Music by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en_US
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