For the rest of us, the intricacies of PEMDAS are less important than the larger lesson that conventions have their place.
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Likewise, it’s essential that everyone writing software for computers, spreadsheets and calculators knows the rules for the order of operations and follows them. It doesn’t matter which convention is adopted, as long as everyone follows it. The same goes if everyone else is driving on the left, as in the United Kingdom. If everyone else is driving on the right side of the road (as in the U.S.), you would be wise to follow suit. We know this whenever we take to the highway. But now, having been enlightened by some of my computer-oriented friends on Twitter, I’ve come to appreciate that conventions are important, and lives can depend on them. The last time this came up on Twitter, I reacted with indignation: It seemed ridiculous that we spend so much time in our high-school curriculum on such sophistry.
We would insert parentheses to indicate our meaning and to signal whether the division should be carried out first, or the multiplication.
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No professional mathematician would ever write something so obviously ambiguous. Furthermore, in my experience as a mathematician, expressions like 8÷2×4 look absurdly contrived. Now realize, following Aunt Sally is purely a matter of convention. Still others tell their pupils to remember the little ditty, “Please excuse my dear Aunt Sally.” Other teachers use an equivalent acronym, BODMAS: brackets, orders, division and multiplication, and addition and subtraction. To help students in the United States remember this order of operations, teachers drill the acronym PEMDAS into them: parentheses, exponents, multiplication, division, addition, subtraction. Read more writing in The Times from Steven Strogatz about math Finally come addition and subtraction, which are also of equal priority, with ambiguities broken again by working from left to right. Next come multiplication and division, which, as I said, are considered to have equal priority, with ambiguities dispelled by working from left to right. More generally, the conventional order of operations is to evaluate expressions in parentheses first. So the division goes first, followed by the multiplication. To break the tie, we work from left to right. Which way is correct? The standard convention holds that multiplication and division have equal priority. Transgender Youth: Educators are facing new tensions over whether they should tell parents when students change their name, pronouns or gender expression at school.Heavy Losses: A new global analysis suggests that children experienced learning deficits during the Covid-19 pandemic that amounted to about one-third of a school year’s worth of knowledge and skills.Ron DeSantis of Florida and other conservatives, the College Board stripped down much of its new Advanced Placement course in African American Studies. Course Dispute: After heavy criticism from Gov. Some schools are asking their students to think critically about rapid advances in artificial intelligence and consider their impact. Critiquing Chatbots: Move over, coding.So here are seven more brutally difficult math problems that once seemed impossible until mathematicians found a breakthrough. That’s the beauty of math: There’s always an answer for everything, even if takes years, decades, or even centuries to find it. That turned out to be much harder-as in, no one was able to solve for those integers for 65 years until a supercomputer finally came up with the solution to 42. But what about the integers for x, y, and z so that x³+y³+z³=42? Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. It’s called a Diophantine Equation, and it’s sometimes known as the “summing of three cubes”: Find x, y, and z such that x³+y³+z³=k, for each k from one to 100. In 2019, mathematicians finally solved a math puzzle that had stumped them for decades. These Are the 7 Hardest Math Problems Ever Solved - Good Luck in Advance
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