I can summarize: The equation is ambiguous, because there are two equally valid ways to interpret the relationship between the 2 and the parentheses. Pre-computer written math would have assumed that the 2(x) was a unit, as the 2 could be distributed across the parenthetical expression. With the advent of calculators and computers, equations written this way are executed left to right, and so the 8 ÷ 2 would go first, and then that result would be multiplied by the result of the parentheses.
It’s worth noting that both interpretations follow the PEMDAS rule, so such debates are irrelevant. It is a question of grouping terms and solving the holistic equation, vs solving step by step left to right.
The argument in that article is basically “Most calculators do it this way now, so that must be our convention to use, so 16 is the correct answer. Please ignore that this goes against the conventions established before calculators became transistorized.”
I’m decent at math, versed in PEMDAS / BOMDAS, and confess that I arrived at 1 until I read this mathematician’s take on the topic: https://mindyourdecisions.com/blog/2019/07/31/what-is-8-÷-22-2-the-correct-answer-explained/ (hint: it’s as much about typography and changing interpretations as it is about math).
I am a strong believer in PEBKAC myself.
They seem to be saying that however a calculator would calculate it is ipso facto correct.
Which is odd because I had at least one, maybe more, teacher show us this as a reason not to blindly trust your calculator
I can summarize: The equation is ambiguous, because there are two equally valid ways to interpret the relationship between the 2 and the parentheses. Pre-computer written math would have assumed that the 2(x) was a unit, as the 2 could be distributed across the parenthetical expression. With the advent of calculators and computers, equations written this way are executed left to right, and so the 8 ÷ 2 would go first, and then that result would be multiplied by the result of the parentheses.
It’s worth noting that both interpretations follow the PEMDAS rule, so such debates are irrelevant. It is a question of grouping terms and solving the holistic equation, vs solving step by step left to right.
The real solution is to shoot the person who wrote it, because they should have used more parens.
That’s odd. I tried the URL in a couple of different browsers and it loaded correctly. Anyone else have problems loading it?
The argument in that article is basically “Most calculators do it this way now, so that must be our convention to use, so 16 is the correct answer. Please ignore that this goes against the conventions established before calculators became transistorized.”