Sally doesn't address the order of multiplication and division thoroughly enough. She leads implies that multiplication comes before division, just one of the many ways she's led young men astray.
Multiplication and division are done in the order that they appear in the problem.
I don't know or care what a calculator with a "=" button sez, I sez it's 1. dammit...
Stolen without proper permission from somewhere, sue me
Originally answered for “What is the correct answer of [6÷2(2+1)], 1 or 9?”
It is a typical divisive question, there is not a single true answer, it depends on your previos knowledge and your belief.
Many people use BOMDAS, if they follow the B - O - M - D - A - S rule mechanically (ignoring that D-M and A-S are interchangeable), the result is 1.
More advanced people, who use BOMDAS are taking M-D and A-S interchangeability (sometimes referred as PEMA) will come to 9 as a result, because within equal precedence operators the evaluation order is left-to-right. Google and some other calculators are also using this method. But that’s not the full picture.
Some people notice, that ÷ is an old sign for division, and it had higher precedence than * or /. That’s true, but as of today, its precedence is the same as * or /.
If you write “2(1+2)”, it is different from “2*(1+2)”, because it omits the multiplication sign. It suggests that these factors “stick together”, this operation has higher precedence than others within the same precedence level. It’s called juxtaposition. Using this observation the result is still 1. Many scientific calculators are also using this rule.
Finally, mathematicians etc. who are working with formulas generally treat the division as if it was fraction, therefore they put the “2(2+1)” part into the denominator, automatically. For mathematicians, the formula is inconsistent, but the contradiction can be resolved, and the result is 1.
Bottom line: Since there’s a heated debate about the result, let’s accept those opinion who are expert of this field. The practice of the mathematicians say that this formula should be interpreted as “6 / (2 * (2 + 1))”, so the result is 1.
Our teacher had put in his time in the Navy. He knew quite a list of similar mnemonic phrases. The second G was Gives and the W was Willingly. Perfect for a classroom of hormone-incensed teenage boys who wanted to find Violet.
that's the one I learned.
Get Some Now were the final determination of the quality of the resistors
@holy-cow my father worked for the FAA at air traffic control microwave relay stations in buildings that were filled with ancient computers that ran on tubes, resisters and the like. One particular tube was 18" in diameter and three feet tall. They always had a spare on hand but when that tube blew, I got excited because I knew there would be a road trip to pick up a new reserve tube from hundreds of miles away and I got to ride shot gun with him.
His job was high pressure when things went wrong with the electronics as he had a limited number of minutes to diagnose the situation and fix it before the whole facility went off line and created a hole in radar coverage in busy east coast air space in the Philadelphia/NYC metro area with several major airports.
I can still see him sitting at the kitchen table studying schematics of system upgrades and using a slide rule for his calculations while preparing for a new upgrade. When TI came out with their first scientific calculator, it was mind blowing to him and changed his whole world, when he got his first one in the early 70's, it cost about a third of what it cost to buy a basic new car!
His work environment back in the day was very non politically correct and there were no females that I am aware of in his career field so lets just say that his version of the color coding would get him fired these days in a New York minute.
@holy-cow Hey! I resemble that remark. I'm the youngest of five. 25 year spread between me and my oldest brother. His two kids are older than me. Two of my sister's kids are as well. Grew up with a nephew that is eight days younger than me.
