Mathematical Twitter is normally a quiet, well-ordered place, a refuge from the aggravations of the internet.
Mathematical Twitter is normally a quiet, well-ordered place, a refuge from the aggravations of the internet.But on July 28, someone who must have been a troll off-duty decided to upset the stillness, and did so with a surefire provocation.Another posted a photo showing that even two different electronic calculators disagreed.Tags: Phishing Research PaperDescriptive Essay Using Spatial OrderWhite Paper Of Related Research Of Software QualityBeautiful Essay On DisciplineExample Analysis EssayAssumptions Section Of DissertationLiterature Review Of Teenage Pregnancy
No professional mathematician would ever write something so obviously ambiguous.
We would insert parentheses to indicate our meaning and to signal whether the division should be carried out first, or the multiplication.
The question above has a clear and definite answer, provided we all agree to play by the same rules governing “the order of operations.” When, as in this case, we are faced with several mathematical operations to perform — to evaluate expressions in parentheses, carry out multiplications or divisions, or do additions or subtractions — the order in which we do them can make a huge difference. Now that we’re faced with a division and a multiplication, which one takes priority?
When confronted with 8 ÷ 2(2 2), everyone on Twitter agreed that the 2 2 in parentheses should be evaluated first. If we carry out the division first, we get 4×4 = 16; if we carry out the multiplication first, we get 8÷8 = 1. The standard convention holds that multiplication and division have equal priority. So the division goes first, followed by the multiplication. More generally, the conventional order of operations is to evaluate expressions in parentheses first. Next come multiplication and division, which, as I said, are considered to have equal priority, with ambiguities dispelled by working from left to right.
So on behalf of all math teachers, please excuse us for drilling your younger selves on this tedium.
My daughters spent weeks on it each school year for several years of their education, as if training to become automatons.No wonder so many students come to see math as an inhuman, meaningless collection of arbitrary rules and procedures.Clearly, if this latest bout of confusion on the internet is any indication, many students are failing to absorb the deeper, essential lesson.Other teachers use an equivalent acronym, BODMAS: brackets, orders, division and multiplication, and addition and subtraction.Still others tell their pupils to remember the little ditty, “Please excuse my dear Aunt Sally.”Now realize, following Aunt Sally is purely a matter of convention. Furthermore, in my experience as a mathematician, expressions like 8÷2×4 look absurdly contrived.All operations within brackets get completed first.The 'E' refers to any exponents; all exponents are calculated after the parentheses.For those students destined to become software designers, writing code that can handle ambiguous expressions reliably whenever they arise, by all means exhume Aunt Sally from her crypt.For everyone else, let’s spend more time teaching our students the more beautiful, interesting and uplifting parts of mathematics. This will help them write and solve expressions and use the order of operations to simplify expressions in pre-algebra and algebra. Ask them to pick out 2 dozen eggs, 3 packets of hot dog buns, 2 packets of candy and 2 boxes of cereal. Now, ask your child the number of eggs in a dozen, number of buns in a packet, number of candies in a packet and calculate the total number of items bought.Ask them to form an expression and use the order of operations to find the answer.