Yes, it has been used to trick and confuse others… but today the answer is 9, there is reason to look at the historical significance of it being the argument for 1, but I like it to be 9 rather than 1
Wrong. The answer is 1. The 2 outside of the parenthesis is separated from the 6 by a division sign and is therefore more closely aligned with the parenthesis content (1 + 2) giving us an overall divisor of 2×(1+2) or 2×3 which =6. 6 ÷6 =1 QED
No, it is left to right whichever comes first multiplication or division, but only left to right so 6 ÷ 2 is the way to go. But because this problem is only meant to fool people, there is no wrong or right answer according to many people But it is 9 in today’s standards, there is reason to believe its historical significance for the conclusion of 1, it’s not that way anymore.
2x is equal to: (x + x) So the statement "2x divided by 2x" is: [ x + x ] ÷ [ x + x ] ...which, given that x is not zero, has a quotient of 1. In the statement "6 ÷ 2(1+2)," the numerator "6" can be factored out as: 2(1+2) ...making the statement: 2(1+2) ÷ 2(1+2) and if we replace what's inside the parentheses with the variable "x," the statement is: 2x ÷ 2x which can also be written as the horizontal fraction... 2x / 2x or as the vertical fraction... 2x __ 2x ...since all of those symbols mean "divided by" & separate the numerator from the denominator. The "2" in "2x" is not a stand-alone number unto itself -- it's the coefficient in a monomial which tells you how many times to multiply the factor (which is actually how many times to add the quantity to itself), in much the same way that an exponent tells you how many times to multiply the base number by itself. Just as the exponent is "attached" to the base number, the coefficient of a monomial is "attached" to the variable (factor) -- and never needs parentheses around it to understand that it has a SINGLE VALUE. So the monomial division statement "2x divided by 2x" is: [ x + x ] ÷ [ x + x ] Notice that the coefficient number of 2 "disappears" when the statement is written out in its most basic form (as the indicated additions). That proves, once and for all, that using the coefficient of the monomial (the "2" in "2x") in some other operation is not valid. If x equals 3 [expressed as (1+2) ], then the statement 6 ÷ 2(1+2) is 6 divided by 6, which of course has a quotient of 1 -- no matter which division symbol is used. Division is fractions. Fractions is division. Do all the operations indicated in the numerator, then do all the operations indicated in the denominator, and finally divide the numerator by the denominator. Division goes LAST. PEMDAS is the incorrect method to work through division statements.
Math notation is a convention and the order of operations is part of that convention. Nothing more nothing less. Write it in fraction form of it's confusing.
There are actually a couple different ways of doing this problem. 6÷2(1+3) or 6/2(1+3) or Parenthesis (1+2)=3 Multiplication 2(3)=6 Division 6÷6 =1 (6÷2)(1+2)=9 Let's be honest here though. 1 makes the most Sense. Calculators agree.
PEMDAS does not work for division statements -- because division is a fraction. In calculating the quotient of a fraction, first do all of the operations indicated in the numerator, then do all of the operations indicated in the denominator, and then finally, divide the numerator by the denominator -- division always goes LAST. The "6" in 6÷2(1+2) can be factored as 2(1+2), making the statement 2(1+2) ÷ 2(1+2). Replace what's inside the parentheses with the variable "x," making the statement 2x ÷ 2x [also written as 2x / 2x, or as the top-and-bottom fraction 2x over 2x]. A monomial is one term with a single value, which is the PRODUCT of the coefficient multiplied by a variable (factor). In the case of 6÷2(1+2), the statement is one monomial being divided by another monomial: 2x divided by 2x, when x = (1+2) Do an internet search for, "How to divide one monomial by another monomial," and you will find that the monomial division is always performed as a top-and-bottom fraction -- even when the original statement is written using a division sign (obelus) or slash (solidus). Here's an example: from Algebra Practice Problems. com: www.algebrapracticeproblems.com/dividing-monomials/ “Any division of monomials can also be expressed as a fraction: 8x³y²z ÷ 2x²y = " …which is then shown as a top-and-bottom fraction with 8x³y²z as the numerator (above the fraction bar) and 2x²y as the denominator (below the fraction bar). The quotient of that division statement is given as: 4xyz Note that the original monomial division statement “8x³y²z ÷ 2x²y” uses a division sign (obelus) & there are no parentheses anywhere in the statement. Young math students are currently being taught to process horizontally written monomial division statements as fractions, with the numerator being everything to the left of the division symbol (obelus or solidus) and everything to the right of the division symbol as the denominator - sans parentheses. 2x ÷ 2x is exactly the same division statement as the top-and-bottom fraction 2x over 2x -- which equals 1, given that x does not equal zero.
You're wrong I'm afraid. If you type the problem into a standard scientific calculator (I used a Casio fx-83GT X) the answer is 1. Shame on you for spreading misinformation.
PEMDAS does not work. It is taught before the implied or juxtaposed multiplication is taught. Both the American Mathematical society and the American Physical society treat implied multiplication higher priority than division. Casio calculators treat it higher as do may other ones. TI is an exception. Even they admit that it should be but American mathematics teachers want it to have the same priority. This video explains it with real world examples: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-lLCDca6dYpA.htmlsi=S5wIUlNhJJ_erlAe This continues it: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4x-BcYCiKCk.htmlsi=FAyy7OumV-bHFh7G You should not look at what people sat they so but look what they do when they are not trying to teach things. These can be different and when people consciously think something they may think they do it differently than what they actually do.
This was interesting - thanks for the links - as soon as people stat to argue over what the correct meaning of the problem is though it's not solvable in my eyes or you give all the answers.
It is Parentheses Exponents Multiplication or Division Addition or Subtraction Many schools teach to this way already, the answer is 9, but in history the answer would be 1, but this does not fit today’s standards
