The Order of Operations is based on Logic and the History of all Mathematics, it is not a mere whim, it is not a mere convention that people use just because other people use it. It was born when Multiplication was invented as a shortcut for additions, and has evolved along with mathematics ever since. ANY convention or technique that Breaks the rules only adds confusion that is totally unnecessary.
MY calculator is programmed correctly, it knows that All division is Fractions and does NOT give super priority to Juxtaposition multiplication. Some calculators and programs outright Reject juxtaposition multiplication as invalid and force you to use a multiplication symbol.
For instance, the Arithmetic Expression 6^2/2(3)+4 is 58. Why? Well let's replace ANY number with X then solve for X:
6^2/X(3)+4=58
Subtract 4 from both sides
6^2/X(3)=54
Divide both sides by 3
6^2/X=18
Multiply both sides by X
6^2=18*X
Divide both sides by 18
6^2=36, 36/18=2
X=2
Does X equal the 2 I replaced? Yes, it does, therefore 58 Is The Only Correct Answer!
Making the 2 times 3 come first is exactly like putting a dead mouse in a trap before putting the cheese in it. It's ass backwards. It's stupid. It's breaking the rules that apply to All mathematics All the time.
So, how do you fix calculators and programs with this totally idiotic convention programmed into them? Simple. Reject the idiotic convention entirely. Every time you see it, no matter what type of mathematics being used, put in a multiplication symbol. It's not that hard. Just turn the above expression into 6^2/2*3+4, and it will all work out as it should. Bug Fixed!
Example of a correctly programmed calculator:
Example of an incorrectly programmed calculator:
Notice that both of these calculators are Casio calculators? Notice that the Plus calculator gets it Wrong?! Yah, shocking huh? Remember to always replace Juxtaposition, Implied, multiplication with Expressed multiplication, and everything will work out just fine.
thanks for Sharing these all information and you also can get more updates and detail online from here at Sunrise Exchange
ReplyDeleteCASIO describe their PEJMDAS as:
ReplyDelete" take following process about calculations because they said that it is natural to calculate inside parenthesis and multiplication with abbreviated multiplicative mark right before parenthesis as top priority, after that to calculate the divisions at the both side:
6÷(1+2)
=6÷6
=1
"Since 2005 we have launched our calculator fx-ES series to the market ... we adopted an idea supported mainly in North America. They say it is natural to calculate a formula with abbreviated multiplicative sign just the same as a formula without multiplicative one. Based on our hearing result at that moment and under the calculation process below:
6÷2(1+2)
=6÷2x3=3x3
=9
"After launching out calculator FX-ES PLUS series, such as fx-95SG PLUS ... since 2008, our calculator returned to the same specification on the calculation order in a formula as the unit like FX-570MS, base on latest hearing result; we adopted the way of thinking to calculate inside parenthesis and multiplication with abbreviated multiplication sign right before parenthesis as top priority, after that to calculate the divisions at the both side. And this way of thinking is to be kept using as a specification at Casio future calculator products, such as fx scientific series."