Order of Operations

Why does order matter when simplifying expressions? Does "PEMDAS" mean you need to multiply before dividing (since M comes before D) and that you need to add before subracting (since A comes before S)? Does "parentheses" really mean parentheses (and only parentheses)? Is there a time when I see parentheses when I do not deal with them first? AND how do you spell "parentheses?"

Category:

Education

Tags:

• math
• algebra
• order of operations
• Heidi Meyer

[jorundr]

In your last equation, some people would argue that you would multiply the 5 by the 4 first, due to the distributive rule. What would you say to them?

[hmeyer827]

@jorundr Sometimes I get a similar question from my students, so I'm wondering if you're asking the same thing. With PEMDAS that "P" on the front really jumps out and screams, "Parentheses first." But what is meant by "parentheses?" Really it should be GEMDAS because it is really work INSIDE Grouping symbols that has to be done first. In this case we actually have the same thing as 100 divided by 5 times 4, so no grouping (or distribution) is involved. Have I answered what you are asking?

[highbornblood]

100/5(4) = 5

why?

because 5(4) is treated as 1 term, 5 quantity 4

example: 1a÷5b

is equal to 1a over 5b

let a = 100, let b = 4,

substitute the values on the expression

1(100) over 5(4) = 100 over 20 = 5

[hmeyer827]

@highbornblood There are many ways to write multiplication - a dot, parentheses, an x, an asterisk, a number set right next to variable, etc. We do multiplication and division at the same time left to right no matter which symbol for multiplication is used. This problem is the same as 100/5 x 4=80. Even in something like 5b the coefficient and variable are not as connected as they seem. 5b is the same as 5 x b, just shorthand for it. Similarly, this is why 5b^2 is 5xbxb and not 5bx5b.

[holdon527]

can you please answer this 4 + 2[6 - (-5)3]

any one and tell me how is the answer is 46

[hmeyer827]

@holdon527 Oops - sorry I missed your question! If you're still interested, here goes:

You start inside the brackets (grouping symbols) and do x before -

So you get 4+2[6 - - 15]

"Minus negative" becomes "plus positive" so you have 4+2[6+15]

Next you have 4+2[21]

We must multiply before adding, so you have 4+42, which is equal to 46.

[tuan16582]

I love your name and your voice!!!

[kelsey123239]

You look like Jim Carry man Laugh Out Loud....No offence.... Like if i was funny-Dislike if it was mean :) But it's true she does look like Jim Carry they must be so related some how Laugh At Loud- LOL.... Plus they acted the same to ^-^ because of the saying in grey ever try to act like a teenager to that old laddie there lol. :) No offence lol Cough Cough. STUPID!!!! lol

[LiVeNleRn123]

thank you soo much for this!

[longsiu]

@hmeyer827 if you refer to Elizabeth Stapel's purplemath website, she would disagree with you on that (See: order of operations page 2 of 3)

[cutiepie550226]

This Helped Me Alot!!! Thanks! :)

[51Saffron]

Wouldn't be less confusing to use a dot for multiplication than brackets?

I guess if you are use to looking at problems like that, but most problems that we work with use a dot.

[TheBreebree6]

im stuck on this please help =/ 2.48 divided by (1-0.504)+ 24.3 -11x2

[BaB3B001]

i wish my teacher was like this =( thanks to my teacher not knowing how to do her job I dont know nothing about algebra 1!

[PhantomAct]

@unpredictably13teen My advice would be try 100/5*4 in Excel or equivalent (Google spreadsheet...), you enter a calculation by typing this =100/5*4 and then hit enter.

[unpredictably13teen]

what happened to Bodmas? Brackets, Order, Division, Multiplication, Addition, Substraction ??