Here’s a video that explains why you need to memorise PEMDAS (or BODMAS, BIDMAS, depending where you are in the world) order of operation and why you don’t need to. Minute Physics who made this video made a mistake in assuming that PEMDAS is taught in schools without emphasising that multiplication and division should be done whichever comes first from left to right. But he does explain the ‘why’ behind the rule plus the importance of knowing fundamental ideas such as the distributive property and the associative property. This is what makes the video worth viewing.
You want to test your PEMDAS skill try this problem.
I actually have one more comment about that video, speaking about the ambiguity of order of operations. The example shown questions whether 8-2+1 = 5 or 7. Since neither addition nor subtraction take priority, you can just solve this by performing the operations left to right, which gives 8 minus 2 (=6) plus 1 equals 7. To consider an answer of 5, one must assume that the 2+1 is in brackets, and the minus sign outside the brackets then distributes through, essentially giving 8-2-1=5. But since there are no brackets, just do the operations as you see them, without changing signs or doing anything more complicated.
I learned BEDMAS and BOMDAS in school. PEDMAS is a new term for me. However, there never seemed to be any difficulty in understanding the concept. “B”rackets are solved first, then “E”xponents (or “O”rder), and then “M”ultiplication/”D”ivision followed by “A”ddition/”S”ubtraction. It was taught that in order of operations, neither multiplication or division takes priority over the other, and same thing for addition and subtraction. I don’t think there was necessarily any instruction about solving anything left-to-right. The point is to logically simplify and condense your equation until you are left with something easily solvable. I agree with Norsy Moffo’s comment about it being explained in 4 steps. Actually, it was somewhat explained like this to us, as it was often written as BE(DM)(AS).
I agree that PEMDAS can be very ambiguous. First you are telling your kids to solve all parenthesis and exponents, and not necessarily from left to write, but first. Then, you are telling them they must solve multiplication/division and addition/subtraction as it appears from left to write. It is all very confusing. It might be easier to break PEMDAS down to four steps instead of six letters as it appears. In other words, Step 1: complete parenthesis. Step 2: complete exponents. Step 3 multiply or divide from left to right. Step 4: add or subtract from left to right.
The uk has the same problem,we teach BIDMAS or BODMAS, it is I’ll understood and even worse not remembered or applied. Any suggestions on how to improve this situation.
US teachers, at least teachers who should be in front of kids, are not telling their kids to do multiplicaiton before division or addition before subtraction. They are telling them to do division first if it comes before multiplication as we read left to right. The same goes for subtraction and addition.