Which I think is the source of the confusion. Multiplication is just a way of counting groups of things that are already there, so if you start with one frisbee you never would be multiplying by 0 in the first place. Multiplying by 0 means you never had a frisbee.
Maybe these examples will help the OP.
Bob, Mary, Joe, Bill, and Sue each bring one frisbee to the park. So:
5 people × 1 frisbee per person = 5 frisbees at the park.
Bob brings 5 frisbees to the park:
1 person × 5 frisbees per person = 5 frisbees at the park.
Bob, Mary, Joe, Bill, and Sue each bring 0 frisbees to the park:
5 people × 0 frisbees per person = 0 frisbees at the park. The frisbees didn’t go anywhere; there never were any frisbees at the park.
3 x 0 = 0, because 0+0+0=0
4 x 0 = 0, because 0+0+0+0=0
5 x 0 = 0, because 0+0+0+0+0=0
so no matter how often you add 0 to 0 it stays 0 … which was the OP’s question
if you multiply 26 x 0 … you have added 26 times nothing, which leaves you with nothing… which is the easy to understand answer to “why multiplying by zero equals zero” (see title)
Think if instead of my one frisbee, I had zero frisbees for every frisbee I have, how many frisbees would I have? Regardless of the number of frisbees you had, if you instead had zero frisbees for each of those, you’d have no frisbees.
That seems to me the easiest way to wrap your head around this.
as I was thinking about this thread the other day and it was addressed in an earlier post
1 x 3 = 3
.1 x 3 = .3
.001 x 3 = .003
…
keep going until you have nothing to multiply… zero x 3
Or this : multiplication is a machine. Put one frisbee into the “×2” machine and it puts out two (maybe one of them is the original, maybe not). Put in 100 and it puts out 200.
Just ran across a great article about zero, both its mathematical history and its neurological place in the brain. It’s also (to my eye) not to technical, so everyone should find it a decent read.
I never learned about PEMDAS in school, for obvious reasons. But I did learn about it a few months ago for some ADHD info-junkie reason I can’t remember now.
Today I came across this viralish equation, 3x3-3÷3+3, and had to stare at it for quite some time before fully understanding why PEMDAS applied (making the answer 11, when I wanted it to be 5) in the absence of parentheses, but it did finally become clear. And it was a very rewarding moment. But now I am wondering if there is any way to create the equation so that the correct answer is 5?
Is
(3x3)(-3)(÷3)+3
an acceptable way to write an equation, just isolating each step like that?
No; anything inside parentheses should be a number or an expression that can be evaluated to a number (so no (÷3)).
But you can, by judiciously inserting parentheses, force the operations to be evaluated in whatever order you want. @beowulff’s post directly above mine shows a way of doing what you want.
I am not readily parsing that. And almost certainly the word “parse” does not apply, since it is about language, but y’all know what I mean it to mean… what would be the word?
As long as I brought it up… now I am confoozed again. (I confuse easily) In a NYT essay, I read this:
When confronted with 8 ÷ 2(2+2), everyone on Twitter agreed that the 2+2 in parentheses should be evaluated first. That’s what our teachers told us: Deal with whatever is in parentheses first. Of course, 2+2 = 4. So the question boils down to 8÷2×4.
Forget the parentheses or order, why does the absence of an operator mean you assume multiply?